Document [original]

Exploring Sou Fujimoto’s “Complexity” Using

Five Graphics of Order

vorgelegt von

Luo Li, Master of Architecture

an der Fakultät VI – Planen Bauen Umwelt

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften

- Dr.-Ing. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Ignacio Borrego Gomez Pallete

Gutachter: Prof. Ralf Pasel

Gutachter: Prof. Dr. Jörg Gleiter

Gutachter: Prof. Dr. Yuhang Kong

Tag der wissenschaftlichen Aussprache: 20. November 2023

Berlin 2024

Acknowledgments

The work presented in this doctorate was carried out at the Institut für Architektur of the

Technische Universität Berlin. This research could not have been achieved without the help

and support of many individuals. To all those who provided guidance, encouragement, or

support throughout this journey, I extend my heartfelt thanks.

I am immensely grateful to my supervisor, Prof. Ralf Pasel. His insightful feedback on

this study has been a beacon of clarity in times of doubt and uncertainty. His comprehensive

outlook, meticulous academic rigor, and unwavering commitment to students have

profoundly influenced the direction and caliber of my research. I am fortunate to have had

his support and companionship on this remarkable journey.

I would like to thank Prof. Kong Yuhang, my mentor in architecture. It was only later

that I realized that this thesis is the fruit of seeds planted under his tutelage. It was a piece

of good fortune that he participated in my defense, which brought full circle the guidance

he began. I am deeply thankful for his enduring influence.

My profound appreciation also extends to my domestic supervisor, Prof. Changfu Wu.

His extensive expertise provided me with invaluable guidance and support throughout my

research. His inspiration and encouragement have been boundless, always driving me

toward excellence.

I wish to express my gratitude to Prof. Jörg Gleiter from the Technische Universität

Berlin for his comments on my thesis, which will serve as a guiding light for the rest of my

academic life. I am also thankful to Prof. Ignacio Borrego of the Technische Universität

Berlin for all his contributions to my defense. My thanks also go to Associate Prof. Dr.

Shanchao Xin, whose support and expertise were pivotal in charting the course of this study

in its initial phases. I am grateful to my colleagues—Franziska Sack, Lorena Valdivia, Otto

Paans, Javiera Zarzar, and Katharina Neubauer—for their generative discussions and

invaluable feedback. While I regret not being able to list everyone, please know that your

assistance is valued deeply. Special appreciation is directed to Dr. Qiang Li, whose

interdisciplinary insights from physics enriched this research immensely. Each

conversation with him was illuminating and his input was crucial for the advanced stages

of my work. His support was indispensable in completing this dissertation in a timely

fashion.

Finally, I wish to express my deepest gratitude to my wife. You are the force of

negentropy in my life, the essential structure that stabilizes me, allowing for the continuous

exchange of energy and information despite the presence of uncertainties. Without you, I

would have been irretrievably lost during those numerous nights.

II Acknowledgments

Abstract

In the nuanced landscape of contemporary Japanese architecture, a series of pervasive

themes resonate—ambiguity, openness, the interplay with nature, the fluidity between

interior and exterior spaces, alongside nebulous zones. These motifs have been widely

regarded as important touchstones since the inception of the iconic Sendai Mediatheque in

2000. Typically, these themes are discussed in isolation, and research into their

interconnectedness has been limited. This dissertation advocates for an interlinking of these

themes from the perspective of complexity.

Sou Fujimoto emerges as an illustrious protagonist in this narrative. His architectural

philosophy embodies two facets: first, it encapsulates these pervasive Japanese

architectural themes; second, it explores the concept of complexity. In Fujimoto’s lexicon,

discourse, and works, there is a resounding coherence and consistency with regard to

complexity, which serves as a conduit between the essence of the Japanese architectural

ethos and the intricate web of complex thought.

A significant hurdle in expanding on this interconnection is the inherent broadness,

uncertainty, and ambiguity of the term “complexity.” Its significance is profound and it is

heavily reliant on a context that can be traced back to the 1930s, when certain scientists

began reconsidering reductionism and simplicity. Their research, which is broadly

encapsulated by the term “complexity,” posits that there are fundamental laws underlying

irreducible systems, hinting at a convergence between soft and hard sciences and the

prospect of a scientific revolution. These researchers have repeatedly ascribed new

meanings to “complexity,” yet the full scope of the term remains elusive. In the words of

Thomas Kuhn, it is a semi-incommensurable concept, and so consequently there is no

stipulative description within architectural discourse.

Against this background, the Five Graphics of Order (FGO) were introduced.

Originating from elementary cellular automata or manual drawing, these graphics

transcend textual descriptions and are perceived as manifestations of natural phenomena,

providing untainted reference points for the comprehension of order. They assist in

elucidating certain aspects of complexity, offering a simplistic and graphic perspective for

architectural discussions.

Through this lens, various conceptualizations of order might be anchored and

Fujimoto’s philosophy might be understood in a more cohesive way. Additionally, from

this reevaluated perspective, some of Japan’s recurrent architectural clichés receive a

semblance of unification, which enables us to situate complexity among the familiar

themes of Japanese architecture and provide a holistic view of the nation’s current

architectural thought.

IV Abstract

Zusammenfassung

In der facettenreichen Landschaft der zeitgenössischen japanischen Architektur zeichnen

sich eine Reihe allgegenwärtiger Themen ab – Ambiguität, Offenheit, das Zusammenspiel

mit der Natur, die Durchlässigkeit zwischen Innen- und Außenräumen sowie nebulöse

Bereiche. Seit der Entstehung der ikonenhaften Sendai Mediathek im Jahr 2000 gelten

diese Themen weithin als wichtige Bezugspunkte. Typischerweise werden die Themen

jedoch isoliert diskutiert, und die Forschung zu ihrem Zusammenhang war bisher begrenzt.

Diese Dissertation plädiert für eine Verknüpfung dieser Themen aus der Perspektive der

Komplexität.

Sou Fujimoto tritt in dieser Erzählung als herausragender Protagonist auf. Seine

architektonische Philosophie weist zwei Facetten auf: Erstens sind diese beherrschenden

japanischen Architekturthemen in ihr enthalten; zweitens erforscht sie das Konzept der

Komplexität. In Fujimotos Lexikon, Diskurs und Werken besteht eine durchgängige

Kohärenz und Konsistenz in Bezug auf Komplexität, die als Bindeglied zwischen dem

Wesen des japanischen Architekturdenkens und dem vielschichtigen Netz komplexer

Überlegungen dient.

Ein wesentliches Hindernis beim Ausbau dieses Zusammenhangs ist die dem Begriff

„Komplexität“ inhärente Breite, Ungewissheit und Mehrdeutigkeit. Seine Bedeutung ist

tiefgründig und stark kontextabhängig, und reicht bis in die 1930er Jahre zurück, als

bestimmte Wissenschaftler begannen, Reduktionismus und Einfachheit neu zu überdenken.

Ihre Forschung, die weitgehend durch den Begriff „Komplexität“ zusammengefasst wird,

postuliert, dass es grundlegende Gesetze gibt, die irreduziblen Systemen zugrunde liegen,

was auf eine Konvergenz zwischen den exakten Wissenschaften und

Geisteswissenschaften hinweist und eine wissenschaftliche Revolution in Aussicht stellt.

Diese Forscher haben der „Komplexität“ wiederholt neue Bedeutungen zugeschrieben,

dennoch bleibt der volle Umfang des Begriffs schwer fassbar. In den Worten von Thomas

Kuhn handelt es sich um einen nicht vollständig messbaren Begriff, und folglich eignet

sich im architektonischen Diskurs keine stipulative Beschreibung.

Vor diesem Hintergrund werden die Five Graphics of Order (FGO) eingeführt. Diese

Grafiken, die aus elementaren zellulären Automaten oder manuellem Zeichnen stammen,

übersteigen textliche Beschreibungen und werden als Manifestationen natürlicher

Phänomene wahrgenommen, die unbeeinträchtigte Bezugspunkte für das Verständnis von

Ordnung bieten. Sie helfen dabei, bestimmte Aspekte der Komplexität zu verdeutlichen

und bieten eine vereinfachte und grafische Sichtweise für architektonische Diskussionen.

Mithilfe dieser Perspektive könnten verschiedene Konzeptualisierungen von

Ordnung verankert werden, und Fujimotos Philosophie könnte in einer kohärenteren Art

VI Zusammenfassung

und Weise verstanden werden. Zusätzlich könnten aus dieser neu bewerteten Perspektive

einige der wiederkehrenden architektonischen Klischees Japans eine Art

Zusammenführung erfahren, die es uns ermöglicht, Komplexität unter den vertrauten

Themen der japanischen Architektur zu verorten, und die einen ganzheitlichen Blick auf

das aktuelle architektonische Denken der Nation bieten könnte.

Contents 
Acknowledgments................................................................................................................ I 
Abstract ............................................................................................................................. III 
Zusammenfassung.............................................................................................................. V 
Contents ........................................................................................................................... VII 
Introduction ................................................................................................................. 1 
1 Japanese Architecture and Complex Thinking .............................................. 1 
1.1 The Collective Subconscious in Japanese Architecture ................................. 1 
1.2 The Concept of Complexity: A Complementary Thought to Reductionism . 2 
2 Major Obstacles in the Research.................................................................... 3 
3 Why Choose Fujimoto as Research Object? .................................................. 5 
4 Research Objectives ....................................................................................... 6 
5 Research Process and Steps ........................................................................... 7 
6 Research Outline ............................................................................................ 8 
Research Background .................................................................................................. 9 
1 Some Key Concepts Related to Complexity .................................................. 9 
1.1 The Lexical Definition of Complexity ........................................................... 9 
1.2 An Overview of Complexity in Natural Science ......................................... 10 
1.3 Randomness as Complexity ......................................................................... 13 
1.4 Chaos as Complexity ................................................................................... 14 
1.5 Co-existence of Order and Disorder as Complexity .................................... 15 
2 Three Phases of Complexity Science ........................................................... 23 
2.1 Origins—Belief, Methodology, and Worldview ......................................... 24 
2.2 The First Phase: The Systems Theory Era ................................................... 25 
2.3 The Second Phase: The Stage of Nonlinear Science and Chaos Theory ..... 25 
2.4 The Third Phase: The Dawn of Complexity Science ................................... 27 
2.5 Beyond 2000: Twilight ................................................................................ 28 
3 Three Stages of Architecture Influenced by Complexity Science ............... 29 
3.1 First Stage: Juxtaposition ............................................................................. 30 

VIII   Contents 
3.2 Second Stage: Superimposition ................................................................... 30 
3.3 Third Stage: Nonlinear Volume ................................................................... 32 
4 Japanese Architectural History in Comparison (1960-2000)....................... 33 
4.1 The Optimistic Period .................................................................................. 34 
4.2 The Closed Period ........................................................................................ 40 
4.3 The Open Period .......................................................................................... 45 
4.4 The Free Period ............................................................................................ 58 
5 Summary ...................................................................................................... 65 
Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic ...................... 67 
1 A Standpoint: Rule 110 ................................................................................ 67 
1.1 Weak Architecture ....................................................................................... 67 
1.2 One-Dimensional Cellular Automata .......................................................... 70 
1.3 Stephen Wolfram’s Rule 110 ....................................................................... 72 
1.4 Comparing Rule 110 with Sou Fujimoto ..................................................... 76 
2 Pivotal Aspects for the Advent of Complexity ............................................ 89 
2.1 Behind Rule 110 .......................................................................................... 89 
2.2 The Significance of “Parts” ......................................................................... 91 
2.3 The Function of “Numerous Constituents” .................................................. 92 
2.4 The Metaphor of the Cloud .......................................................................... 93 
2.5 The Nature of Telescopic Nesting ............................................................... 95 
2.6 The Essence of Self-Organization ............................................................... 96 
2.7 The Role of Randomness ............................................................................. 97 
2.8 The Perception of Centerlessness ................................................................ 97 
2.9 The Symbol of the Co-existence of Order and Disorder ............................. 98 
3 Connecting with “Nihonteki na mono” (Japaneseness) ............................... 99 
3.1 “Architecture of Parts” in Japan ................................................................ 101 
3.2 “Gradation” in Japan .................................................................................. 106 
3.3 “Clouds” in Japan ...................................................................................... 109 
3.4 “Centerlessness” in Japan .......................................................................... 111 
3.5 The Evolution of “Japaneseness” ............................................................... 114 
4 Summary .................................................................................................... 121 

Contents IX 
The Nexus Between “Japaneseness” and “Complexity” under the FGO ................ 125 
1 What is the FGO?....................................................................................... 125 
1.1 The Other Three Graphics ......................................................................... 125 
1.2 The Addition of Equilibrium State ............................................................ 128 
1.3 The Order of the Orders ............................................................................. 132 
2 First Step: Locating the Orders .................................................................. 133 
2.1 Forms of Difference ................................................................................... 133 
2.2 Complexity or Chaos?................................................................................ 140 
2.3 Why does Fujimoto Use “Chaos”? ............................................................ 143 
3 “Complexity” Under the Evolution of Order ............................................. 147 
3.1 “Complexity” Under the FGO ................................................................... 147 
3.2 The Unity of Opposites .............................................................................. 153 
3.3 Ambiguity .................................................................................................. 157 
3.4 Openness .................................................................................................... 163 
4 Harmonization at the Cognitive Level ....................................................... 169 
4.1 What is Complex Thinking? ...................................................................... 170 
4.2 The Ambiguous Whole and the Distinct Parts ........................................... 175 
4.3 Nature: Japanese Emergence ..................................................................... 187 
5 Summary .................................................................................................... 191 
Epilogue ................................................................................................................... 193 
1 Conclusion ................................................................................................. 193 
1.1 Sou Fujimoto’s “Complexity” ................................................................... 193 
1.2 The Bond Between Japaneseness and Complexity .................................... 193 
2 Contribution ............................................................................................... 196 
2.1 The FGO .................................................................................................... 196 
2.2 Interpretation of the Correlation Between Japanese Architectural Ideas and 
Complexity .............................................................................................................. 196 
3 Outlook ...................................................................................................... 196 
Bibliography ................................................................................................................... 199 
Sources of Illustrations ................................................................................................... 209 
 

X Contents

1 Introduction

1.1 Japanese Architecture and Complex Thinking

1.1.1 The Collective Subconscious in Japanese Architecture

Since the end of World War II, the landscape of Japanese architecture has undergone a

series of divergences and convergences which paint a vivid picture of evolution and

introspection.

This story begins in the late 1950s and is marked by a harmonious relationship

between the orthodox modernism epitomized by Kenzo Tange and the avant-garde flourish

of Metabolism. This period was characterized by a sense of unity, particularly if Tange is

considered as a pivotal figure in Metabolism, which would accentuate the era’s optimistic

undercurrent.

A second epoch surfaced in around 1974, initiated by a burgeoning dissent against

modernism that took root around 1968, was further propelled by the 1970 Osaka World

Expo, and reached a critical juncture with the oil crisis. This period witnessed architects

retreating into the realm of “closed boxes,” crafting forms of architectural solitude that

befitted an era defined by enclosure.

The third act unfolded in around 1984, with Toyo Ito’s Silver Hut signifying a sharp

change in direction from the preceding narrative in its championing of “openness” in

architectural thought. This era birthed a plethora of structures, unified in their approach yet

diverse in their execution.

The 1980s and 1990s emerged as a contemplative period, often labeled as “lost.”

Amidst the swift encroachment of postmodern thought, societal upheavals, the bubble

economy’s zenith and nadir, and a relentless quest for a modernist identity, Japanese

architecture found itself adrift in a sea of chaos and aimlessness, punctuated by buildings

that, while “interesting,” seemed to search for grounding.

Emerging from this introspective journey, the dawn of the 2000s heralded a

resurgence of coherence in Japanese architecture, symbolized by the completion of the

Sendai Mediatheque. This era’s architectural discourse and creations share a unified voice,

which echoes into the present day.

This newfound harmony articulates itself through a lexicon of concepts—nature,

forest, openness, ambiguity, centerlessness, and beyond—terms that weave through the

fabric of Japanese architectural discourse, forming the cornerstone of a narrative that

stretches from the completion of the Sendai Mediatheque to the present day. These terms,

while often criticized for being clichés, are in fact the distillation of a collective

2 1 Introduction

architectural pursuit, which can be traced all the way back to explorations of modernization

in the 1920s.

Moreover, these concepts reveal an intrinsic logic, a testament to the interconnectivity

of ideas within the architectural realm. From the granularity of “parts” that coalesce into a

“whole,” to the ethereal “cloud” embodying density without division, these ideas champion

a narrative of “openness,” “centerlessness,” and “ambiguity,” alluding to a space beyond

physical borders.

Yet, the different strands of this discourse often traverse in isolation, and the

underlying essence that binds these concepts together is seldom addressed. The narrative

sometimes becomes fragmented, tending to find cohesion in individual interpretations but

not through a collective understanding. The challenge lies in transcending these individual

narratives to unveil a more profound, unified framework—a holistic view that encapsulates

the essence of Japanese architecture.

This enquiry employs the term “collective subconscious,” a nod to Terunobu

Fujimori’s exploration of a “ubiquitous and causal awareness” in Sou Fujimoto’s

architecture, to encapsulate the shared essence that permeates through the architectural

fabric of Japan. This essence, which emerges from the interaction between an architect’s

subconscious and their cultural, social, and historical influences, presents a picture of

convergence that is unique to the Japanese context.

Reflecting on the critique of reductionism in the natural sciences that has imbued

complexity with new meanings, this narrative embarks on a quest to unravel the

interconnectedness of these architectural concepts, exploring the dramatic cycles of

divergence and convergence that characterize Japanese architectural history. In this journey,

the clichés of yesterday become the insights of tomorrow, inviting a deeper understanding

of the structural framework that shapes the collective identity of Japanese architecture.

1.1.2 The Concept of Complexity: A Complementary Thought to Reductionism

Since the early twentieth century, beginning notably with Ludwig von Bertalanffy’s

general systems theory, there has been a paradigm shift within the natural sciences—a

move away from the reductionist lens toward the contemplation of complexity. This shift

heralded the inception of what would eventually be recognized as complexity science, a

discipline that crystalized in the 1980s with the founding of the Santa Fe Institute.

Complexity science, with its focus on the intricate and often unpredictable interactions

within systems, stands as a rebuttal to the simplicity that once dominated scientific

enquiry.

The field’s essence is encapsulated in complexity theory, which champions a

holistic approach over the reductionist dissection of phenomena. Thus, the discourse

M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (New York:

Simon & Schuster, 1992), p329.

1.2 Major Obstacles in the Research 3

challenges the dichotomy between complexity and simplicity thinking, advocating for a

richer, more interconnected understanding of the world.

The limitations of traditional scientific approaches are exemplified in one of the most

profound challenges acknowledged across both the physical and life sciences—unraveling

the enigma of consciousness. Despite the meticulous deconstruction of matter into ever

smaller particles, the essence of consciousness remains elusive. This conundrum

underscores the ambitious goal of complexity science: to serve as a conduit between the

deterministic realms of physics and the emergent, vibrant landscape of the life sciences.

The aim is to bridge what has historically been seen as a chasm between hard and soft

sciences by suggesting a unified theory that could apply seamlessly across all domains of

complex systems—a theory that would be akin to Newton’s laws and Maxwell’s equations

in its universal applicability.

As complexity science has evolved over the past century, it has occupied a theoretical

domain that, this dissertation suggests, overlaps significantly with the thematic landscape

of Japanese architecture. This intersection presents an opportunity to weave together the

seemingly disparate threads of Japanese architectural thought, converting perceived clichés

into deeper, more nuanced insights. By applying the lens of complexity theory to Japanese

architecture, this dissertation advocates for a holistic perspective that not only enriches the

understanding of architectural philosophy but also provides a concrete framework for

navigating the abstract goals that have long characterized the field. This approach promises

to redefine the comprehension of space, form, and function, illuminating the path to

achieving the elusive and often mystical objectives that define Japanese architectural

excellence.

1.2 Major Obstacles in the Research

Conducting research from a complexity perspective means that one cannot avoid

addressing the meaning of “complexity.” However, here one encounters the biggest

obstacle, which, this dissertation argues, is also the key to answering the research

question— “what is complexity?”

Many architectural researchers associate complexity with a particular characteristic.

For example, some directly equate complexity with nonlinearity, while others equate it

with “emergence.” Some equate complexity with chaos, or with the coexistence of order

and disorder, or to fractals, or nested self-similarity. Others equate complexity with self-

organization, with parameterization, or with randomness or contingency.

John Horgan, The End of Science. trans. Sun Yongjun, Zhang Wujun (Beijing: Tsinghua University

Publishing House, 2017), p208.

4 1 Introduction

Charles Jencks, for example, states that nonlinear dynamics is “a generic name for the

complexity sciences.”

Youguo Qin notes that complexity is “the process of architectural

design.”

In his dissertation, Qi Chen remarks that complexity often refers to the

complexity of form and space, and the visual complexity it creates. Qi goes on to identify

a “clear commonality of complexity” in contemporary architecture: a departure from and

transcendence of the traditional Cartesian coordinate system and the Euclidean geometry

of form, space, and structure.

Discussions cannot proceed effectively without a consistent definition or a foundation

on which to build. Moreover, not one of the expressions of complexity listed above can be

seen in Fujimoto’s work.

It is not only Japanese architecture, but also the scientific community as a whole,

including the natural sciences, that still lacks a stipulative description of “complexity.”

the natural sciences and philosophy, there are over fifty distinct meanings attributed to

“complexity.”

Not only the term “complexity,” but many other concepts related to order

are entangled with one another.

If one refers to Thomas Kuhn’s “incommensurability of theories,”

it is possible to

see the chaotic state of the current definition: “complexity,” as well as different kinds of

Charles Jencks, The Architecture of The Jumping Universe: A Polemic: How Complexity Science is

Changing Architecture and Culture, 1997. p13.

Youguo Qin, “Non-linear Volume: Expressing Complexity,” World Architecture, 2006.9.

Qi Chen, “Analyses for the Thinking Paradigms of Contemporary Architecture Creation by Edgar Morin’s

Complexity Thought” (PhD diss., Tsinghua University, 2013), p7.

Per Bak, How Nature Works: The Science of Self-organized Criticality, trans. Xu Cai, Wei Chen (Wuhan:

Central China Normal University Press, 2001), p5.

John Horgan provides a number (45), based on the work of Seth Lloyd, a physicist at MIT who has

computed an inventory of definitions of complexity. They are: information (Shannon); entropy (Gibbs,

Boltzman); algorithmic complexity; algorithmic information; Renyi entropy; self-delimiting code length

(Huffman, Shannon-Fano); error-correcting code length (Hamming); Chernoff information; minimum

description length (Rissanen); number of parameters, or degrees of freedom, or dimensions; Lempel-Ziv

complexity; mutual information, or channel capacity; algorithmic mutual information; correlation; stored

information (Shaw); conditional information; conditional algorithmic information content; metric entropy;

factual dimension; self-similarity; stochastic complexity (Rissanen); sophistication (Koppel, Atlan);

topological machine size (Crutchfield); effective or ideal complexity (Gell-Mann); hierarchical complexity

(Simon); tree subgraph diversity (Huberman, Hogg); homogeneous complexity (Teich, Mahler); time

computations complexity; space computations complexity; information-based complexity (Traub); logical

depth (Bennet); thermodynamic depth (Lloyd, Pagels); grammatical complexity (position in Chomsky

hierarchy); Kullbach-Liebler information; distinguishability (Wooters, Caves, Fisher); Fisher distance;

discriminability (Zee); information distance (Shannon); algorithmic information distance (Zurek); Hamming

distance; long-range order; self-organization; complex adaptive systems; edge of chaos.

Take “order,” for instance; it can stand in seamlessly for all other forms of order across various contexts.

Similarly, “randomness” manifests in at least three distinct variations. Moreover, the notion of “disorder”

encompasses profound depth. In specific scenarios, order, disorder, and chaos are interchangeable or may

even convey opposing concepts. This analysis does not even begin to address “complexity,” a term prone to

engendering confusion and misinterpretation.

The “incommensurability of theories” constitutes a fundamental element of Kuhn’s philosophy. In

elucidating this idea, Kuhn offers an illustration with the concept of “motion.” While studying Aristotle, he

observed what appeared to be mere “errors.” Eventually, Kuhn had an epiphany: these were not errors;

1.3 Why Choose Fujimoto as Research Object? 5

“order,” are “Semi-incommensurable.” Research into complexity, which began nearly a

century ago, reached its peak in the 1990s and was widely regarded as a scientific

revolution. However, it gradually declined after 2000. This so-called revolution is

unfinished, and the concept was left open to interpretation. The exploration of complexity

by scholars has led to a proliferation of nuanced understandings, yet an integrative, clear

articulation of these insights remains elusive. This conundrum places the concept of

complexity in a unique quandary—on the surface, it appears that everyone claims an

intuitive grasp of complexity, acknowledging its presence across various domains of study.

Nonetheless, a paradox emerges, as a clear, unified definition of complexity proves to be

as complex as the concept itself. This situation underscores a fundamental challenge: while

the recognition of complexity is nearly universal, the capacity to succinctly define and

convey its full scope and significance is notably absent.

In conclusion, the intricate nature of complexity, characterized by its non-uniformity,

context-dependence, and subjectivity, makes it a challenging concept to grasp. This often

leads to the problem, highlighted by Bailin Hao,

of misinterpreting the term, which paves

the way for various pseudoscientific debates. Consequently, the initial step toward

addressing this issue lies in the accurate interpretation of complexity. By taking up this

challenge, the present research aims to offer a grounded understanding that navigates away

from misconceptions and provides a solid foundation for further exploration.

1.3 Why Choose Fujimoto as Research Object?

[Fig. 1.1] Sou Fujimoto serves as a bridge between “Japan” and “Complexity.”

The selection of Sou Fujimoto for this study is informed by two pivotal facets of his

architectural ideology. First, his designs manifest commonalities that resonate deeply with

the essence of Japanese architecture. Second, he delves into the realm of complexity.

instead, the connotations of the concept had been transformed after the scientific revolution. During

Aristotle’s time, “motion” was not just about spatial change; it included any transition between two states,

such as a seed maturing into a tree or an individual healing from sickness. This interpretation differs vastly

from that of the Newtonian era. “Mass” exemplifies a similar notion: Newton perceived it as an immutable

entity, while Einstein recognized its potential to interchange with energy. “Complexity” is akin to these terms,

albeit residing in an intermediary zone.

Hao Bailin is Professor at the Institute of Theoretical Physics and Academician of the Chinese Academy

of Science.

6 1 Introduction

Fujimoto, who made his debut around the year 2000 without the backing of a

distinguished architectural lineage, quickly earned the admiration of Toyo Ito. With a

modest portfolio, including notable works like House N, and a small collection of

theoretical essays, Fujimoto swiftly climbed the ranks of Japanese architecture. Within a

remarkably short time span, he had gained international acclaim, positioning himself as

one of the leading figures among Japan’s new wave of architects.

Fujimoto’s philosophy is a testament to the presence of these Japanese commonalities.

He frequently explores notions such as “nature,” “inside-outside,” “in-betweenness,” and

“de-materialization”—themes that are inherently Japanese. Discussions about his early

career, especially those around the concept of “weak architecture” which took place until

about 2015, emblematize these commonalities. His architectural expressions further align

with contemporary currents among Japanese architects, which demonstrates a coherence

in the conceptual explorations of the period. Moreover, Fujimoto navigates the concept of

complexity, a theme ostensibly removed from the Japanese context. Influenced early on by

Ilya Prigogine’s Order out of Chaos, Fujimoto’s thinking is imbued with ideas from

complexity theory, marking his distinct approach to architecture. Fujimoto’s work and

discourse are replete with complexity-related features, including terminology related to

order, such as “order,” “complexity,” “disorder,” and “generation.”. Yet, Fujimoto’s

engagement with complexity is implicit, and occurs most notably through his discussion

of “weak architecture,” which fundamentally addresses complexity.

Fujimoto’s work serves as an interpretive bridge, melding Japanese architectural

principles with the framework of complexity theory. He exemplifies how the collective

subconscious manifested in certain strands of Japanese architecture, with its coherent

objectives, might be realized through the lens of complexity. Addressing two critical

aspects of the complexity gap—“context” and “subjectivity”—Fujimoto’s perspective

offers a valuable vantage point. His approach not only facilitates a deeper understanding

of the interplay between Japanese architectural thought and complexity but also aids in

establishing a foundational link between these seemingly disparate domains.

1.4 Research Objectives

The main objective of this dissertation is to demonstrate that complex thinking can offer a

holistic perspective on prevalent ideas in Japanese architecture. This can be outlined in

three key goals:

1. To identify a suitable definition of complexity to underpin the project

Exploring Fujimoto’s interpretation of complexity reveals that there is no comprehensive

study on the specific concept of complexity he employs. Although it is well acknowledged

that Fujimoto is influenced by complexity theory, the exact nature of the complexity he

adopts requires elucidation. In the realm of complexity definitions, distinctions surely exist,

necessitating an identification of the most fitting basis for discussion.

1.5 Research Process and Steps 7

2. To define Fujimoto’s interaction with complexity

The tendency toward “complexity” in Fujimoto’s work is not overt. He refrains from

engaging with theories directly, and the scholarly discourse often fails to connect his work

back to the core principles of natural sciences, opting instead for subjective interpretations.

The field of “complexity theory” is vast, lacking a definitive scope, much like the broad

and elusive influence of “science” itself. This prompts further investigation into Fujimoto’s

rationale behind adopting “complex,” the origins of his thinking, and his method of

articulating complexity. The scarcity of literature on these aspects underscores the need for

a clearer delineation of Fujimoto’s relationship with complexity in order to facilitate a

deeper understanding of Japan’s architectural nexus with complexity.

3. Elucidate the nexus between Japan and complexity

The term “complexity” struggles to find a foothold in Japanese architectural history. The

dialogue concerning complexity’s integration with Japanese architectural philosophy is

infrequent—it is missing from seminal texts and appears only sporadically across

publications. Despite the intrinsic connection between complexity and concepts like non-

linearity, chaos, and fractals, which are often discussed in articles, it is imperative to

determine which idea resonates most with Japanese architects. Additionally, the profound

impact of complexity science on architecture, particularly evident in digital parametric

architecture, can be less clearly observed within the Japanese context. It is crucial to

identify whether a parallel exists between the different interpretations of complexity and

to pinpoint the divergences that have led to distinct architectural developments. This

discourse seeks to uncover how Japanese architectural ideology interweaves with the fabric

of complexity.

1.5 Research Process and Steps

The research can be divided into three phases:

First, a definition of complexity must be established. While a ready-to-use definition

might be elusive, a foundational understanding certainly exists. Hence, prior to engaging

with architectural discourse, it is necessary to conduct a thorough examination of the

various definitions and theories surrounding complexity. The research must penetrate the

intricate definitions and theories, resulting in a comprehensive comparison and

categorization. Additionally, it is essential to make a parallel assessment of definitions

within the Japanese architectural context, assimilating Fujimoto’s architectural ideologies

to pinpoint a relevant foundation. The prospect of a singular, all-encompassing notion of

complexity appears to be unattainable at present. This dissertation does not intend to

consolidate every aspect of complexity into one definition. Nevertheless, delineating a

foundational reference pertinent to architecture is both beneficial and achievable. Therefore,

the initial stage of this work is to find a foundation that aptly interprets the complexity

pertinent to Fujimoto and Japanese architecture at large.

8 1 Introduction

Second, the imperative for a tool arises. As it stands, there is no solitary, pre-

formulated definition of complexity that can unambiguously explain Fujimoto’s

complexity without interpretative aid. Having a foundational understanding alone is

insufficient, given the open-ended essence of complexity, which demands contextual

deciphering. The complexity seen in Fujimoto’s perspective is distinctly subjective, rooted

in a blend of theoretical insight and architectural experience. This necessitates crafting an

auxiliary tool tailored for dialogue, which first systematizes various order-related concepts

to mitigate the confusion stemming from their overlap. To clarify complexity, it is vital to

secure a consensus on order concepts, providing a solid base for the ensuing discussion.

Moreover, this tool must be adept at elucidating the complexity specific to Fujimoto and

Japanese architecture.

Third, this tool will be applied to articulate the interplay between Japan and

complexity. With a framework for interpreting complexity established, a detailed analysis

exploring the interconnection between it and Japan is warranted.

1.6 Research Outline

This project is divided into five chapters in total:

Chapter 1: Introduction, presents the current research gap.

Chapter 2: Research Background, outlines essential concepts, traces the evolution of

complexity science, and examines the progression of architecture impacted by complexity.

It also explores the integration of complexity theory into Japanese architectural

development from the 1960s onward, setting the stage for further investigation.

Chapter 3 evaluates the viability and constraints of adopting Rule 110 as a basis for

examining Fujimoto’s approach to complexity. It establishes an initial link between

Japanese attributes and complexity.

Chapter 4 introduces the FGO and delineates its characteristics. It aims to define the

interplay between Japanese architectural ideology and the principles of complexity

thinking.

Chapter 5 is a summary conclusion of the entire research.

2 Research Background

This chapter is devoted to laying the necessary foundational groundwork for the ensuing

discourse. It delineates essential concepts, traces the origins and subsequent evolution of

complexity science, explores the predominant ways in which complexity theory has

influenced architectural thought, and examines the backdrop of Japanese architectural

history from the 1960s through the lens of complexity. The objective is to establish a

compelling rationale for analyzing Japanese architectural philosophy from a complexity

standpoint, thereby setting the stage for the detailed discussions that will unfold. This

approach aims not only to contextualize the significance of complexity science within the

architectural realm but also to underscore the potential of this perspective in offering novel

insights into the nuances of Japanese architectural thought.

2.1 Some Key Concepts Related to Complexity

2.1.1 The Lexical Definition of Complexity

In Chambers Encyclopedic English Dictionary, “complex” has three different definitions

as both a noun and an adjective. Its adjectival meanings are: 1. Composed of many

interrelated parts; 2. complicated; involved; tangled; 3. Grammar, said of a sentence having

a main clause and one or more subordinate clauses. As a noun, it is defined as: 1. Something

made of interrelating parts, e.g. a multi-purpose building: a leisure complex; 2. Psychol. In

psychoanalysis, a set of repressed thoughts and emotions that strongly influence an

individual’s behavior and attitudes; 3. an obsession or phobia.”

The definitions of “complexity” in Random House Webster’s College Dictionary are

also concise: 1. The state or quality of being complex. 2. a complication; and intricacy,

something complex. In comparison, there is only one additional definition in The Oxford

English Dictionary: 1. Composite nature or structure. In Encyclopedia Britannica, the

explanation of complexity is: a scientific theory which asserts that some systems display

behavioral phenomena that are completely inexplicable by any conventional analysis of the

systems’ constituent parts. These phenomena, commonly referred to as emergent behavior,

seem to occur in many complex systems involving living organisms, such as a stock market

or the human brain.

It can be seen that the definition here has completely distinguished

complexity from its everyday meaning.

“Complex,” Chambers Encyclopedic English Dictionary, 1994. p280.

“Complexity,” Random House Webster’s College Dictionary, 1991. p278.

“Complexity,” Encyclopedia Britannica, August 23, 2023.

https://www.britannica.com/science/complexity-scientific-theory.

10 2 Research Background

In Chinese and Japanese, it is important to note the relationship between “复杂性”

and “complex” or “complexity.” The Chinese word “复杂” corresponds to the English

words “complex” and “complexity.” In Chinese and Japanese, “复杂” can be used as both

an adjective and a noun, while in English “complex” can be used as both a noun and an

adjective, and “complexity” is only used as a noun. Therefore, when Sou Fujimoto uses

“复杂,” he sometimes refers to “complex” and sometimes to “complexity.” In English

literature, “complexity” is commonly used to describe the attribute of complexity, and

various articles discussing the concept of complexity also use “complexity.” Overall, in

Chinese, “复杂性” can also be translated as “复杂.”

2.1.2 An Overview of Complexity in Natural Science

In addition to the inventory of 45 definitions of complexity provided by Seth Lloyd, there

are some other well-known understandings of complexity: information theory pioneer

Warren Weaver’s “organized complexity” and “disorganized complexity”; Friedrich

Gramer’s “fundamental complexity,” “critical complexity,” and “subcritical complexity”;

Per Bak’s “self-organized criticality”; Claus Emmeche’s “ontological complexity”, and

Ming Li and Paul Vitanyi’s “descriptive complexity,” which serves as a counterpart to

“ontological complexity.” These are well-established and widely discussed concepts of

complexity that have been elaborated by researchers across various fields.

Moreover, some scholars have attempted to provide a holistic description of the

properties of complexity in an effort to arrive at a definition or characterization.

Hongsen Wei proposes that complexity has the following forms and characteristics:

multiple factors and broad scope, involving multiple factors and a variety of forms; closely

connected and structurally complex, with multiple connectivity, multilevel and cross

structures; closely connected and dynamic, with strong randomness, instability,

differentiation, interaction between order and disorder, and randomness; non-linear and

non-additive, with self-organizing evolution, chaos, and fractals; counter-intuitive

causality: emergence, bifurcation.

Zhong Chen and Zhikang Wang provide a descriptive definition of “complexity” from

a philosophical perspective. Complexity is a property of objective things; it is a cross-

domain between different levels of objective things; it is a relationship between objective

things that cannot be directly reduced to traditional scientific theories across levels.

Hongsen Wei. “Complexity Research and Systematic Thinking Approach,” Journal of Systemic Dialectics,

2003, Vol.11, No.1. p8.

Tong Wu, “Review of Complexity, nonlinear research and their philosophical issues,”

哲学动态

, 1999, Vol

12.

2.1 Some Key Concepts Related to Complexity 11

Xuefeng Song believe that complexity is the external manifestation of certain

mechanisms within a system.

Tong Wu also offers a definition of complexity. He believes that complexity, in

ontological terms, refers to the irreducible new states and interrelationships of objective

things that integrate across levels through certain movements or states. Wu Tong further

subdivides ontological complexity into two types of movement complexity (catastrophe

theory and chaos) and two types of structural complexity (fractal and non-stable). From an

epistemological perspective, complexity refers to the effective understanding and

expression of objective complexity.

In a later article, influenced by Guangle Yan and Huanchen Wang from Shanghai Jiao

Tong University, Tong Wu adds the concept of “boundary complexity” and points out that

“structural complexity” refers to the complexity of the arrangement and combination of the

elements within the system through interactions, while “boundary complexity” refers to

the complexity generated by the interaction between the system and its environment at the

boundary. The boundary is not a mathematical line without mass, width, area, or space, but

is composed of the boundary and the cross-boundary parts between the system and its

environment.

The aforementioned notions of complexity all have definite definitions and meanings

but they differ greatly. We might take three of the most common definitions as examples.

Ilya Prigogine, the pioneer of self-organization theory, argues that self-organization is

complexity. He defines complexity from the perspective of self-organization. The founder

of chaos theory, Lorenz, believed that chaos is sometimes complexity. He defined

complexity from the perspective of physics. Kolmogorov argues that the maximum

randomness corresponds to the maximum complexity. His complexity is defined from the

perspective of computer science, as “the shortest program length that describes an object.”

It is evident that these three well-known theories take entirely different angle to address

complexity. Another example, Per Bak, a pioneer in the theory of self-organized criticality,

contends that the essence of self-organized criticality is nature’s constant deviation from

equilibrium, yet it is organized into a stable/critical state. He views complexity as an

inherently critical state. Consequently, Bak equates self-organized criticality with

complexity. In his seminal work “How Nature Works,” published in 1987, Bak directly

addresses this concept in Chapter 6, which is entitled “The Game of Life: Complexity as

Xuefeng Song, “Complexity, Complex System, and the Science of Complexity,” National Natural Science

Foundation of China. 2003. Vol.17(5): p262-269.

Tong Wu, “The Some Philosophical Problems in the Research of ‘Complexity’,” Studies in Dialectics of

Nature, 2000, Vol.16, No.1.; Tong Wu, “Review of Complexity, nonlinear research and their philosophical

issues,”

哲学动态

, 1999, Vol 12.

Tong Wu, “Objective Complexity in the View of Philosophy of Science,” Journal of Systemic Dialectics,

2001, Vol.9, No.4.; Guangle Yan, Huanchen Wang, “Boundary Thinking,” Journal of Management Sciences

in China. 2000, Vol.3, No.1: p19-86.

12 2 Research Background

Criticality.” He elaborates on this notion by suggesting, “So let us think of complexity

simply as variability,”

thereby offering another perspective on the nature of complexity.

The definitions of complexity mentioned above come from different periods of

development in complexity science. They are all important components of complexity

science, and some are even the basis for the majority of complexity definitions. However,

the complexities they describe are completely different.

It can be said that complexity has a whole family of definitions; that there is no unified

standard for complexity. Its scope covers almost all disciplinary fields. Almost every

discipline has its own research object of complexity, and therefore has different definitions.

The reason for this is that complexity involves a common problem in different scientific

fields, and due to the different research objects and methods used, it is impossible to

achieve strict uniformity in defining complexity.

Equally, the definition of complex systems, the research object of complexity, cannot

be unified. According to Xuefeng Song’s statistics, there are at least 30 different definitions

currently in existence.

Researchers in the chaos theory school believe that complex

systems are chaotic systems. The Santa Fe school believes that complex systems are

evolving systems with adaptive capabilities. Some people believe that complex systems

are hierarchical systems that include multiple agents with different behaviors. The Xuesen

Qian school refers to complex systems as “complex giant systems.” Steven N. Durlauf

identifies four primary features that a complex system has from an economic perspective:

non-ergodicity; phase transition; emergence; universality.

Different disciplines have different definitions of complexity and different research

objects. Some researchers also believe that complex systems, like complexity itself, can

never be precisely defined.

These are the main reasons why complexity science has been criticized. Guo and Jin,

for instance, write: “Complexity is almost a theological concept. Everyone talks about it,

but no one knows what it is.”

Or, as Hao puts it: “The concept of complexity is one that

can easily be misunderstood and can give rise to various pseudo-scientific discussions.”

Per Bak, How Nature Works, trans. Xu Cai, Wei Chen (Wuhan: Central China Normal University Press,

2001), p5.

Song, “Complexity,” 263.

Steven N Durlauf, “Complexity and Empirical Economics,” The Economic Journal Vol.115, (June 2005):

F225-243.

Michael Batty, Complexity in city systems: Understanding, evolution, and design. 2007.

Yuanlin Guo, Wulun Jin. “What is Complexity?,” Science, Technology and Dialectics. 2003, Vol.20, No.6.

Bailin Hao, “Characterization of Complexity and ‘Complexity Science’,”

科学

(Bimonthly), 1999, Vol.51,

No.3.

2.1 Some Key Concepts Related to Complexity 13

This section has offered an outline of the current definitions of complexity within

natural science. The next few sections will introduce several definitions of complexity in

further detail.

In line with the content discussed in this dissertation, complexity will be divided into

three categories, which will be the subjects of the following three sections: randomness as

complexity; chaos as complexity; and the co-existence of order and disorder as complexity.

2.1.3 Randomness as Complexity

Randomness was once seen as equivalent to complexity. As a typical example, we might

consider Kolmogorov Complexity, a complexity measurement method based on

information theory which was proposed in 1965 by former Soviet mathematician Andrei

N. Kolmogorov. Its core idea is to use the shortest computer program to describe the

information content of an object.

It holds a “maternal” position in the complexity family, as the majority of definitions

of complexity are based on it.

This type of complexity concept is also known as

“algorithmic complexity,” “computational complexity,” or “algorithmic information

content” (AIC). These terms are similar and all focus on the amount of computational

resources required to solve a problem. The computational resources mainly include space

and time.

“Algorithmic information content” was independently proposed in the 1960s by three

founders: Kolmogorov, Gregory Chaitin, and Ray Solomonoff. Murray Gell-Mann offers

the following definition of it: imagine an ideal, multi-functional computer that can store an

infinite amount of information (or has limited information storage that can be arbitrarily

expanded as needed). This computer is equipped with special hardware and software. Then

they (the founders) consider a particular information string and seek a computer program

that prints out this information string and then stops. The length of the shortest program is

the algorithmic information of that information string.

The basic idea of this type of complexity implies that if it is difficult to obtain the

information contained in a thing, then that thing is complex. They are all called complexity

in the sense of Shannon’s information theory and cannot include pragmatic factors such as

ambiguity and ambiguity in meaning. The description of effective complexity

understanding is incomplete.

Andrey Nikolaevich Kolmogorov, “Three Approaches to the Quantitative Definition of Information,”

International Journal of Computer Mathematics 2, no. 1–4 (January 1, 1968): 157–68.

https://doi.org/10.1080/00207166808803030.

Tong Wu, Jinlong Yu, “Kolmogorov: Euclid in the Complexity Research,” Journal of Dialectics of Nature.

2003, Vol. 25, Sum No 148, No.6.

Murrary Gell-Mann, The Quark and the Jaguar, trans. Yang Jianye (Changsha: Hunan Science &

Technology Press. 1998), p36.

Tong Wu, “The Some Philosophical Problems,” p8-9.

14 2 Research Background

Moreover, these concepts only express the difficulty of understanding complexity, and

are meaningless for actually understanding complexity itself. That is to say, they are not

about the objects of knowledge, but about the cognitive abilities of the knower. For this

reason, Wu Tong comments that “Kolmogorov provided an effective concept of

‘complexity’ for measuring computational difficulty, but it led people to misunderstand the

complexity of objective objects.”

2.1.4 Chaos as Complexity

Chaos is conflated with complexity in numerous discourses. An early statement by E.

Lorenz

underscores this conflation: “In essence, complexity is often invoked to describe

the sensitivity to initial conditions and all phenomena associated with this sensitivity.”

Such sensitivity to initial conditions epitomizes chaos. Therefore, Lorenz posits that

complexity and chaos often serve as synonyms, albeit with nuanced distinctions. To

delineate between “chaos” and “complexity,” he suggests, “the former pertains to

irregularities over time, while the latter denotes irregularities in space. These forms of

irregularities are often encountered concurrently, as seen in turbulent fluid dynamics.”

Hence, according to Yuanlin Guo and Wulun Jin, Lorenz essentially equates complexity

with chaos, or rather frames complexity as a broader interpretation of chaos, due to their

shared characteristic of sensitivity to initial conditions.

In a similar vein, some scholars propose substituting complexity with high-

dimensional chaos, leveraging insights from chaos theory to enrich the study of

complexity.

This perspective finds its grounding in foundational concepts, such as those

of Boltzmann, who coined the term “entropy,” describing it as “microscopic chaos.”

Furthermore, the concept of the “edge of chaos” has been introduced as a definition

of complexity. This term, akin to High Dimensional Chaos, intuitively suggests that

complexity represents a specific manifestation of chaos, thus encouraging the

conceptualization of complexity within the domain of chaos.

Beyond the deliberate equivalence drawn between chaos and complexity from varied

viewpoints, there are instances where such comparisons are made possible due to a lack of

precise scientific vocabulary.

Tong Wu, “On Relationships between Complexity and Randomicity,” Journal of Dialectics of Nature.

2002, Vol.24, No.138. p21.

E.N. Lorenz, the founder of chaos theory, the inventor of the Butterfly Effect.

E.N. Lorenz, The Essence of Chaos, trans. Shida Liu. Beijing: China Meteorological Press. 1997. p156.

Lorenz, The Essence of Chaos, p158.

Yuanlin Guo, Wulun Jin, “What is Complexity?,” p23.

“Concepts: Chaos vs. Complex Systems,” New England Complex Systems Institute,

https://necsi.edu/chaos-vs-complex-systems.

Ricard Solé, Brian Goodwin. Signs of life: How complexity pervades biology (New York: Basic books,

2002), p30.

2.1 Some Key Concepts Related to Complexity 15

For instance, in the book Signs of Life, the author elucidates the concept of complexity

through the use of three illustrative images. In reference to Figure 2.1, the author points to

the depiction of complexity and explains: “The structure is neither totally random nor

completely ordered. We observe triangles of many different sizes, and in between we can

see domains of disorder. We perceive some underlying structure at many different scales.

This pattern is complex.”

[Fig. 2.1] Three types of order.

Yet, according to Wolfram’s Classification,

the depiction in question fails to capture

the essence of complexity. Triangles of varying sizes might be seen as exhibiting fractal

characteristics, but they lack structural formation. This implies that both the author’s

narrative and the graphic representation align more closely with the chaotic attributes

exemplified by Rule 30 in Wolfram’s Class 3. The discussion pertains to chaos, despite

the author’s classification of it as complexity.

Furthermore, Stephen Wolfram’s terminology concerning Rule 30 in his seminal

work, A New Kind of Science, has the potential to create confusion. Rule 30 serves as a

quintessential example of chaos within Wolfram’s framework. Yet, the liberal application

of terms such as “complex” and “complexity”

in Wolfram’s description may

inadvertently equate chaos with complexity.

Whether by accident or design, chaos, in certain contexts, is indeed interpreted as a

form of complexity.

2.1.5 Co-existence of Order and Disorder as Complexity

The Coexistence of Order and Disorder

The coexistence of order and disorder is often used to imply or understand complexity.

Early studies on phase transitions provided some evidence from a fundamental level for

this understanding.

Ricard Solé, Brian Goodwin. Signs of life, p33.

Wolfram’s Classification is the basis of the Five Graphics used in this article, and will be introduced in

more detail in Chapter 3.

Stephen Wolfram, A New Kind of Science (Wolfram Media, 2002), p27-28.

16 2 Research Background

The same substance exhibits markedly different levels of order and disorder in

molecular motion under different external influences (primarily temperature and pressure),

a phenomenon which has attracted the attention of scientists. If we take water as an example,

we can see that, while retaining the same molecular structure, it can exhibit the three phases

of liquid, solid, and gas, which are the three major states of aggregation that exist in most

of the natural world. The transition between each phase is caused by a change in the

interaction of molecules at the microscopic level. In the ice crystal structure, the molecules

exhibit extreme order, while in water vapor, the relationships between the molecules appear

to have no regularity, showing extreme disorder. The microscopic interactions determine

the patterns exhibited at the macroscopic level, and the interactions between parts

determine the properties of the whole. Different microscopic interactions give rise to

different macroscopic properties (Fig. 2.2).

In this process of transformation, scientists have observed two important phenomena:

first, a substance can transition from a state of extreme order to one of extreme disorder;

second, the phase transition occurs at a clear and fixed point (for example, water freezes at

0 degrees and boils into water vapor at 100 degrees) (Fig. 2.3). This means that at a clear

point, the overall state of the system transitions from order to disorder (and vice versa).

[Fig. 2.2] Left: At high temperatures, iron atoms no longer act in an “orderly” fashion.

[Fig. 2.3] Right: Magnetization per site.

This dissertation uses electromagnetic phase transition to illustrate this issue. In

physics, electromagnetic phase transition is a typical critical phase transition. A magnet

can attract metal. However, if the magnet is heated to a certain temperature, the magnetic

force disappears.

Electromagnetic phase transition is a typical critical phase transition. The magnetism

of a magnet comes from the magnetic force within each iron atom. The iron atoms, which

have positive and negative poles, are arranged in an extremely orderly manner to form a

2.1 Some Key Concepts Related to Complexity 17

magnet. A single iron atom only interacts with its neighboring iron atoms. This means that

each iron atom will spontaneously align itself with its neighbors in the same direction.

In an ordered state, all iron atoms have a common orientation, so the magnetic property

is manifested at the macroscopic level. For example, in the diagram, the squares represent

iron atoms, and white and blue represent two different orientations. At room temperature,

white iron atoms will conform to their neighbors and change to a consistent direction.

However, as the temperature rises, the iron atoms are constantly disturbed by noise and

lose this consistency with their neighbors. Neighbors no longer affect their orientation. At

this point, iron atoms may flip. Local information is no longer communicated, and the

system becomes disordered, with the sum of magnetic forces being greatly reduced or even

tending toward zero.

Like water vapor, the entire system transitions from order to disorder at a certain point.

An important question at this juncture is: what happens during the transition from order to

disorder?

Scientists have provided an answer to this. They have continuously measured the

magnetic force while slowly cooling a high-temperature magnet. They discovered an

interesting phenomenon: at a certain temperature point, the magnetic force suddenly broke

through zero and continued to increase sharply within a certain interval. After passing

through a certain interval, the increase in magnetic force was greatly reduced. This means

that there may be a coexistence of the transition from order to disorder within this interval.

[Fig. 2.4] The simulation of phase transition.

The following explanation is based on the Ising model in a two-dimensional cellular

automaton. The Ising model was proposed by mathematician Ernst Ising in 1924 as a

mathematical model for studying the ferromagnetism of materials. It is a classic model in

condensed matter physics.

Lilian Witthauer, Manuel Dieterle, “The phase transition of the 2D-Ising model.” Summer Term, 2007.

7(1):p1-5.

18 2 Research Background

In order to avoid excessive descriptions of physics, the Ising model provides a very

approximate theoretical explanation for this phenomenon as a virtual model. It uses

extremely simplified rules (and also contains only two directions—positive and negative)

to describe the relationship between temperature and magnetic force. At high temperatures,

we can see a random distribution of positive and negative poles (represented by blue and

red). However, at a critical point, an unexpected phenomenon occurs: fractals begin to

appear automatically. Fig. 2.4 is a snapshot of a two-dimensional Ising model, showing a

potential order very close to the critical temperature: at any scale, a nested self-similar

structure can be found. The Ising model spontaneously self-organizes into a fractal body

when approaching the critical temperature. And when the number of positive and negative

squares is statistically counted to calculate the total value of the magnetic field, the result

is almost identical to the experimental results obtained in reality. The drastic change occurs

at T=Tc, which is the critical point of the phase transition.

The example provides several important observations. First, after the phase transition,

the entire system changes from disorder to order. Second, at a specific point, order and

disorder coexist. Third, even though virtual iron atoms (and real iron atoms) only interact

with their neighbors, long-distance connections and large-scale patterns can still emerge.

Local information can spread throughout the entire system, creating a macroscopic pattern

that cannot be known from the properties of individual entities. At this point, fractals begin

to appear. This kind of result has excited many scientists, who see the coexistence of order

and disorder as a sign of complexity. As exemplified in the previously mentioned Signs of

Life, there’s a prevalent notion that the simultaneous presence of both order and disorder

heralds the emergence of complexity. J. H. Miller articulates a similar observation:

In daily life, we see that many phenomena inherently embody both ordered and

disordered elements. Take ecosystems, for example, where despite the presence of

discernible patterns, population numbers often exhibit constant fluctuations. Similarly,

the brain, while storing copious amounts of information, operates through highly

irregular patterns of activity.

These perspectives suggest that the interplay of order and disorder is indicative of

complexity’s manifestation.

Morin argues that it is problematic to address the concepts of order and disorder

separately due to the profound depth and potential interchangeability of these concepts.

They do not exist in a hierarchical relationship but are instead deeply entangled with each

other. As Morin emphasizes: “Neither a deterministic universe nor a completely random

universe is feasible.” It is only through the synthesis of order and disorder that the world,

life, and evolution can materialize. Thus, the intertwined existence of order and disorder is

John H. Miller, Scott Page. An Introduction to Computational Models of Social Life, trans. Yuntao Long.

(Shanghai: Shanghai People's Publishing House. 2012), p29.

2.1 Some Key Concepts Related to Complexity 19

not only vital but intimately connected to the essence of complexity, aligning with the

common thread found in numerous definitions of complexity.

The following sections will examine several concepts that encapsulate this notion of

complexity.

Effective Complexity

In response to the tendency to equate complexity with randomness, Murray Gell-Mann

proposes “effective complexity.” Gell-Mann argues that “effective complexity” can be

roughly expressed by the length of a brief description of the regularity of the system or

string.

Effective complexity is a conceptual expression of properties such as orderliness of

system evolution, hierarchical structure, and diverse forms.

Using the concept of

information strings, we see that algorithmic complexity focuses on randomness, whereas

effective complexity centers on patterns and regularity. A fully random string of

information ranks highest in algorithmic complexity; however, its lack of pattern means

that it scores nil for the length of the description of regularity, resulting in an effective

complexity of zero. Conversely, an entirely patterned information string bears minimal

algorithmic complexity due to its simplicity, which leads to only a brief description of its

regularity. Hence, its effective complexity is also near zero. From this, we can infer that

for information strings of a set length, their effective complexity is either zero or

approaching zero when their algorithmic complexity is at its peak or trough. When the

algorithmic complexity is moderate, the effective complexity peaks. This suggests that to

achieve high effective complexity, an information string must strike a balance, avoiding

extreme randomness or predictability.

In general, Gell-Mann believes that algorithmic complexity is equivalent to

randomness. Its characteristics of incompatibility, incomprehensibility, and

unpredictability should not be used to define complexity. The more incomprehensible and

random something is, the less effective, more simple, and uncomplex it is, like the

molecules of gas in a bottle. Complexity has its special meaning, and it should be

somewhere between order and disorder.

Self-organization

Self-organization refers to the process whereby a system spontaneously moves from a state

of chaos and disorder toward ordered structures, through exchanging energy and

information with the environment, without the need for external commands or controls.

During this process, different parts of the system interact and co-evolve, leading to the

emergence of self-organized structures and functions. Self-organization is a common

phenomenon in many natural and artificial systems, such as atmospheric circulation, water

Gell-Mann, The Quark and the Jaguar, p36.

Wei, “Complexity Research and Systematic Thinking Approach,” p8.

20 2 Research Background

flow, biological communities, the operation of cities, and so on. It occurs in non-

equilibrium physical or chemical reactions and describes a process whereby order or

coordinated wholes emerge from initially disordered local interactions within a system,

without central control or reliance on external action. The entire process is spontaneous

[Fig. 2.5] For example, the natural phenomenon of a sand dune is a form of matter caused by a pattern of

airflow. Under the scorching sun in the desert, hot air rises and cold air descends. The confrontation between

the rising and descending air currents produces a pattern, as shown in the figure. When this pattern reaches a

critical point, something miraculous happens. The sand in the desert seems to have acquired intelligence and

forms an efficient way of dissipating heat, which is the sand dune we see. The reason behind it is the

emergence of a self-organizing phenomenon: a large number of free, independent individual molecules in

the liquid suddenly and spontaneously organize into a flowing pattern, and this pattern has a more effective

ability to dissipate heat than ordinary heat conduction. A new emergent behavior, convection, is formed in

the self-organizing spatial structure, and heat is transferred through collective movement.

and requires the continual input of external energy. Self-organizing phenomena—sand

dunes, for example—can be commonly observed in daily life. They give the impression of

being intelligent, similar to the least action principle in physics: the natural elements like

rocks, sand, wind, and sun seem to act in the most energy-efficient way (Fig. 2.5).

Haken defines self-organization as follows: if a system acquires spatial, temporal, or

functional structures without specific interference from the outside, we can say that the

system is self-organizing. Here the word “specific” means that the structure or function is

not imposed from the outside, and the outside acts on the system in a non-specific way.

Ilya Prigogine, another pioneering figure in this area, directly aligns “complexity”

with self-organization. In his book Exploring Complexity, Prigogine considers complexity

to refer to self-organization. Prigogine believes that biological systems are inherently

complex. However, systems like a pendulum or a falling object are simple, and liquids or

gases in equilibrium state are not complex due to their lack of order and regularity. But

self-organization can transform a system from a state of disorder to a state of order through

Hermann Harken, “Information and Self-organization: A Macroscopic Approach to Complex systems,”

Berlin & New York: Springer-Verlag, 1988. https://doi.org/10.1007/978-3-662-07893-8; Hermann Haken,

“Synergetics: An Introduction. Nonequilibrium Phase Transitions and Self- Organization in Physics,

Chemistry and Biology,” 1977. https://ci.nii.ac.jp/ncid/BA00415087.

2.1 Some Key Concepts Related to Complexity 21

the exchange of matter or energy with the environment. Self-organization possesses the

unique properties of biological systems, making it synonymous with complexity.

The Edge of Chaos

John Gribbin equates “the edge of chaos” with complexity.

M. Mitchell Woldrop also

claims that complexity, computation, and life itself exist on the edge of chaos—the only

dynamical regime.

“The edge of chaos” is apparently another definition of complexity

that is accepted by many.

The edge of chaos is a loosely defined notion first proposed by Christopher Langton

in 1990. When Langton used cellular automata to study the relationship between dynamical

behavior and computational capability, he found that the system was neither ordered nor

disordered when it was in a certain range between order and disorder (a phase transition).

Jim Crutchfield mathematically proved that there is a peak in this regime, where there is a

maximum of information. That is, the complexity of the system reaches its maximum.

As the name suggests, it is a state that lies on the edge of chaos without actually

reaching it. This definition was popular for some time after it was proposed. In 1992,

Roger Lewin published “Complexity: Life at the Edge of Chaos,” and in the same year, M.

Mitchell Waldrop published Complexity: The Emerging Science at the Edge of Order and

Chaos. The metaphor was subsequently elevated and expanded to include organizations,

management, artificial life, and so on, becoming very widespread. However, it also led to

some misunderstandings and controversies. Some scholars, for example, believe that the

term “edge” is inappropriate because the regime demonstrated by cellular automata is more

like a dynamic discontinuous surface or volume. In addition, since the edge lies between

chaos and order, could it also be called “the edge of order”?

So far, the basic concept of the edge of chaos, in more ordinary language, is as follows.

Within highly ordered and stable systems such as crystals, it is impossible for new things

to emerge; completely chaotic or aperiodic systems on the other hand, such as turbulent

fluids or heated gases, tend toward invisibility;

it is only when the system is at the edge

of chaos that life can occur.

Emergence

The phenomenon described by the concept of emergence is also often seen as a symbol of

this type of complexity. Therefore, emergence has also been a prominent concept in

architecture, with academic institutions like the London Architectural Association, MIT’s

Emergent Design Group, and Columbia University’s Paperless Studio offering courses on

Gregoire Nicolis, Prigogine Ilya, G. Nocolis, Exploring Complexity, trans. Jiuli Luo (Chengdu: Winshare.

1986), p05; Guo, “What is Complexity?,” p23;

John Gribbin, Deep Simplicity: Chaos, Complexity and the Emergence of Life, tans. Ziheng Ma (Taipei:

Business Weekly, 2018), p6.

Waldrop, Complexity, p234.

Horgan, The End of Science, p209.

22 2 Research Background

the subject. Architects such as Eisenman, Koolhaas, Tschumi, Libeskind, and Jencks have

engaged with emergence in their work. Eisenman has expressed a preference for emergence

over control, and Jencks has discussed it extensively, focusing on how complexity science

is reshaping architecture and culture, as detailed in his book The Architecture of the

Jumping Universe.

What is emergence? Holland posits that the essence of emergence is the transition

from the simple to the complex, from small beginnings to intricate patterns. This

characteristic is uniquely associated with complexity. Emergence refers to the phenomenon

where interactions at a micro-level lead to new, identifiable patterns at a macro-level. It

signifies the appearance of new hierarchical levels.

Emergence, like complexity, lacks a precise definition. Our understanding of

emergence is largely derived from classic examples, such as the human body, which is a

cascade of emergences across multiple levels. From DNA and molecules to cells, tissues,

organs, and organ systems, each step in this hierarchy represents an emergence, introducing

higher-level structures and behaviors. Phenomena like consciousness, intelligence, and the

ability to run emerge at the body’s highest level, with no hints of these behaviors detectable

at any lower levels.

Merely studying molecules will not reveal these emergent phenomena, much like the

properties of water cannot be deduced from hydrogen and oxygen alone. These phenomena

appear suddenly, rooted in micro-level interactions but not hinted at within these

interactions, making them somewhat detached from their origins and inherently

unpredictable. No prior level can foresee the behaviors emerging at the next, especially in

a system as complex as the human body with its multiple layers of emergence.

Hierarchy

Hierarchy is a system that is composed of interrelated subsystems; each of the latter are, in

turn, hierarchic in structure, descending to the lowest level of elementary subsystem.

To turn again to the human body as an example, the formation of organelles from

molecules represents one level of hierarchy, while the formation of cells from organelles

represents another. The interaction between cells to form organs represents another level,

and the formation of organ systems from organs represents yet another, and so on. Each

level has emergent features, and these features mean that it can be considered a hierarchy.

Some treat the individual human as a whole. However, at the level of society and

economy, humans are still “parts.” They interact to form markets and politics, nations and

states. Writing from a systemic perspective, Kong Xiaoli notes: “In fact, the object we want

to study, from the smallest basic particle to the entire universe, from a single cell to a

Herbert A. Simon, “The Architecture of Complexity,” Proceedings of the American philosophical society,

Vol. 106, No. 6. (Dec. 12, 1962), p.467-482.

2.2 Three Phases of Complexity Science 23

country or even the entire human society, should be regarded as a system with irreducible

properties.”

A complex system is therefore composed of such a structure: each level contains

subsystems below it. Thus, a complex system is composed of levels upon levels. Each

“whole” is just a part of a larger “whole.” In a system with multiple levels of emergence,

it is not appropriate to simply use the concepts of whole or part to name it. Rather, it should

be understood using the concept of hierarchy, or by using the concepts of micro-level and

macro-level to describe the two ends of the research object. This is the structure of complex

systems. Every former “part” serves as a building brick for the subsequent “whole.”

Similarly, in an “organic whole,” there are no “parts” or “wholes,” only hierarchy.

Hierarchy is also a common feature of all complex systems. Emergence is the

appearance of new hierarchies. These two concepts are closely related and are both

attributes of complexity. Hierarchy describes the structure of complex systems, while

emergence describes new behaviors or properties that suddenly appear at different levels.

Their different focuses also result in different architectural expressions in complex thinking.

Hierarchy and emergence are both important objects of study in complex systems.

Nobel laureate in economics Herbert Alexander Simon even defines complexity from the

perspective of hierarchy. He believes that hierarchy is a structure that most complex

systems in nature possess, and asserts that complexity evolves from simplicity and that all

complex systems have a hierarchical structure.

In daily life there are many observable emergent phenomena, including the emergence

of biological types such as trees, the intelligence of ant and bee colonies, the flocking of

birds and fish, the volatility of the stock market, climate change, population fluctuations,

the immune system, and the Internet. However, it is difficult to be aware of abstract

hierarchies.

2.2 Three Phases of Complexity Science

The concept of “complexity science,” as it is currently understood, can be traced back to

general systems theory, nurtured by the collaborative efforts of diverse groups over time.

This evolution signifies that complexity science is multifaceted, enriched by a myriad of

concepts. The founding of the Santa Fe Institute in the 1990s played a pivotal role in

Xiaoli Kong, “On Scientific Method from the Perspective of the Part-Whole Relationships,” Journal of

Dialectics of Nature, 1993, Vol.15, No.4, Sum No.86. p13.

Herbert A. Simon, The Science of Artificial, trans. Yishan Wu (Shanghai: Shanghai Scientific &

Technological Education. 2004), p200.

For more information, see the article by U. Wilensky. All of these have specific models in the NetLogo

software he created. They can very intuitively demonstrate the "surprises" and "unexpected" phenomena

brought about by emergent phenomena.

24 2 Research Background

unifying these diverse strands under the grand endeavor of complexity, aiming to create an

integrated scientific framework.

This integration resembles a vast tree where the myriad leaves of individual concepts

give rise to branches of distinct schools of thought, which in turn converge into the trunk

of complexity science. This metaphorical tree, much like the principle of self-organization

it mirrors, does not originate from its trunk but emerges from the leaves—the manifold

concepts and ideas that form the essence of complexity science.

The growth of this tree is indicative of the dynamic and evolving nature of complexity

science, showcasing how various elements from different disciplines and perspectives

come together to form a cohesive understanding of complex systems. This evolutionary

path underscores the interdisciplinary foundation of complexity science, highlighting its

capacity to bridge disparate fields through a common pursuit of understanding the intricate

interconnections and emergent behaviors inherent in complex systems.

2.2.1 Origins—Belief, Methodology, and Worldview

The origins of complexity science are subject to varied interpretations. What should be

considered the genesis of complexity science? Clearly, defining the discipline’s history

solely by the term “complexity science” would omit much understanding.

For instance, Miao Dongsheng believes that the Prigogine school was the earliest

institution to term its research complexity science and to articulate it systematically.

This

is because Prigogine’s French edition of La Nouvelle Alliance, published in 1979 (later

appearing in English as Order Out of Chaos in 1984), already offered a systematic and

unique discourse on the history, goals, basic problems, methodologies, significance, and

cultural backgrounds of complexity science. Thus, Miao concluded that the Prigogine

school had begun advocating for the establishment of complexity science in the 1970s.

However, the exploration of complexity clearly predates this. For example, Prigogine

himself regarded Fourier’s thermodynamics research as the starting point of complexity

science.

Opinions on this matter vary. Some believe that the systemic thinking that

emerged around 1921 in Gestalt psychology is the origin, while others consider the

“Process Philosophy” of English mathematician and philosopher Alfred North Whitehead

in 1925 as the starting point.

This text adopts George Cowan’s

viewpoint. Cowan considers the establishment of

Bertalanffy’s general systems theory as marking the birth of complexity science. The

reason is that general systems theory was the first scientific theory to oppose reductionism.

“Wholeness” rather than “parts” had to become the object of study. This represents a

Dongsheng Miao, “The Achievements and Vexation of the Complexity Studies,” Journal of Systems

Science. 2009, Vol.17, No.1. p1.

Ilya Prigogine, Isabelle Stengers. Order Out of Chaos (London: Heinemann, 1984), p104.

Founder of Santa Fe Institute.

2.2 Three Phases of Complexity Science 25

fundamental shift in scientific thinking from reductionism to holism. It is called “the first”

because it was the first scientific theory against reductionism. It is considered “had”

because it studied the “relationships” between parts of a system. These relationships

provide key answers for understanding the organization as a whole, which could never be

obtained by studying parts alone.

2.2.2 The First Phase: The Systems Theory Era

The first phase in the development of complexity science is normally considered to be the

emergence of general systems theory, Shannon’s information theory, Wiener’s cybernetics,

operations research, and systems engineering in the 1940s. They are often categorized as

modern systems science.

Miao Dongsheng summarized this period as follows: 1. the primary focus was on

engineering technology, and there was a lack of theoretical depth; 2. the research objects

were still simple linear systems and theoretical achievements were also mainly in linear

systems theory; 3. a reductionist methodology still dominated the research.

The contribution of modern systems science was a systematic reflection on the

methodological principles of reductionism. These theorists provided a set of important

concepts, such as systems, self-organization, information, and feedback. Key figures

include Bertalanffy, Wiener, Weaver, and von Neumann. Methodologically, the “whole”

became a formal object of research during this period and there was an emphasis on the

relationships between parts rather than the parts themselves, which stood in opposition to

reductionism. Systems theory advocated recognizing the whole while understanding the

parts. However, the holism characterized by systems science in this period was still largely

based on reductionist methods. The difference is that it recognized the limitations of

reductionism and the ubiquity of complexity, attempting to understand the whole by

reducing and analyzing from the viewpoint of the whole. This approach works for simple

systems but is no match for facing real complexity problems.

While this naive holism could not and did not produce a modern scientific method, it

contained methodological ideas for recognizing and handling problems from a holistic

perspective that was missing from reductionism.

It has sounded a clarion call for the

exploration of complexity.

2.2.3 The Second Phase: The Stage of Nonlinear Science and Chaos Theory

The evolution of complexity science surged into its second phase in the 1970s, heralded by

the groundbreaking dissipative structures theory championed by Ilya Prigogine, the

Xinrong Huang, Tong Wu, “The Context Analysis to the Arising of Complexity Sciences,” Journal of

Tsinghua University. 2004, Vol.19, No.3. p41.

Dongsheng Miao, “Current Situation and Prospect of Complexity Research,” Journal of Systemic

Dialectics. 2001, Vol.9, No.4. p4.

Huang, Wu, “Some Methodological Principles,” p76.

26 2 Research Background

synergetics framework formulated by Hermann Haken, and the innovative theories of

bifurcation. This wave of intellectual exploration continued into the 1980s, enriched by the

advent of chaos theory and the intricate beauty of fractal theory. Central to these theories

is the focus on nonlinear problems, which earned them the collective designation of

“nonlinear science.” Together with the preceding phase, these periods are jointly referred

to as the era of “systems science.”

As Xinrong Huang delineates meticulously, dissipative structure theory scrutinizes

the environmental prerequisites for self-organization; synergetics delves into the dynamic

forces underpinning self-organization; bifurcation theory abstractly probes the pathways

leading to self-organization, while hypercycle theory elucidates the complex forms of self-

assembly. Collectively, these intellectual pursuits are often branded as “self-organization

theory,” a cornerstone of complexity theory.

The period is particularly noted for its

seminal concepts—order, disorder, self-organization, nonlinearity, fractals, chaos—which

have very much permeated architectural discourse.

This era contrasts starkly with the preceding one: whereas traditional systems theory

was preoccupied with analyzing the static attributes of systems—structure and function—

in an almost passive context, the foray into dissipative structures theory shifted the lens

toward the vibrant narrative of “evolution.” This paradigm shift brought to light the

transformative journeys of systems from states of disorder to order, or from one ordered

configuration to another.

While the notion of self-organization, with its resonance in fields such as biology and

even within the philosophical debates of Immanuel Kant, was neither a novel invention of

Prigogine nor something confined to his domain, Miao Dongsheng posits that Prigogine’s

brilliance was in transcending the confines of technical science to elevate the concept to

the foundational strata of physical chemistry. This move endowed the study of complexity

with a formidable theoretical arsenal.

Viewing challenges through a systemic lens, discerning the universal threads that

weave through the structure, function, and evolution of systems across various fields,

became a hallmark of this intellectual epoch. This panoramic perspective, which aimed to

uncover the shared principles guiding the intricate dance of systems across disparate

domains, encapsulates the essence of these transformative phases.

Huang, Wu, “The Context Analysis,” p39.

Huang, Wu, “The Context Analysis,” p42.

Miao, “The Achievements and Vexation,” p1-2.

Huang, Wu, “The Context Analysis,” p39.

2.2 Three Phases of Complexity Science 27

2.2.4 The Third Phase: The Dawn of Complexity Science

The Santa Fe Institute was founded in 1984, and marked the official entry of complexity

science into its third phase. Complexity thinking began to flourish across various

disciplines, with representative figures like John H. Holland, who proposed the concept of

emergence, the theory of complex adaptive systems, and the basic proposition of adaptivity

creating complexity, as well as the echo model.

Other major theoretical contributions

during this period included Brian Arthur’s theory of increasing returns in economics,

Stephen Wolfram’s research on elementary cellular automata, Langton’s concept of the

edge of chaos, Stuart Kauffman’s research on the origins of life, and the study of self-

organized criticality with Per Bak’s sandpile model. Topics such as complex adaptive

systems, artificial life, and neural networks dominated the direction of complexity research.

The principle of interdisciplinary that characterized this period of complexity research

was encapsulated by the ethos of the Santa Fe Institute. While the first two phases were

still conducted separately in their respective fields, this period saw the beginning of true

disciplinary integration. It involved participants from various disciplines and had a high

degree of fluidity, with a grand attempt at disciplinary integration as one of its founding

principles. One of its founding ideas was to promote knowledge unification and eliminate

the notion of “two cultures,”

that is, the opposition between scientific culture and

humanistic culture.

The impact of all this was far-reaching, as demonstrated by the enormous influence

of complexity science on architecture in the 1990s. A complexity science vocabulary that

included terms such as organic, self-similarity, fractals, strange attractors, and nonlinearity

frequently appeared in architects’ talks at the time.

There were, however, many schools of thought, all with their own focus and areas of

expertise. According to Waldrop’s summary, in addition to the Santa Fe Institute, there

were four other schools of thought in the United States: system dynamics, chaos theory,

structuralist foundations, and ambiguity.

In addition, there was fractal theory and Zadeh’s

fuzzy theory,

as well as the Belgian school led by Prigogine and the European school led

by Haken.

The appearance of dedicated research institutions such as the Santa Fe Institute and

specialized journals such as Complexity and Emergence marked the formal entry of

complexity science into its third phase. In addition, scientific research groups are no longer

John H. Holland, Hidden Order: How Adaptation builds Complexity

，

trans. Xiaomu Zhou, Hui Han

(Shanghai: Scientific & Technological Education Publishing House. 2011), p138-143.

Snow, C.P. The Two Cultures and a Second Look. Cambridge: Cambridge University Press, 1965.

Wulun Jin, Yuanlin Guo. “国外复杂性科学的研究进展(Research Progress in Complexity Science

abroad),”

国外社会科学

(Foreign Social Sciences). 2003, 6.

Siwei Cheng, “Complex Science and Management,” Report of the 112th Xiangshan Science Conferences.

1993.

Miao, “The Achievements and Vexation,” p3.

28 2 Research Background

built on individual disciplines, but rather unified complexity science research have

emerged. These developments fulfilled Kuhn’s paradigmatic theory, leading some

researchers to believe that the third phase marked the initial formation of the complexity

paradigm.

2.2.5 Beyond 2000: Twilight

The 1990s witnessed the flourishing of complexity science, sparking a wave of optimism

among scholars and visionaries alike. Stephen Hawking famously proclaimed the twenty-

first century as the epoch of complexity, a sentiment echoed within Chinese academic

circles by Academician Ruwei Dai, who lauded complexity science as the defining science

of our era.

It was heralded as the dawn of the “Third Wave,” marking the transition into

a “Post-Industrial Age” and a “Post-Modern Society” characterized by innovation,

advanced complexity studies, and a burgeoning ecological consciousness.

Yet, as the new millennium unfolded, the financial woes of the Santa Fe Institute cast

a long shadow over the field, signaling a potential decline in the momentum of complexity

research. The once-celebrated discipline found itself besieged by skepticism as critical

voices grew louder and more persistent.

The debate over complexity science’s legitimacy as a formal discipline surfaced with

renewed vigor. Dongsheng Miao, among others, voiced skepticism, acknowledging that

while complexity had indeed risen to prominence across a myriad of disciplines, each field

grappled with a unique set of complex challenges—challenges that eluded the grasp of

traditional reductionist approaches. He argued that true complexity science could only

emerge from a comprehensive synthesis of these diverse challenges,

its inherently

interdisciplinary nature precluding its consolidation into a singular discipline.

The quest for a unified complexity theory also faced scrutiny. Wu Tong highlighted

the superior explanatory power of complexity theory over traditional models, as evidenced

by the successful simulation of natural forms through fractal theory. Despite this,

complexity theory had not had the same paradigm-shifting success that relativity or

quantum mechanics had achieved over Newtonian mechanics but rather coexisted with

mainstream theories, explaining phenomena within specific domains as opposed to

achieving a unified understanding.

John Horgan encapsulated this dilemma, questioning

whether a unified complexity theory was feasible when a consensus on even definition of

complexity remained elusive.

Jin, Guo, “Research Progress,” p4-5.

Ruwei Dai, “Research on ‘Complexity’— A science in the 21st Century (关于‘复杂性’的研究——一

门21 世纪的科学),” in Science Frontiers and Future (

科学前沿与未来

), ed. Tao Zhang (Beijing: Beijing

Science and Technology Publishing Co.,Ltd. 1998), p182-207.

Miao, “Current Situation,” p7.

Tong Wu,“On Complex Reality,” p4.

Horgan, “The End of Science,” p208.

2.3 Three Stages of Architecture Influenced by Complexity Science 29

Critiques also targeted the field’s perceived overreliance on metaphorical

methodologies.

In a candid debate at the Linnean Society of London, John Maynard

Smith dismissed complexity theory’s contributions as failing to shed light on any tangible

natural phenomena.

Dongsheng Miao pointed out that many of the achievements

attributed to the Santa Fe Institute in the 90s were in fact rooted in the research of the 70s,

suggesting an impasse in innovation. Furthermore, this body of work, often mired in

empirical, hypothesis-driven models, fell short of providing foundational research.

Theories, including the notable CAS theory, were criticized as “preliminary” and lacking

in profound theoretical insights.

These reflections articulate the broader skepticism that surrounds complexity science.

It becomes clear that complexity thinking has not displaced traditional scientific

approaches but rather complemented them, offering new perspectives for tackling

previously unresolved problems. It advocates for a paradigm shift in viewing and

addressing issues, employing novel methodological principles to deepen our understanding

of the natural world that envelops us.

2.3 Three Stages of Architecture Influenced by Complexity Science

According to Prof. Yuhang Kong from Tianjin University, architecture’s interest in

complexity can be traced back to organic architecture. Organic architecture shares an

important characteristic with complexity: both focus on human behavior and perception. It

is the buildings that are crafted with a focus on human needs.

From the 1960s, it began

to combine with nonlinear science, forming a powerful force that Prof. Kong named

“nonlinear organic architecture.”

There is some truth to this phrase, for the meaning and

subsequent interpretation of the term “organic” has indeed been expressed mainly in a non-

linear fashion. Since then, it has become clear that architecture has been influenced by

complexity science. According to Charles Jencks, the Western architectural expression of

complexity can be roughly divided into three stages: collage, superimposition, and non-

linear volume. These three stages represent the development of complexity in architecture

from the 1960s to the 1990s.

Ted Fuller, Paul Moran. “Moving Beyond Metaphor,” Emergence, Vol.2, No.1, 2000, p50-71, DOI:

10.1207/S15327000EM0201_05.

Bak, How Nature Works, p9.

Miao, “The Achievements and Vexation,” p3.

Kenneth Frampton, The Evolution of 20th Century Architecture: A Synoptic Account, trans. Qinnan Zhang

(Beijing: China Architecture & Building Press, 2007), p49.

Yuhang Kong, Nonlinear Organic Architecture (Beijing: China Architecture & Building Press. 2012).

30 2 Research Background

2.3.1 First Stage: Juxtaposition

The complexity in The Complexity and Contradiction in Architecture is related to that of

complexity science. In Charles Jencks’s book, he referred to Venturi’s representation of

the first stage of complexity in architecture:

his main drift, is aesthetic: for him, complexity represents a psychological and social

advance over simplicity, an evolution of culture and urbanism to cope with

contradictory problems such as the conflict between the inside and outside pressures

on a building.

Venturi’s notion of complexity is imbued with rebellious feelings and has something of the

connotation that complexity has in everyday language.

In the 1970s, with the development of nonlinear science and chaos theory, architecture

also showed a clear interest in these two concepts. For example, Jencks claims that

nonlinear dynamics is, “a generic name for the complexity sciences.”

Jencks’s statement

in fact expresses the principal direction in expressing complexity that architecture has taken

for a significant length of time.

2.3.2 Second Stage: Superimposition

In the 1980s, a group of architects began to use the term which had been proposed by Santa

Fe: “emergence.” According to Jencks, emergence is the second type of expression in

Western architecture under the influence of complexity theory. Peter Eisenman’s

“Superposition” is a typical expression of this type (Fig. 2.6). As a concept, superposition

can be traced back to Colin Rowe’s ideas from the early 1970s, which resulted in the

publication of Collage City in 1978. In this book, Rowe theorized layering, ambiguity,

transparency, and juxtaposition.

Shortly after this, during the 1980s, various practices of superimposing new layers

onto the existing urban fabric became popular. The main figures include Eisenman,

Bernard Tschumi, Rem Koolhaas (Design for the Parc de la Villette) (Fig. 2.7), Daniel

Libeskind (Jewish Museum), and Lan Lennox McHarg (Design with Nature).

Jencks, The Architecture of The Jumping Universe, p26.

Jencks, The Architecture of The Jumping Universe, p13.

Colin Rowe conducted his analysis of transparency from the perspective of Cubist painting, which was

heavily influenced by Japanese Ukiyo-e.

2.3 Three Stages of Architecture Influenced by Complexity Science 31

[Fig. 2.6] La Villette by Peter Eisenman.

Over time, “superposition” in architecture became a fashionable design method

guided by complexity theory (and, some would say, by Gilles Deleuze and Michel

Foucault). The common feature of “superposition” is to put several “organizational”

layouts on top of one another, and, according to Jencks, with reference to Koolhaas’s

Design for the Parc de la Villette, to “put them in no apparent order in his soufflé and then

[hope] they might rise.”

This approach clearly embodies the architect’s expectation for “emergence,” “self-

organization,” and “complexity.” Overlapping, as an architectural style guided by

complexity theory, has become a method of achieving the “emergence of the emergence.”

Followers of overlapping believe that it offers an alternative to the functionality of

modernism, as time and complexity are incorporated into the method. It is therefore

considered a “democratic method,” standing in opposition to “colonialism” and

“fundamentalism.”

Jencks, The Architecture of The Jumping Universe, p79.

32 2 Research Background

[Fig. 2.7] Design for the Parc de la Villette. Jencks praised this work highly, considering it a classic example

of overlapping. Eisenman also held it in high regard, because although the project was not constructed, it had

a profound impact on the theory of overlapping at the time, as Jencks states: “The reason why Eisenman and

others placed this proposal on a pedestal was that: Its complex order would seem to emerge from within the

nonlinear dynamics of the ingredients themselves, not imposed from without […] Thus, overlapping has

become a democratic method, a bottom-up design where the architect provides the systems, but they do the

significant self-organization.”

2.3.3 Third Stage: Nonlinear Volume

In the latter half of the 1990s, nonlinear volume seemed to increase in popularity with

architects due to the rapid development of computers. A large number of buildings with

streamlined forms mushroomed. This operation included integrating some sequential

parameters (conditions) into a program that resembled a “black box.” By adjusting the

input parameters to control the output of the program and obtain results that meet one’s

expectations, the process is similar to that of a complex system, where results emerge from

the action of the nonlinear mechanism (black box program). As a result, architecture was

considered to have acquired emergent characteristics. Moreover, because the operation of

this black box program is nonlinear, it is related to nonlinearity in nonlinear science, and

is called a nonlinear volume.

From the onset of the second phase, a central theme started to define discussions on

complexity: emergence. This renowned concept rose to prominence as the shining star of

complexity science in the 1980s. It serves as the definitive marker of complexity’s

appearance and has exerted a profound influence on a myriad of architectural endeavors.

As Peter Eisenman puts it: “too bad, you are interested in control, I am interested in

emergence.” Similarly, Jencks articulates that emergence is the fulcrum of the entire

narrative of his book. This paradigm continues to resonate deeply within contemporary

2.4 Japanese Architectural History in Comparison (1960-2000) 33

digital and parametric architectural practices. Henceforth, this dissertation will refer to this

phenomenon succinctly as “emergence architecture.”

None of the ideas and expressions mentioned above can be seen in Fujimoto’s

statements and works.

2.4 Japanese Architectural History in Comparison (1960-2000)

While the concept of “emergence” in “emergence architecture” has rarely been present in

Japanese history, neither in the past nor the present, the influence of complexity theory on

Japanese architecture has always been palpable. Fujimoto’s embrace of “complexity” is

not without foundation. This dissertation will broadly delineate Japan’s architectural

evolution since 1960 into four distinct periods for analysis: the optimistic period, the closed

period, the open period, and the free period.

[Fig. 2.8] Four stages of Japanese architecture along the timeline of complexity science.

One of the main reasons for choosing this time as the beginning of the discussion is

that 1960 was a critical year for human society as a whole. During the 60s, there was a

global wave of critical reflection on modernism. In the natural sciences, the 60s was also

an important period for the development of complexity thinking. Systems science,

represented by general systems theory, information theory, and cybernetics, was distilled

over decades, reaching its peak in the 50s and 60s. Together, postmodernism in the field

of philosophy and systems science in the natural sciences caused a cognitive shift from

simple to complex thinking, leading to “the third wave of architectural thinking,” and a

focus on grasping the meaning of life.

The postmodernist movement emerged in the discipline of architecture during this era

and is often understood to be an influence from the field of philosophy. Life and Death of

Great American Cities and Complexity and Contradiction in Architecture were also

published at this time. These two milestone works in the field of architecture provided a

theoretical foundation for the popularity of postmodern architecture. Modernism gradually

declined, and society became increasingly skeptical of its principles.

Yuhang Kong, “The Third Wave of Architectural Thinking,” Chinese and Overseas Architecture. 2009.

34 2 Research Background

2.4.1 The Optimistic Period

Orthodox modernist architectural thought was the predominant facet of this period in Japan.

However, information theory and cybernetics, which represented a counter to modernism,

also had great influence on Japanese architecture. This is particularly evident in the works

of Kenzo Tange.

The 60s were an important period for the Japanese design industry. If one word could

be used to describe the Japanese architectural situation in the early 60s, it would be

“optimistic.” After the Gyokuon-hōsō (Imperial Rescript) in 1945, Japan experienced rapid

economic growth. This provided a foundation for a series of major events in the 60s: the

1960 World Design Conference in Tokyo, the 1964 Tokyo Olympics, and the 1970 Osaka

World Expo.

The important international projects that occurred during this decade were seen as

activities that facilitated Japan’s “return to the international community” after the Second

World War. Because of these events, a large number of designers and artists had the

opportunity to participate in countless national-level projects. This gave birth to the last

avant-garde movement—the Metabolism movement—and led to a series of visions for the

future, including mega-structures and the first bullet train. The festival square of the Osaka

World Expo 70 was considered to be the culmination of this utopian moment.

There was, however, a certain sense of “consistency” in the 60s. This was provided

by Kenzo Tange.

During this period, Japanese architectural ideology was largely based on classical

modernism. The period of Westernization that began during the Meiji era (1868-1912) led

Japan to immerse itself in an imitation of Europe in areas such as economic systems,

education systems, daily life, architecture, policies, and legal systems. The technological

development after World War II made Japan one of the wealthiest countries in the world,

but, as Atsushi Katagi points out, “culturally, modernization means complete

westernization.” This statement describes the situation of Japanese architecture at that time.

In the early Showa period, modern European architectural forms had already been

introduced to Japan by architects such as Sutemi Horiguchi (1895-1984). The Japanese

architects of this era, including Tange, Togo Murano (1891-1984), Seiichi Shirai (1905-

1983), Kishida Hideto (1899-1966), Maekawa Kunio (1905-1986), and Junzo Sakakura

(1901-1969), had either traveled to Europe or studied under modernist masters, and

certainly viewed modernism as the standard. In this post-war recovery period, these

architects focused on how to build an ideal city and create new life on the scorched earth

after the war. As Saikaku Toyokawa

writes: “The so-called ‘new life’ here is actually the

Toyokawa is Associate Professor in the Department of Urban Environment Systems, Faculty of

Engineering, Chiba University.

2.4 Japanese Architectural History in Comparison (1960-2000) 35

urban life proven by the economic power of the United States, and the ‘ideal society’ is the

society that was conceived by Le Corbusier.”

Kenzo Tange was regarded as an orthodox modernist. Born in 1913, he graduated

from the university of Tokyo in 1938. Tange worked at the Maekawa Kunio architectural

office before officially establishing his own research laboratory at the University of

Tokyo’s Department of Architecture in April 1946.

In 1951, Tange unveiled his Hiroshima Peace Memorial Park project at the 8th CIAM

Congress in Hoddesdon, United Kingdom. This endeavor not only paved the way for

Japan’s resurgence onto the world stage in the 1960s but also garnered him international

acclaim. It served as a cornerstone in solidifying his esteemed position within Japanese

architecture. The project had a clear central axis, and the buildings were symmetrically

arranged on either side of the axis at the southern end of the construction site. The design

was modern in style, and featured a colonnade structure and a large amount of space

underneath. The axis passed through the nuclear explosion site square and pointed directly

to the nuclear explosion site on the north side of the site, which symbolized the “other side.”

With the completion of the Old Tokyo Metropolitan Government Building in 1957

and the Kagawa Prefectural Office Building in 1958, Tange gradually surpassed his peers

and became the most influential architect in Japan. His work was mainly based in university

research laboratories, and Tange and his students and were collectively known as the

“Tango School.” Subsequently, the Tango school participated in a series of projects：the

A Plan for Tokyo 1960, the Yoyogi National Gymnasium for the 1964 Tokyo Olympics, the

Yamanashi Press Center in 1967, and Expo’70. It can be said that most of the large-scale

reconstruction projects after the war were completed by Tange’s team. And all of these

projects focused on how to apply the principles of urban reconstruction and planning of

modernism such as CIAM.

Against a background dominated by modernism and accompanied by a shift in

thinking that was taking place on a global scale, the Metabolism movement emerged as

another major force during this period.

Four years after the dissolution of CIAM, the Metabolist movement was launched as

a prelude to the 1960s in Japan. Metabolism made its debut at the World Design Conference

held in Tokyo in 1960 and “Metabolism 1960” was published as Japan’s first manifesto to

express the principles of the age. As the last architectural movement, the Metabolist

architects were ambitious and, drawing inspiration from the development of technology,

proposed a series of visions for the future of the city, all of which had a very pronounced

utopian element.

Saikabu Toyokawa, Tange Kenzo: Sengo Nihon No Kososha (Tange Kenzo: Conceptualizer of Postwar

Japan), trans. Liu Ning Beijing: New Star Press. 2021. p16.

Riichi Miyake, “Pursuit for internal Microcosmos,” The Japan Architect, 1987, No.357：6.

36 2 Research Background

Metabolism covered many topics: constantly changing process, impermanent

beauty, immaterial beauty, movability, autonomy, renewability, and a host of biological

concepts such as cell walls, organelles, nuclei, and leisure cells.

The Metabolists gradually realized some of those ideas, in works including: Kiyonori

Kikutake’s Bridgestone Tonogaya Apartments (1958), based on the concept of “move-

net”

, Sky House (1958), based on the concept of “artificial ground and changeability”,

and Kodomo-no-kuni (1967); Kenzo Tange’s Yamanashi Press and Broadcasting Center

(1964) and the Shizuoka Press and Broadcasting Center (1967); Fumihiko Maki’s Hillside

Terrace (1969-1992); Kisho Kurokawa’s series of capsules, represented by the Nakagin

Capsule Tower (1972), the Takara Beautilion, and the Osaka World Expo (1970), which

is considered the climactic work of the Metabolist movement.

These works are representative of the Metabolist ideas that were realized. However,

the majority of Metabolist ideas remained merely on paper, where they took the form of

designs for mega-structures:

Around 1960 was also the beginning of the urban era: architects began to cross the

boundaries of individual buildings and enthusiastically discussed urban design –

particularly noteworthy is that the utopian vision for this city was built on the target

of exaggerated, delusional giant structures.

During this period in Japan, architects presented a series of fantasies about the city of the

future. Most of the proposed designs were for mega-structures: Kiyonori Kikutake’s

Tower-Shaped Community and Marine City, both in 1958; Fumihiko Maki and Masato

Otaka’s Shinjuku project (1960), based on the Group Form Theory; Kenzo Tange’s Plan

for Tokyo 1960 (Fig. 2.9); Isozaki’s City in the Air (1960) and Clusters in the Air (after he

left Tango Lab in 1962); and Helix City (1961), which was privately designed at the Tange

Lab by Kurokawa. These are all large-scale plans and designs.

This can be understood as a concept of the capsule that is on a par with that of Kisho Kurokawa. Kikutake

believed that the difference was that “move-net” was more related to Japanese tradition, while the “capsule”

was more related to the automobile industry. Rem Koolhaas, Hans Ulrich Obrist. Project Japan: Metabolist

talks. New York: Taschen, 2011.

Igarashi Taro, Iso Tatsuo,

ぼくらが梦见た未来都市

, trans. Zhuo Yuxiu (Taipei: Garden City, 2014), p33.

2.4 Japanese Architectural History in Comparison (1960-2000) 37

[Fig. 2.9] Plan for Tokyo 1960 by Kenzo Tange.

The creation of giant structures in Japan at this time was part a global phenomenon,

and included projects such as Richard Buckminster Fuller’s Manhattan Dome (1961),

Paolo Soleri’s Mesa City, Paul Maymont’s underground city along the River Seine in 1962,

and Archigram’s Plug-in City and Walking City in 1964. The optimistic trend in

megastructures continued until Expo’70, which marked the end of this era.

The content discussed above appears to be unrelated to complexity science, but by the

early 1960s, the response of urban planning and architecture to the arrival of the

information society had already been a research topic in Kenzō Tange’s lab. Wiener’s

“cybernetics” was favored by Tange for its comprehensive study of the general laws of

control and communication in machine and life societies. The design specification of Plan

for Tokyo 1960, led by Tange, refers to Wiener, the founder of cybernetics, and points out

that:

whether the organizational structure of Tokyo, with a population of tens of millions,

can be transformed into an organic life form essentially depends on communication.

A city with a population of 10 million can become an open organization connected by

communication means.

38 2 Research Background

Wiener’s view that “communication is the concrete of society” is directly quoted in the

subsequent project, The Greater East Asia Co-Prosperity Sphere.

[Fig. 2.10] Yamanashi Press Center (1966) by Kenzo Tange.

Yamanashi Press Center 1966 (Fig. 2.10) was designed with the aim of “creating

architecture that fits with the information society.” At the time, the focus of Tange’s design

was on information technology, information flow, and the mobility and flow of people and

objects. According to the records, Tange explained the relationship between building size

and communication as follows:

In a specific spatial field, solving the problem of how to communicate and how

information flows are equivalent to creating the structure of architectural space and

urban space. Previously, people tended to abstractly define space as a place to live or

work, but space cannot be defined only in this static mode. The decisive elements that

define space are the mobility of people and objects, the flow, and human vision.

This shows the influence of information theory on Tange at that time.

In another large project, Expo’70, Osaka, also led by Tange, Arata Isozaki was

commissioned to plan the “Festival Plaza.” In May 1967, Isozaki drafted a report entitled

Research on the Comprehensive Display of Water, Sound, Light, and Other Media in the

External Space Centered on the Festival Plaza. The report points out that Crystal Palace

of the London Expo and the Eiffel Tower in Paris are memorials based on a kind of

Saikabu Toyokawa, Tange Kenzo: Sengo Nihon No Kososha (Tange Kenzo: Conceptualizer of Postwar

Japan), trans. Liu Ning (Beijing: New Star Press. 2021), p69.

Toyokawa, Tange Kenzo: Sengo Nihon No Kososha, p74.

2.4 Japanese Architectural History in Comparison (1960-2000) 39

foresight about a future society. The Festival Plaza was also to offer a form of symbolic

prescience relevant to its contemporary society—the information age. That involved a

vision of how people and robots would be integrated in time and space. Isozaki defined

such an environment as a “cybernetic environment” and used it as the framework to

conceive of the core of the future information city.

Information theory was an important part of the systems science era and is often

considered to be an important theoretical component of systems science in the first stage

of complexity science.

Morin refers to cybernetics as a “ladder leading to complexity

research.”

Although Norbert Wiener does not directly apply the term “complexity” in his

writings, his research on information theory and cybernetics had a significant impact on

the development of complexity science. Wiener’s focus was on the “unified depiction of

machines, animals, and society,” which provided an ideal theoretical basis for the vision of

a “high-tech future city” in Japan.

One can see, therefore, that there was a direct influence from “complexity science” in

Japan at that time. The issues of “energy connections” and “information connections,” as

well as the theme of the information society, gradually became the focus of architects’

discussions. This was not only reflected in large-scale architectural projects such as Plan

for Tokyo 1960, The Greater East Asia Co-Prosperity Sphere and Expo’70, but also in the

planning of actual nuclear power plants. According to records, on August 8, Showa 45, the

first test power generation of Mihama Nuclear Power Plant, was exported to the Osaka

World Expo. From this point of view, it can be said that these large-scale projects were all

directly influenced by “complexity thinking.”

Moreover, the notion of the “information society” featured prominently in Toyo Ito’s

discourse until the 1990s. However, much like Kenzo Tange, this term evidently held the

promise of offering a solution that was “in tune with the times,” according to Ito’s

perspective. The success of modernism lies in its ability to adapt to the spirit of the age. As

the era unfolds, architecture’s apt response to it gave birth to the most rational architectural

Toyokawa, Tange Kenzo: Sengo Nihon No Kososha, p108.

As mentioned earlier, in 2.2.2, the work of L.V Bertalanffy in 1928 marked the birth of complexity science,

where the focus was on studying the “whole” instead of the “parts.” This represented a shift from

reductionism to holism in scientific thinking, and was the first scientific theory to oppose reductionism. This

shift was prompted by the study of the relationships between the parts of a system, which provided key

insights into understanding the organization of the whole that could not be obtained through studying the

parts in isolation. Following this, Bertalanffy published a series of papers and began teaching in the United

States in the 1930s, participating in a series of workshops that had a huge impact. Around the same time,

Shannon proposed information theory, Wiener proposed cybernetics, von Neumann created the cellular

automata to simulate self-replication of cells, and operations research and systems engineering emerged.

Together with Bertalanffy's general systems theory, they formed modern systems science, widely regarded

as the first phase of complexity science. They emerged in the 1940s and formed a force called “systems

science.”

Edgar Morin,

迷失的范式

人性研究

, trans. Yizhuang Chen. Peking University Press. Beijing: 1999, 10.

p6. Originally published in 1973 as Le Paradigme perdu. La nature humaine.

40 2 Research Background

solutions. For both Tange and Ito, this aspect appears to be of paramount importance within

the context of the information society, transcending its inherent complexity of thought.

2.4.2 The Closed Period

Between approximately 1968 and the early 1980s, Japanese architecture traversed a period

marked by enclosure. This era aligns with the second stage of complexity science.

Eizo Iganaki designated 1968 as the dividing line between modern and contemporary

Japan. Various ideological shifts constantly challenged the thinking of architects.

According to Atsushi Katagi’s recollection, the styles they could choose from in school

were very diverse, ranging from modernist boxes to the paper houses of Pennsylvania and

New York. This compromising attitude even persisted into his early career. Architects were

influenced by Rossi’s typology, as well as the deconstructionism of the AA school and the

postmodern classicism of Johnson and Graves. Ideological shifts in architecture frequently

occurred, and while everyone appears to have their own opinions, “Rootlessness in time

and space is rooted in the very heart of our generation.”

Although architects appeared somewhat confused about “what to do,” they shared a

common point when asked about “what not to do”: the rigid application of modernism.

Around the 1970s, Arata Isozaki began to openly oppose his mentor. He left Tange’s

studio to strike out on his own, completely abandoning Tange’s module system in his

designs

and proposing “architectural deconstruction” in an effort to surpass Tange, which

some historians have dubbed “patricide.” In his 1970 work Decomposition of Architecture,

Isozaki, like Archigram and Superstudio, focused on criticizing and negating the dogmas

of modernism.

The Gunma Museum of Modern Art, completed in 1974, abandoned

Tange’s modularity and used only cubes to compose its architectural form. The Tsukuba

Center Building, completed in 1983, continued to use the cube composition technique

while combining various elements of postmodern history in the building. Through this

project, Arata Isozaki questioned whether there should be a national architectural style.

The building caused a great sensation and was acclaimed as an example of “postmodern

architecture that breaks through the boundaries of modern architecture.”

In the 1970s, architects gradually began to oppose their mentors, who held modernism

at the core of their architectural philosophy. While Arata Isozaki’s patricide was well-

Atsushi Katagi, “Against the Consumption of Architecture,” The Japan Architect. 1988, Nov-Dec,

No.379/380, p76.

A set of standard architectural parameters were developed by Tange using the Modulor system created by

Le Corbusier, incorporating ergonomic elements to fit the dimensions of the Japanese people. Tange required

his apprentices to respond to his module within his studio.

Miyake, “Pursuit for internal Microcosmos,” p7.

Toyokawa, Tange Kenzo: Sengo Nihon No Kososha, p220.

2.4 Japanese Architectural History in Comparison (1960-2000) 41

known as the pinnacle of the anti-modernist movement in Japan, it was not the first example

of such a thing.

In 1968, a series of student movements broke out worldwide. The “May 68” protests

took place in Paris, France, and the “Prague Spring” in Czechoslovakia. Influenced by

these events, Japan also experienced student protests in the same year. In the field of

architecture, the anti-Expo’70 movement was initiated by Hiroshi Hara, and was part of

the broader anti-modernist movement in Japan.

1966 Hiroshi Hara’s book, What is Possible in Architecture, was written for the

purpose of reflecting on modernism. The student movement in Japan, “Anti-Expo’70,”

took place from 1968 to 1970, and called for the dismantling of the imperialist university

system, viewing international events like Expo’70 (Fig. 2.11) as “nothing more than a

superficial display meant to conceal underlying social conflicts.”

Although the anti-Expo’70 movement was gradually forgotten due to the successful

hosting of the event, Riichi Miyake believed that it planted seeds in the minds of Japanese

architects that led them to question modernism. It provided a theoretical foundation for the

initiation and challenge to the authentic value of modern architecture in the future.

Another major force worth mentioning is the architectural magazine Toshi-jutaku

(Urban Housing) (Fig. 2.12). This magazine offered reflections on modernism and

successfully gathered together a group of people who wanted to make a clean break with

modernism. Drawing on Toshi-jutaku, a group of architects approached the real situation

faced by Japanese cities, pointed out that specific issues cannot be solved by a universal

modernist formula, and made architects more aware of the difference between ideal and

reality. The magazine made some architects realize that the modernist order could not cope

with the chaotic nature of Japanese cities at that time.

At the time, Kenzo Tange was the chief architect of Expo’70, along with Arata Isozaki and many other

talented architects who were planning for the event. After the event, Isozaki criticized himself for taking part

in it, but this incident set him apart from the Metabolists who persisted in their previous ways. Miyake, Riichi.

“Deconstructivists in architecture.” The Japan Architect. No.362 (June1987): p6-9.

Riichi Miyake, “Deconstructivists in architecture,” The Japan Architect. 1987, p6.

Miyake, “Deconstructivists in architecture.” p6.

This magazine is considered by some researchers to be merely one part of Japanese architectural thought

at that time, because it did not include Kazuo Shinohara's theory. The magazine ceased publication in 1986,

after 18 years of circulation.

42 2 Research Background

[Fig. 2.11] Expo’70 as a testing ground for the “City of the Future.”

Toshi-jutaku’s approach toward facing the realities of the city influenced a large

number of people. Architectural historian Riichi Miyake stated that the “70s was the period

where the architects of Toshi-Jutaku were to differentiate themselves from the initial point

of concentration.”

[Fig. 2.12] TOSHI-JUTAKU (Urban Housing).

Miyake, “Deconstructivists in architecture.” p6-9.

2.4 Japanese Architectural History in Comparison (1960-2000) 43

It is worth pondering the implications of this series of anti-modernist gestures.

Miyake’s remarks suggest that, around this juncture, researchers began to gradually depart

from their initial starting point and develop their own methodologies. If the core of

modernism is classical science, characterized by homogeneity, i.e., the focal point of

reflection in complexity science, then although this series of events may not necessarily

have had a direct association with complexity science, they nonetheless fostered an

environment conducive to the acceptance of this overarching philosophy.

As the 1970s unfolded, following the conclusion of Expo’70 in Osaka and the onset

of the oil crisis, the economy entered a downturn. Architects gradually awakened from the

“bliss” of the 1960s and began to soberly contemplate reality. This marked the period when

utopian ideals began to crumble. One striking characteristic was the retreat into closed

boxes, which persisted in the construction of utopias. A surge of enclosed architecture

emerged, fashioning insulated internal realms, detached from the outside world. Japanese

architecture had always been proud of its “openness,” and this had been reflected in both

traditional and contemporary architecture. However, during this period, a feature

contradictory to “openness” emerged in Japanese architecture.

Representative works of this period include Toyo Ito’s White U (1976) (Fig. 2.18);

Tadao Ando’s New Version of the Old Row House (1976); a series of works by Kazunari

Sakamoto, based on his concept “Closed Box”: House in Sanda (1969) (Fig. 2.14),

Machiya in Minase (1970), Kumono-Nagareyama House (1973), Seiichi Shirai’s Shinwa

Bank Computer Tower (1974) (Fig. 2.16); Hiroshi Hara’s Hara’s House (1974) (Fig. 2.13);

and Osamu Ishiyama’s Gen An (1975) (Fig. 2.15). The goals of this architecture were

surprisingly consistent with the concept discussed above: the aim was to construct an

internal space that is isolated from the outside world.

[Fig. 2.13] Left: Hara’s House by Hiroshi Hara. A hallmark of the architect’s work from this period, “fissure,”

appears to suggest the “fissure” of inside and outside.

[Fig. 2.14] Middle: House in Sanda by Kazunari Sakamoto. As per the architect’s own words, the design

inherently conveys a stance of enclosure, large windows notwithstanding.

[Fig. 2.15] Right: Gen An by Osamu Ishiyama. The building is submerged underground. Despite its metallic

exterior, Teronobu Fujimori describes it as still being defined by its enclosed nature.

44 2 Research Background

building with almost no exterior windows, forming an inner courtyard. The building is

characteristic of a style in which an inner world is shaped without concern for the external

urban conditions.

New Version of the Old Row House (Fig. 2.17) is Ando Tadao’s debut work and was

the reason for his instant success. The old row house is located on a narrow and densely

populated plot in the center of Osaka, and Tadao responded to dissatisfaction with the city

by creating an inward-looking “traditional” residence with a closed concrete box. Historian

Riichi Miyake writes: “(Tadao) used concrete to create a clear ‘interior’, which is not only

a physical indoor space, but more importantly, it materializes the values of the residents

towards the city and the external world at that time.”

[Fig. 2.16] Left: Seiichi Shirai’s Shinwa Bank Computer Tower.

[Fig. 2.17] Middle: The Row House in Sumiyoshi by Tadao Ando.

[Fig. 2.18] Right: White U by Toyo Ito.

The sudden fame of Tadao Ando reflects the opposition of society and academia to

the academy style (which in this case reflects the ideas of European modernism) and its

urban practices in Japan. On the other hand, Ando’s sensitivity to nature and Japanese

tradition has created a retreat “inside” the architecture industry. This is because the “outside”

during this period was full of problems, such as randomness, high density, and chaos. The

retreat approach of Ando, who had never received an orthodox architectural education, was

consistent with the thinking of some avant-garde architects at that time.

During the same era, another architect, Hiroshi Hara, similarly embraced these

tendencies. In his creation, Hara’s House, the expansive exterior walls contrasted starkly

with the “fictional community inside.”

What is intriguing is that this building was not

even situated amidst the “chaotic” urban backdrop.

Fujimoto’s “box-in-a-box” might be traced back to Kazunari Sakamoto’s “box-in-a-

box,” which will be discussed further in 3.3.1. “Box-in-a-box” and “closed box” were the

central ideas proposed by Sakamoto during his early career in the 1970s. Sakamoto was

Toyo Ito Interview. Architectural review. 2013(4): 18.

Miyake, “Pursuit for internal Microcosmos,” p7.

Miyake, “Deconstructivists in architecture,” p6.

2.4 Japanese Architectural History in Comparison (1960-2000) 45

also clearly orientated toward internal space in this period, as all of his projects at this time

were to construct “a self-enclosed world (cosmos).”

Speaking of this period, Igarashi Taro once commented:

In the 1960s, while architects such as Kenzo Tange, Kisho Kurokawa, and Kiyonori

Kikutake proposed futuristic urban plans, actual cities were also undergoing large-

scale development. However, in the 1970s, after bidding farewell to the Expo’70 and

facing the oil crisis, architects began to withdraw from the city and design self-

enclosed residences.

But after one short decade, an interesting phenomenon occurred: almost the exact

same group of architects who were building “closed box” works started to exhibit the

complete opposite approach: they began to open up.

2.4.3 The Open Period

This dissertation dates this period to the mid-1980s for three reasons. First, in 1984, Toyo

Ito designed his Silver Hut, which can be said to have opened the era of “consumption

architecture” that followed. Second, Santa Fe was established in 1984. Third, in terms of

the social context, Japan experienced its famous economic bubble in this period. In 1985,

the Plaza Accord was signed, in which the five major world powers jointly intervened in

the foreign exchange market to resolve the U.S. trade deficit. The end result was a

significant increase in the value of the Japanese yen, which triggered Japan’s economic

bubble.

The “openness” of the wild samurais

From around 1984 onwards, a virtually identical group of architects, who had previously

favored “closed” works, began to embrace “open” architecture. Leading figures in this

movement include Toyo Ito, Kazunari Sakamoto, Itsuko Hasegawa, Tadao Ando, and

Riken Yamamoto. Concepts such as lightness, thinness, temporariness, the nomadic, and

consumer society surged in popularity. Moreover, their architectural expressions, rooted in

these shared concepts, bore striking similarities.

In 1984, a breezy house, Toyo Ito’s Silver Hut (Fig. 2.19) was completed.

Interestingly, this residence was located right next to his White U, which featured

“enclosure” in 1976. Afterwards, Ito used the concept of the “nomadic” to build The Pao

as a Dwelling For the Tokyo Nomad Woman in 1985, the same concept applied to the

Restaurant Nomad and the Tower of Winds in 1986, and Yatsushiro Municipal Museum in

1991. At the same time, many similar structures were built, such as Sakamoto’s Project

KO (1984) (Fig. 2.20); Project SH (1986) (Fig. 2.22); House F (1988) (Fig. 2.23); Isuko

Kazunari Sakamoto, House: Poetics in the ordinary. Tokyo: TOTO Shuppan. 2001, p18.

Kazunari Sakamoto, Guo Yimin (ed). The Poetics in Architecture. Dialogue with Kazunari Sakamoto.

(Nan Jin: Southeast university Press. 2011), p314.

46 2 Research Background

Hasegawa’s House in Nerima (1986) (Fig. 2.24); Shonandai Culture Center in Fujisawa;

Riken Yamamoto’s Rotunda Building (1987) in Hamlet; Kazuyo Sejima’s Platform

Houses I and II. (Fig. 2.25 and Fig. 2.26)

[Fig. 2.19] Left: Silver Hut by Toyo Ito.

[Fig. 2.20] Right: Project KO by Kazunari Sakamoto.

[Fig. 2.21] Left: MAC Commercial Complex Project by Toyo Ito.

[Fig. 2.22] Right: Project SH (1986) by Kazunari Sakamoto.

[Fig. 2.23] Left: House F by Kazunari Sakamoto.

[Fig. 2.24] Right: House in Nerima by Isuko Hasegawa.

2.4 Japanese Architectural History in Comparison (1960-2000) 47

[Fig. 2.25] Left: Platform I by Kazuyo Sejima.

[Fig. 2.26] Right: Platform II by Kazuyo Sejima.

The common features of these buildings include the abundant use of industrial materials

such as steel columns and aluminum sheets, which create a strong industrial feel both

indoors and outdoors. These materials have not been tampered with, nor have architects

used them to create a heavy look. The nature of the materials has been respected, resulting

in buildings that seem as lightweight as the materials themselves. The inherent

relationships between the architectural elements have been expanded and extended. For

example, the connection between columns and beams has been clearly extended, to the

point where the traditional relationship between beams and columns is not visible. Thin

lines have been intertwined to form the structural system of the buildings. Some

components of architecture have been deliberately separated, which results in numerous

“gaps” between the roof and enclosure, structure and roof, and structure and enclosure. The

roof and enclosure have as many openings as possible.

In appearance, these buildings usually lack a sense of unity. Overall, when compared

to the “closed box” structures of the 1970s, this series of buildings seems to have suddenly

gone to the other extreme. Riichi Miyake offers the following comments on this period:

Contemporary architecture in Japan in the latter half of the 1980s has changed

drastically from what it was ten years ago. In terms of architectural forms as well as

in the ideas that architects are trying to realize, we can clearly sense a new trend.

There are many angles from which to interpret the phenomena of this period: concepts

such as lightness, thinness, temporality, the nomadic, as represented by Toyo Ito, Kazunari

Sakamoto, and Itsuko Hasegawa; the “anti-object” tendency, as represented by Kazunari

Sakamoto;

an architectural disintegration caused by a postmodern symbolic design

Riichi Miyake, “The Generation of Sensitiveness.” The Japan Architect. (nov-dec 1986), NO.355/356. p8.

Kazunari Sakamoto, “From Architecture as an Object to Space as an Environment.” The Japan Architect.

8611/12. 1986, p64. According to Sakamoto, “object” denotes a building that has a dominant form, while

48 2 Research Background

tendency, or deconstructivism characterized by dislocation in postmodernism;

100

a social

response, such as a response to a consumer society, fin de siècle consciousness, a chaotic

society, or an information society; a human instinct. As Riichi concludes: “they (architects

in the 80s) are profoundly related to the very nature of human sensibility and existence.

This is a necessary perspective when looking at their works more closely.”

101

The list above offers a summary of the direction of discussions about architecture

during this period. All seem to point toward “postmodernity.” As Sakamoto puts it: “Each

of these types of contemporary space can be thought of as an exploration or experiment

towards an open or free form of space that somehow rejects completeness or wholeness.”

102

This “new trend,” is indeed open to interpretation. Most historians view it from the

perspective of “from enclosure to openness,” while this dissertation sees it as a complete

about turn in Japanese architects’ attitude toward “chaos.”

Transforming perceptions of “chaos”

Why was there a turn toward enclosure in architecture? Why “withdraw from the street

front so as to create a new sphere of inside”? This disarray, in part, originated from the

environmental crises and urban plights that accompanied the city’s hasty evolution amidst

an uncritical embrace of Westernization. Sakamoto reflects: “At that juncture, Japan was

besieged by acute environmental crises, air pollution being a prime example among others.

The vision of an insulated enclosure was conceived against this societal canvas.”

103

Such

a stance of repudiation was indeed imperative.

However, in the 1980s, “chaos” was not only accepted but also celebrated. Architects

of this period put forward the view that “chaos” reflects the nature of the Japanese city, and

began to advocate for it. This is reflected in the fact that Japanese architects during this

period began to use the term “chaos” explicitly. Complexity theory (specifically, keywords

related to nonlinear science and chaos theory) began to appear frequently in articles by

architects. One can clearly sense the significant influence of chaos theory on Japanese

architects during this period. Kisho Kurokawa made a significant number of references to

concepts such as “fractals” (in Mandelbrot’s work) and “dissipative structure” (in

Prigogine’s work) to support his theory of “symbiosis.” Yoshinobu Ashihara used “chaos”

and “fractal” to describe his understanding of the city of Tokyo; Kazuo Shinohara used

“environment” refers to a building with which we or something can be related on different levels in various

ways. Kengo Kuma published a book called Anti-object.

100

For instance, one can easily link Deleuze and Guattari’s concept of “nomadology” with Toyo Ito's

“Nomad,” which according to Ito, is an “Architecture of Consumption.”

101

Miyake, “The Generation of Sensitiveness,” p8-11.

102

Kazunari Sakamoto, “From ‘closed’, to ‘open’, to ‘free’,” in House: Poetics in the ordinary, (Tokyo:

TOTO Shuppan. 2001), p241.

103

Kazunari Sakamoto, “自由、解放、中性的建筑空间 (Free, Liberated and Neutral Space),” in The

Poetics in Architecture. Dialogue with Kazunari Sakamoto. ed. Guo Yimi (Nan Jin: Southeast university

Press. 2011), p297.

2.4 Japanese Architectural History in Comparison (1960-2000) 49

“random noise” and “chaos” to criticize the homogeneous character of modernism and to

express his longing for physical confusion. Moreover, they all showed a great interest in

the order that lies behind chaos.

This philosophy found resonance not merely within architectural discourse but also

across a broad spectrum of the period’s literature and cinema, profoundly influencing

“futuristic imaginings” and establishing foundational narratives. Thanks to the

“technological” scenery of Tokyo, not only the field of architecture but also the film and

television industry began to develop a style known as cyberpunk. The earliest example can

be traced back to Solaris, the 1972 sci-fi film directed by Andrei Arsenyevich Tarkovsky.

The opening scene, featuring a highway in a futuristic city, was filmed in Tokyo, though

the original plan had been to shoot it at Osaka Expo’70—a truly utopian city with a

“futuristic” ambiance.

A series of similar film and television works followed Solaris, including Blade Runner

(1982), Akira (1988), (Fig. 2.27) Ghost in the Shell (1995), and Violence Jack (1973). They

are all classics and can be said to have exerted a great influence, establishing the visual

image of most “futuristic cities” in later science fiction films, music, novels, and games.

These images of the metropolis used Tokyo as a prototype and are related to various

versions of the “Tokyo Plan” that began in the 1960s. Among them, the influence

[Fig. 2.27] The picture shows the 1988 Japanese animation film Akira. Its urban setting to some extent reflects

the exaggerated consumption in Japan at that time, as well as Japanese fantasies and attitudes towards the

future. Many of the settings in this animation became prototypes for subsequent cyberpunk movies, TV shows,

and video games.

50 2 Research Background

of Kenzo Tange and Metabolism can clearly be observed. At this time, the city had

developed an interesting and indeed unique appearance, especially the Kabukicho district

with its colorful store signs, huge holographic projections of Geishas, and Japanese

characters.

The problem of image consumption, the influence of the bubble economy, the residue

of utopianism, the futuristic sense of technology, the apocalyptic discourse: all of these

influences converged in Tokyo and even started to become symbols of the city. A large

number of bars, nightclubs, and restaurants emerged to meet market demand, piled up into

“bar buildings.” “Pachinko,” decorated with huge and exaggerated cartoons, spread across

the entire city. Capsule hotels, further developed after Kisho Kurokawa’s Silver Capsule

Tower, welcomed commuters who missed their last trains home with very low prices.

Variously themed hotels for lovers decorated their exteriors with images including

princesses and princes, Hello Kitty, and even instant noodles. These external images, which

needed to be constantly updated to attract customers’ attention, meant that the cartoon

decorations outside the storefronts were only temporary in nature. The commercial features

of the materials used in the buildings outweighed their architectural properties. A large

number of buildings became part of commercial consumption.

The big difference between Tokyo and cities in Western Europe can be seen in recent

films and TV series which depict the future of London. Western European cities have a

logical structure that does not allow for chaos. Most of them can only envision the future

in the form of “ruins”: the collapse of buildings, abandoned vehicles, and nature taking

over the city. For example, in the recent TV series The Peripheral, (Fig. 2.28) an oversized

white Greek sculpture is placed in the center of the city, among an image of ruins. This

[Fig. 2.28] TV series The Peripheral.

2.4 Japanese Architectural History in Comparison (1960-2000) 51

serves the same purpose as the depiction of European churches—the future city is imagined

in a “miraculous” way. It is difficult to disconnect this from the fact that the structure and

logic of the city are different.

As Taro Igarashi writes:

During the era dominated by modernism, Tokyo was considered a “chaotic and

completely useless place” and was despised. However, in the clamor of

postmodernism in the 1980s, it became ‘interesting because it was full of chaos’— its

chaos received completely opposite evaluations in different eras.

104

Reasons for the shift from closed to open

An examination of the timeline of this attitudinal shift reveals that the dramatic pivot aligns

with the second surge in the prominence of complexity theory. There were notable

breakthroughs in complexity science during this period. In 1975, an astonishing

coincidence occurred in the field of complexity science. Chaos was officially named. The

term fractal was named. The Feigenbaum Constant was discovered. These three studies,

occurring at the same time but from different perspectives, all discussed the same subject:

chaos.

At that time, few people were interested in chaos apart for mathematicians. It wasn’t

until Mitchell Feigenbaum pointed out the broader meaning of chaos and introduced the

concepts of self-referentiality and the Feigenbaum Constant that chaos began to enter into

the purview of scientists.

105

In addition, two important works on chaos were published in

the 1980s: Ilya Prigogine and Isabelle Stengers’ Order Out of Chaos: Man’s New Dialogue

with Nature in 1984, and James Gleick’s Chaos in 1988. These studies formed a large part

of the complexity science in this period: chaos theory.

The mid-1970s was a period of comprehensive development and transformation for

systems thinking. In the 1970s, Prigogine began advocating for the establishment of

complexity science. The 1970s is widely considered to be the second phase of complexity

science, and two important theories of self-organization emerged at this time: the

dissipative structure theory (represented by Prigogine) and the synergy theory (represented

by Haken). Indeed, many of the academic achievements of the Santa Fe Institute, a complex

systems research center established in the 1990s, had already been produced in the

1970s.

106

Hence, the time around 1975 marks a significant upswing in complexity science, with

chaos serving as a pivotal theme. This advancement in scientific cognition provided the

masses with a novel understanding of chaos, elucidating the profound transformation in

Japanese architects’ approach to chaos. Another coincidence that occurred in the same year

104

Taro, The Future City of Our Dreams, p121.

105

Gribbin, Deep Simplicity, p95.

106

Miao, “The Achievements and Vexation,” p3.

52 2 Research Background

was that the silver hut was completed at the same time as the Santa Fe Institute was

established.

Integration of complexity after 1984

During this period, some mainstream celebrity architects also began to use the term “chaos”

explicitly to discuss architecture.

In this period, Kisho Kurokawa had already incorporated the concept of nonlinear

science into his architectural philosophy. In An Architecture of Symbiosis: The Two-Faced

God Janus, Kurokawa states that: “That new world is characterized by a shift from the

theorematic to the problematic; from a closed order to one that permits chaos […]

Mandelbrot pursued the ‘soft’ structure that is to be found in the midst of chaos.”

107

Kurokawa was at that time influenced by non-linear theories such as dissipative

structures and fractal geometry, frequently discussed a “new” relation between part and

whole, and cited David Bohm, Benoit B. Mandelbrot, and Ilya Prigogine. Bohm invented

“implicate order” and “explicate order,” Mandlebrot was the founder of the fractal

geometer, and Prigogine was at the center of complexity science. What Kurokawa wanted

to point out is that the “whole” formed by such a “new” relationship is “the two-faced God

Janus.” The term two-faced actually refers to the “enfolded and unfolded order,” that is,

the order can be seen or unseen. Here, it is used by Kurokawa to allude to the dissolution

of a binary opposition, which can also be found in his concept of “symbiosis.”

The key concepts relating to complexity at that time could also be found in another

important Japanese architect, Kazuo Shinohara. In his article Chaos and Machine,

Shinohara uses the term “random noise” to describe the juxtaposition of discrete elements.

As the research above mentions, from some points of view, the relationship between chaos

and randomness is almost equivalent. The term “randomness” was first used by Shinohara

in The House in Yokohama (1984). In this project, pure geometric forms with no

relationship to each other were forcefully juxtaposed. At first glance, they appeared

completely discordant, and the collision between the forms led directly to the “strangeness”

of the spatial movement streamlines. The overall appearance of the building also looked

like a child’s block construction. However, Shinohara claimed that this treatment produced

a unified and consistent whole in which all elements were centrally controlled—the

opposite of the typical product of modernism. Modernism cannot tolerate a certain

“rationality,” which is precisely what Shinohara’s “random noise” concept points to. In the

Centennial Hall project (Fig. 2.30), different functions were assigned to different

geometric forms. These discrete, fragmentary forms were juxtaposed, interspersed, and

arranged in an improvisational fashion. The differences between adjacent forms were

magnified as much as possible, and even openings such as doors and windows were

107

Kisho Kurokawa, “An Architecture of Symbiosis: The Two-faced God Janus,” The Japan Architect. 8610.

P40-42.

2.4 Japanese Architectural History in Comparison (1960-2000) 53

constructed with unconventional geometric forms. Everything was done to maintain

distance from the overall order. This treatment, like Shinohara’s The House in Yokohama

project, is called “random noise.”

Another architect at that time, Yoshinobu Ashihara, demonstrated a more obvious

influence from complexity science. Ashihara published a book titled The Hidden Order:

Tokyo Through the Twentieth Century. Interestingly, during the same period, John H.

Holland, one of the founders of the Santa Fe Institute and a pioneer in complexity science,

also published a book with the same title, The Hidden Order: How Adaptation Builds

Complexity. At that time, Ashihara had direct contact with Santa Fe, and the interpretation

of his central idea in The Hidden Order was entirely derived from the latest research in

complexity science at that time: the relationship between the “parts”

[Fig. 2.29] Left: Discrete geometric shapes are abruptly juxtaposed together.

[Fig. 2.30] Right: Centennial Hall by Kazuo Shinohara.

and the “whole”; a generative approach from the bottom-up; Mandelbrot’s fractal theory,

etc. constitute the theoretical foundation of the entire book. The popular word “chaos” was

applied to Tokyo—“The Amoeba City”: an amorphous, acentric, temporary, fluid,

regenerating city with ill-defined boundaries. “Tokyo thrives according to an order hidden

within its chaos.”

108

This clearly indicates the direct influence of complexity science on

Japan.

Itsuko Hasegawa also began actively exploring the application of concepts such as

fractals, fuzzy logic, and chaos in architecture.

Soon after, Toyo Ito used “nonlinear” to describe architecture. In Nonlinear

Architecture: From Sendai to Europe, Ito uses the term “nonlinear” to describe a series of

projects he designed that were centered around the Sendai Mediatheque. In short, as Jencks

108

Yoshinobu Ashihara, The Hidden Order. Tokyo through the Twentieth Century. Translated by Lynne E.

Riggs. (University of California Press. 1989), p63.

54 2 Research Background

concludes, “Japan as a nation was actively engaged in exploring the new sciences in this

era.”

109

Scattered Values Under the View of Complexity Science

The debate surrounding the encapsulation of an era through the ideologies of “wild

samurais” or its categorization under the broad umbrella of postmodernism—viewing the

architectural innovations as examples of mere “physical” openness—might not capture the

full spectrum of architectural dynamism witnessed.

Indeed, aside from architecture that appeared to champion “physical openness,” a

significant number of intriguing architectural works emerged during this period. The stance

of the wild samurais does not encapsulate the essence of this tumultuous era, which is more

notably marked by the encroachment of postmodernism and is often regarded as a period

of loss. This era saw the rise of figures such as Hiromi Fujii, Japan’s answer to Peter

Eisenman (Fig. 2.33); buildings like the Tsukuba Center (Fig. 2.34) and M2 (Fig. 2.35),

which showcase Japanese historical eclectic postmodernism; and Shin Takamatsu’s

unvarnished symbolic expressions (Fig. 2.32). Ryoji Suzuki’s architectural deconstruction

(Fig. 2.31) and Frank Gehry’s form-mimicking Fish Dance Monument restaurant in Kobe

were also noteworthy. There were architects like Terunobu Fujimori, who advocated

starting anew (Fig. 2.36), and Kazuo Shinohara, who was optimistic about new technology.

The architectural discourse of this era indeed appears highly disordered. Broadly speaking,

these trends are often encapsulated by the term “postmodernism.”

[Fig. 2.31] Left: Azabu Edge by Ryoji Suzuki. [Fig. 2.32] Right: Syntax by Shin Takamatsu.

109

Jencks, The Architecture of the Jumping Universe, p136.

2.4 Japanese Architectural History in Comparison (1960-2000) 55

[Fig. 2.33] Left: Project Mizoe n°4 by Hiromi Fujii.

[Fig. 2.34] Right: Tsukuba Center Building by Arata Isozaki.

[Fig. 2.35] Left: M2 by Kengo Kuma.

[Fig. 2.36] Right: Tea House by Terunobu Fujimori.

Nevertheless, postmodernism and complexity are intricately linked. First, if we look

at the major shifts in human thought since the advent of modern science, we can distinguish

three phases: modernist thinking, systems thinking, and postmodernist thinking,

110

with

two significant transitions. The first transition to systems thinking, characterized by a

holistic approach, signifies the shift from mechanical to complex thinking. The second

transition moves toward postmodernist thinking, and is fundamentally rooted in

complexity. Scholars like Charles Jencks have categorized these shifts differently,

suggesting three distinct periods of understanding the world: religious, modern science,

and postmodern science, which correspond, respectively to the worldviews of the Genesis

story, machine science, and complexity science.

111

Despite the categorization, such

viewpoints all recognize a paradigm shift in natural science and philosophical thought from

110

Wulun Jin, “The Historical Evolution of the Traditional Thinking Mode from the Perspective of Complex

Systems Theory,” Journal of Hangzhou Normal University [Social Sciences Edition]. 2008, May, No.3. p24.

111

Jencks, The Architecture of the Jumping Universe, p7.

56 2 Research Background

the simplicity of modernism to the complexity of postmodernism, indicating a profound

connection between complexity in natural sciences and postmodernist currents. Paul

Cilliers’s work, Complexity and Postmodernism: Understanding Complex Systems, for

example, explores the concept of complexity from a post-structuralist perspective.

In architecture, Charles Jencks indicates the profound link between complexity theory

and postmodern architecture in his book Complexity Science: The Heart of Post-

Modernism.

The connection with complexity theory is evident in seminal postmodernist

architectural texts such as The Death and Life of Great American Cities (1961) and

Complexity and Contradiction in Architecture (1966). For instance, Venturi’s complexity,

though seemingly related to everyday and populist notions of complexity, is influenced by

theories of complexity science. Jencks states that “Venturi’s was the first stage of

complexity in architecture.” Similarly, Jane Jacobs describes cities as living organisms

with complex interlinkages and holistic behaviors, using complexity theory terminology

rather than postmodernist jargon. She described cities as problems of “organized

complexity,” a concept originating from Warren Weaver’s 1948 article “Science and

Complexity,”

112

which discussed “disorganized complexity” and “organized complexity.”

Thus, the connection between postmodern philosophical trends and complexity

science is undeniable. However, the debate over their common origins persists.

This dissertation aims to sidestep the debate over “postmodernism,” focusing instead

on examining Japanese architecture from the perspective of complexity. The terms

“complexity” and “postmodernism” are both ambiguous, encompassing a broad range of

concepts, and the ambiguity of complexity is the subject of the dissertation’s discussion.

The dissertation seeks to demonstrate that architectural thought in Japan during the 80s and

90s, while often branded as postmodern, was nonetheless deeply intertwined with complex

thinking.

First of all, from a broader historical perspective, complexity studies and postmodern

philosophy are situated in the same process of historical transformation, nourished and

constrained by the era’s same characteristics and conditions, and their theoretical

reflections have similar driving forces, issues, approaches, and resources, as well as

numerous common intellectual sources. Therefore, they must have an inherent connection

and share common or similar ideological genes.

113

From traditional to modern Western philosophy, most philosophical theories are

based on grand narratives that have a center and their own logical foundation and structure.

112

Warren Weaver and Claude Shannon, the father of information theory, jointly published “The

Mathematical Theory of Communication”, which laid the foundation for information theory.

113

Dongsheng Miao, “Complexity Science and Postmodernism,” Democracy & Science (3):29-32.; Huang,

Wu, “The Context Analysis to the Arising of Complexity Sciences,” p38-45.

2.4 Japanese Architectural History in Comparison (1960-2000) 57

However, postmodernism is the opposite, seeking decentralization, anti-logic, and a lack

of structure. In terms of values, postmodernism shares similarities with complexity science.

Although postmodern philosophy is exceptionally versatile, it can be divided into two basic

postmodern trends: destruction and construction The unique vocabulary of the former

includes disjunction, difference, chaos, happenstance, spontaneity, and indeterminacy;

while the latter includes multiplicity, plurality, complexity, ambiguity, connectivity,

relation, dependency, harmony, synthesis, and integration.

114

Therefore, it is not difficult to see that both the destructive and constructive

postmodernist movements share many key concepts with complexity theory. However,

there are also many differences between them. Miao Dongsheng remarks that:

complexity research mainly interprets the era’s issues from the perspective of science

and technology, challenges modernity, constructs theoretical frameworks, and designs

solutions; postmodernism attempts to interpret the same era’s issues from the

perspective of philosophy, science, culture, sociology, cultural studies, and even

religion, and comprehensively challenges modernity, exposes the drawbacks of

modernism, and designs alternative solutions in all directions.

115

In summary, postmodernism and complexity theory do not have a clear common origin.

However, the topics they discuss are very similar. Researchers in complexity science do

not acknowledge the influence of postmodernism on their work. Nevertheless, constructive

postmodernists consider Prigogine as a fellow traveler. Despite this, postmodernism

emerged in the 1960s with great momentum and was highly aggressive. It had a significant

impact on society and, although it may not necessarily have a common root, it created a

favorable cultural atmosphere for complexity research. Understanding postmodernism is

beneficial for grasping the historical significance of complexity. Therefore, in general,

complexity and postmodernism are both reactions to the spirit of the age. It is impossible

for them not to influence one another.

116

In general, when observed from the perspective of complexity, architectural thought

is no longer as scattered as it might seem. Viewed from this angle, the two main facets of

architectural thought during this period are, at least superficially, intertwined with the

principles of complexity science.

114

Tong Wu, “Complexity, Science and Postmodernism,” The 8th National Conference for Young Scientists

on Scientific and Technological Progress and Contemporary World Development, Harbin, August 17-12,

2002. ("

第八届哈尔滨“科技进步与当代世界发展”全国中青年学术讨论会

").

115

Miao, “Complexity Science and Postmodernism,” p38-45.

116

Huang, Wu, “The Context Analysis to the Arising of Complexity Sciences,” p38-45.

58 2 Research Background

2.4.4 The Free Period

In comparison with what had come before, by the late 1990s the concept of “openness”

was not just an interpretative angle but rather took on a leading role as its meanings were

developed. As Sakamoto states: “It’s not disassembled, it’s free.”

After going through the bubble period, the Sendai Mediatheque (Fig. 2.37) broke

ground in 1997 and was completed in 2000.

[Fig. 2.37] Left: Sendai Mediatheque.

[Fig. 2.38] Right: inside of Sendai Mediatheque.

The thin floor plates supported by tree-like structures and enclosed by glass curtain

walls comprise the entirety of the Sendai Mediatheque. The following are some of its

features:

1. Centerlessness: Elements with strong “central control” features, such as a high

overhang, a grand staircase common in public buildings, and corridors that connect

“rooms,” are all eliminated.

2. Equivalence of space: The absence of a center leads to equivalent spaces, not only

horizontally but also vertically.

3. Non-closed interfaces: There are no “rooms,” and hence no walls, and the boundary

between the building and the city is weakened as much as possible by the glass curtain

wall. Different spatial experiences are created only by varying floor heights, furniture

arrangements, and floor undulations. Closed spaces are avoided as much as possible.

4. Lack of functionality: There are no names, such as “reading room,” “movie room,” or

“lobby,” that imply function. Sendai Mediatheque is in fact also a name with no

reference. There is no indication of what to do in any part of the building. Users must

interact with the building on their own and spontaneously seek out spaces that suit their

purposes.

Openness seems to be a concept that can encompass the above features. The tree-like

columns (Fig. 2.38) supporting the “thin” floor plates make it possible for people to move

between the floor plates among the columns without “feeling” the changes in floor levels,

2.4 Japanese Architectural History in Comparison (1960-2000) 59

as if they are moving within the same space.

117

The extensive use of glass in the building

weakens the boundary between the interior and exterior, creating a sense that the building’s

interior spreads infinitely into the city.

In the year 2000, as if by command, architects seemed to shift abruptly from a state of

individualism to one of unity. The ideas conveyed by the Sendai Mediatheque surfaced

simultaneously in the thoughts of various leading architects. First, let’s take a look at

Kazunari Sakamoto’s focus and direction of thinking at this time.

The representative work of Sakamoto during this period was House SA, completed in

1999. Both buildings are well-known, although Sendai Mediatheque is more famous. One

is a large public building, while the other is a small architect’s residence. One grabs

people’s attention, while the other appears to be an ordinary neighborhood house. While

there seems to be no similarity in the appearance of the two buildings, the architects exhibit

an almost identical thought process in them:

[Fig. 2.39] House SA axial view. [Fig. 2.40] House SA section.

1. There is no “wall” in the building. Space is divided only by the furniture and the form

of the floor.

2. Centerlessness: in the article quoted in 3.3.5, Shunsuke Kurakata

118

comments: “No

matter where you are, you don’t feel the center of the space, and every space is

swaying.”

119

3. Another expression in this building that is relatively easy to overlook is the spiral

spatial movement (Fig. 2.39-Fig. 2.40). It is generally understood as a centerless form,

but it is more closely related to Sakamoto’s concept of “freedom.” The building starts

117

Sakamoto, “对话伊东丰雄：制度/消费/符号 (Conversation with Toyo Ito: Institutions/ Consumption/

Symbols).” in The Poetics in Architecture. Dialogue with Kazunari Sakamoto. edited by Guo Yimi, p54-80.

Nan Jin: Southeast university Press. 2011, p61

118

Architectural Historian, Professor of Faculty of Engineering at Osaka Metropolitan University.

119

Shunsuke Kurakata, “并非突然呈现的现代主义诗学 (The Modernist Poetics That Did Not Appear

Suddenly),” in The Poetics in Architecture. Dialogue with Kazunari Sakamoto, ed. Guo Yimi (Nan Jin:

Southeast university Press. 2011), p91.

60 2 Research Background

in the basement and gradually rises in a spiral pattern, and the spiral shape is broken in

the middle layer, returning and continuing until reaching the top of the building.

The original plan of this building in early 1995 employed a single spiral structure (not

the broken double back spiral). Throughout history, the “spiral structure” has appeared in

the works of many modernist masters. To some extent, in addition to the “central control,”

there are symbolic implications. It suggests a certain typology. In addition, Sakamoto stated

that the use of a single spiral “will make architecture like an object, becoming what is called

formalistic architecture,”

120

which is exactly what he wanted to avoid. Therefore, the

“single spiral structure” was broken. Instead, it is an indoor space consisting of a rising

space rotating to the right from the entrance and a descending space rotating to the left.

In this way, the “spiral structure” itself, along with other architectural elements,

became a “part” that possesses a certain degree of independence while also maintaining a

form of interconnection with the rest. A “clear and definite” structure was deliberately

avoided. This avoidance led to a sense of “ambiguity,” underpinned by opposition and

confrontation. This “ambiguity” emerged from a bottom-up approach to treating the “parts”

of architecture.

It is evident that the thought processes of the two architects were remarkably similar

at this time. This was also true for other architects of the same period, including Kazuyo

Sejima, Ryue Nishizawa, Akihisa Hirata, Jun Igarashi, Yoshiharu Tsukamoto, and Junya

Ishigami. The core focus of these architects was strikingly consistent: centerlessness,

ambiguity, non-closed interfaces, layered boundaries, equivalent space (Fig. 2.41-Fig. 2.58)

It indicates that the common values and orientation among Japanese architects had already

formed during this period. And this “unspoken agreement” has continued to the present.

Sou Fujimoto, who debuted in 2000, is also a part of this group.

[Fig. 2.41] Kanazawa Art Museum. [Fig. 2.42] Dematerialized indoors.

120

Sakamoto, “Free, Liberated and Neutral Space,” p301.

2.4 Japanese Architectural History in Comparison (1960-2000) 61

[Fig. 2.43] Moriyama House by Rye Nishizawa.

[Fig. 2.44] Left: Masuya Honda Walk by Akihisa Hirata.

[Fig. 2.45] Right: Group Home in Noboribetsu by Sou Fujimoto.

[Fig. 2.46] CIDORI by Kengo Kuma. [Fig. 2.47] Serpentine Gallery by Sou Fujimoto.

62 2 Research Background

[Fig. 2.48] Planned project for the contemplation of world peace in Copenhagen (2014). The building is

designed with a cloud-shaped shell structure set over the sea.

[Fig. 2.49] Left: House O by Jun Igarashi.

[Fig. 2.50] Right: House O by Sou Fujimoto.

[Fig. 2.51] Left: Zollverein School of Management and Design by SANAA.

[Fig. 2.52] Right: House N by Sou Fujimoto.

2.4 Japanese Architectural History in Comparison (1960-2000) 63

[Fig. 2.53] Okurayama Apartments by SANAA. [Fig. 2.54] House OM by Sou Fujimoto.

[Fig. 2.55] Left: KAIT Workshop by Junya Ishigami.

[Fig. 2.56] Right: The idea of the “forest” is deeply cherished by Japanese architects.

[Fig. 2.57] Left: Dangozaka House by SANAA. Manipulating space in the vertical dimension within small

areas is common practice in Japan.

[Fig. 2.58] Right: House MA by Sou Fujimoto.

64 2 Research Background

It is no coincidence that Fujimoto is favored by Toyo Ito. Terunobu Fujimori once

stated that “the reason Ito responds positively to Fujimoto’s architecture is because he

recognizes similar underlying motives toward architecture.”

121

Fujimoto is unmistakably

of Japanese heritage. What sets Fujimoto apart is that, unlike his predecessors, who might

have explored a single aspect of complexity or were indirectly influenced by complexity

theory, he embarked on a holistic exploration of how complexity could be manifested in

architecture from multiple perspectives. He has demonstrated a coherent understanding and

expression of complexity. It is notable that the term “complex” (complexity) often recurs

in Fujimoto’s discussions, though it is also true to say that the architect tends to minimize

its use. Fujimoto is an architect distinctly influenced by the theory of complexity. Here are

some instances:

The architectural community views the question of how to reinterpret complex and

diverse spaces into a simple form as foundational, now attracting broad attention as a

new focal point [...] The architecture will present itself as “forests of the future,”

prompting us to question: How can humanity create something with the complexity

and diversity of nature without resorting to mere imitation? [...] I have termed this

“Primitive Future,” indicating a return to simplicity that future humanity will confront

with new architecture, where complexity and uncertainty coexist. Indeed, the true

essence of ‘modern’ is the era that allows such architecture to excel.

122

Linking together simple and plain rooms results in a complex entirety, mirroring both

the tranquility of “home” and the diversity of the city [...] The layout created by this

sentiment is complex yet conveys an unusual simplicity [...] In our design, rather than

merely organizing the complex activity of “living” into superficial functionality and

then simplifying it, we envision restoring the inherently complex nature of things

through the language of architecture.

123

We extend such particulars and integrate the resulting complexity of the entire

building into the state of blending with the forest, demonstrated as “weak architecture”

in design competitions [...] These places maintain a strict order in the relationships

between parts, yet viewed as a whole, they appear disordered and even convey

impressions of complexity and unclear positioning [...] The method of “partial

architecture” has realized the long-desired, seemingly unattainable, naturally

occurring, disorderly architectural world. Though complex, it possesses a certain

order [...]

124

121

Sou Fujimoto, Toyo Ito, Taro Igarashi, Terunobu Fujimori, “Artificial Architecture, Natural Architecture:

Dialogue Summary” in Primitive Future, (Tokyo: INAX Publishing, 2008), p136.

122

Sou Fujimoto,

建筑诞生的时刻

, trans. Yu Zhang (Guilin: Guangxi Normal Unversity Press, 2012), p11-

15. Translated by the author.

123

Sou Fujimoto,

建筑诞生的时刻

, p29-30. Translated by the author.

124

Sou Fujimoto,

建筑诞生的时刻

, p36-38. Translated by the author.

2.5 Summary 65

Moreover, expressions like “order,” “complex,” “chaos,” “disorder,” “entirety,” “part,”

“randomness,” “relationship,” “accident,” “order,” “generation,” and numerous other

order-related terms are prevalent in Fujimoto’s remarks. Fujimoto read Prigogine’s From

Chaos to Order during his university days and had long acknowledged the impact of

complexity theory on his work. He does not use the notion of “complex” in the everyday

sense.

The term “complexity” also resonates clearly in Fujimoto’s works. Three of his early

projects—Design Competition for the Aomori Prefectural Art Museum (1999-2000);

Seidai Hospital New Ward (1998-1999); M Hospital Day-Care Wing (2000)—all adopted

a “bottom-up,” generative approach—the sole method in which complexity might emerge.

In his Primitive Future House Concept Model (2001), Fujimoto describes using the

cave, in contrast to Le Corbusier’s Domino System, which corresponds to the idea of a nest.

He argues that a nest is built for humans, whereas caves exclude “purposefulness” entirely

as they are products of “self-organization”—another interpretation of “complexity.” In his

Children’s Center for Psychiatric Rehabilitation (2006), House Before House (2007-2008),

Tokyo Apartment (2006-2009), the assembly of parts creates a “random” sensation—a

manifestation of complexity and a necessary element for it to arise, as well as creating an

intuitive impression for the observer. In his Serpentine Gallery Pavilion (2013), he utilized

the concept of clouds—a well-known metaphor for complexity. In his most renowned work,

House N, nesting, self-similarity, and fractals, among other complexity features, are

prominent. In the House Installation in Paris for the FIAC Art Fair (2014) and Final

Wooden House (2008), there is even a direct resemblance to 3D cellular automata—a

primary tool in complexity research.

Overall, since the 1960s, despite no specific emphasis on the latest understanding of

“emergence” in complexity theory, the theory has significantly influenced Japanese

architecture. Each climax of complexity science corresponds with pivotal shifts in Japanese

architectural practice. Many key moments in the history of Japanese architecture have been

shaped by complexity theory. Furthermore, a coherent evolutionary trend is observable,

illustrating a gradual convergence of Japanese architectural thought with complexity theory.

2.5 Summary

This chapter has introduced some key concepts, followed by an overview of the history of

complexity science, providing a holistic view of the interconnections between various key

concepts. It then outlined the influence of complexity theory on the evolution of

architecture, highlighting the concept of “emergence.” Lastly, it examined the influence of

complexity theory in Japan. Although the concept of emergence is not a mainstream

expression in Japan, the country has been influenced by complexity science since very

early on, and this influence cannot be overlooked.

66 2 Research Background

3 Rule 110 as a Foothold: Fujimoto’s Complexity

Under One Graphic

It is important to note that Sou Fujimoto’s affinity for “complexity” is not immediately

obvious. The architect does not engage directly with complexity theory; instead,

complexity manifests itself subtly as a product of his Japanese lineage. This relates to the

central thesis of our discussion: complexity theory is able to remain concealed within

Japanese architecture due to the similarities of the two phenomena. The One-Dimensional

Cellular Automata (OCA) proves to be a starting point for discussing Fujimoto’s complex

approach. It adeptly materializes one of Fujimoto’s core concepts: weakness.

3.1 A Standpoint: Rule 110

Rule 110, strictly speaking, is not a definition but a pattern. This dissertation argues that

this pattern is ideally suited as a standpoint for this discussion. It simplifies and intuitively

focuses Fujimoto’s architectural philosophy on a specific kind of complexity, facilitating

the formulation of questions and further discussion.

3.1.1 Weak Architecture

Sou Fujimoto’s ideas seem to cover a wide range of areas. Table 1.1 offers a summary of

the topics Fujimoto discusses most frequently. Discussions about him also tend to be

centered around these topics, most of which are common themes in Japanese architecture.

Indeed, one is likely to come across the majority of these topics simply by flipping through

a Japanese architectural magazine. Fujimoto belongs to a new generation with a clear

“Japanese lineage,” both in his works and writings. Many of his ideas are shared with his

peers and can be traced back to his predecessors. Yet one theme stands at the core of his

discourse: weakness.

1. Nest or cave

16. Significance of exteriors

2. Gradations

17. Significance of houses

3. Musical notes without staves

18. Significance of ambiguity

4. City as house–House as city

19. Mountainous architecture

5. Inside out / Outside in

20. Synchronously separated and

connected

6. Nature / Forests

21. Windows

68 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

7. One room

22. Formulation and interactivity

8. Before differentiation

23. Kimono and the body

9. Tokyo

24. Relativity theory/Quantum Mechanics

10. Significance of diagrams

25. Toyo Ito and the Sendai Mediatheque

11. Architecture of in-betweenness

26. Materiality

12. Architecture as clouds

27. The role of temporality

13. Telescopic nesting

28. Architecture as the delicate process of

generating serendipities

14. Garden

29. Ruins

15. Forest

30. Weak architecture

Table 3.1 Sou Fujimoto’s 30 Topics. These themes encompass many of the ideas that Fujimoto frequently

discusses in his writings. The compilation of this table is based on the Fujimoto special edition of El Croupis,

Issue 151.

“Weak architecture” was a concept used by Fujimoto frequently before the year 2005.

At its essence, this notion is foundational to the genesis of Fujimoto’s intellectual journey;

he is consistently drawn back to it in many of his ideas.

The utilization of this concept dates back to Design Competition for the Aomori

Prefectural Art Museum in 2000. (Fig. 3.1)

[Fig. 3.1] Design Competition for the Aomori Prefectural Art Museum.

Fujimoto’s proposal in this competition is expressed through a series of screen-like

walls that “harmonize with the natural order.” These walls seem different from the usual

“holistic” designs that impose their own order, instead curving and stretching along the

terrain, following the “natural order.” Fujimoto claims that the work “respond[s] to the

portion of the forest it confronts,” and that he finally “achieved complexity in the overall

architecture” which “blends in with the forest […] I describe this as weak architecture.”

3.1 A Standpoint: Rule 110 69

There are in fact many different interpretations of the term “weak.” In an interview

with Ryue Nishizawa, Fujimoto explains that: “I used the term ‘weak’ at that time to

describe a different way to make spaces that differed from the rigid way of making spaces

with a grid.”

Such an explanation easily leads the reader to associate it with his “nest and

cave” and place the focus on the challenge to Corbusier’s Domino System.

Another interpretation can be found in Toyo Ito’s statement:

According to Fujimoto’s own explanation, the notion of “weak architecture” that he

was then talking about is “not making architecture from an overall order but from the

relationships between each of the parts,” and as a result, “an order can be made that

incorporates uncertainty or disorder.”

Ito’s explanation indicates a further issue: proceeding from the relationships between the

parts can lead to uncertainty or disorder, while Fujimoto clearly focuses on “heteronomy.”

Yet in the conversation with Nishizawa, weakness is associated with a “different way to

make spaces.”

Furthermore, discussions on this topic also include a “functional concession,” such as

a “relinquishment of defining functions imposed on people by architecture,” “reduction of

the designer’s personal design consciousness,” or “encouragement of users to develop

imaginative concessionary designs,” etc.

This brings the topic of function back into the

conversation. From Fujimoto’s “nest and cave,” one can easily get an impression of the

reflection on functionalism in modernism and the rejection of functionally-oriented

architecture. The difference between a cave and a nest illustrates this point, as one is

essentially formed by nature, while the other is built to meet “needs.” The accompanying

images point out that Le Corbusier’s Dom-Ino House is a typical nest, while Fujimoto’s

Primitive Future House is a cave.

Moreover, Fujimoto also brought up the idea of “architecture without architects”

when discussing “weakness.” Fujimoto compared the Guggenheim Museum in Bilbao with

Italian mountain towns, stating that Gehry’s form lies in his decision to only define the

parts. Gehry

only defined the three-dimensional curves that make up the constituent parts and

combined them using a very simple principle. This formalism does not start from the

whole, but from the parts. This underlying rule is the same as the evolution of ancient

communities or the natural development of cities.

This is followed by his remark that:

Sou Fujimoto,“Conversation between Ryue Nishizawa and Sou Fujimoto,” by Ryue Nishizawa, El Croquis

151 (September 1, 2010).

Toyo Ito, “Casting off ‘Weak Architecture’,” in Primitive future, (Tokyo: INAX Publishing, 2008), p9.

Xiaohui Du, Bingbo Zhai, “Weak Architecture: Living in An Ambiguous Space: Unscrambling Sou

Fujimoto’s Works,” Huazhong Architecture, 2011, 29(8).

70 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

The type of architecture that appears to develop naturally with a sense of randomness,

which was considered as desirable but believed to be unattainable intentionally, is

within our grasp.

In brief, one could argue that “weak architecture” is architecture that “blends in with

nature”; weakness is “heteronomy”; weakness is a reflection on modernism; weakness is

anti-functionalism; weakness is architecture that is made from the relationships between

parts; weakness is “architecture without architects.” “Weakness,” then, is a seemingly all-

encompassing concept, that is related to almost all the topics in the last section.

Something

that brings this concept into particularly clear focus is one-dimensional cellular automata.

3.1.2 One-Dimensional Cellular Automata

[Fig. 3.2] The working principle of OCA is very simple.

One-dimensional cellular automata (OCA) are perhaps the simplest and the most intuitive

way of expressing Fujimoto’s concept of “weakness.”

Cellular automata (CA) is one (if not the most) frequently used methods in the science

of complexity. It is a study of evolutionary behavior from the perspective of discrete time.

(Fig. 3.3)

Sosuke Fujimoto, “Architecture of parts,” The Japan Architect, 2001, Vol.43, p10.

This article investigates the term “weakness” in the context of architecture in Japan, where it is of major

significance. However, due to the constraints of space and the weak connection between the survey results

and the theme of the dissertation, it will not be discussed here, but only summarized: the meaning of

“weakness” in the context of Japanese architecture is diffuse and difficult to clarify. It does not seem to

provide any substantial help in understanding common topics mentioned in the table 3.1. Moreover, The

meaning of “weakness” in the context of Japan are not directly related to complexity.

Wulun Jin, Yuanlin Guo, “The Science of Complexity and Their Evolution,” Complex System and

Complexity Science, (Jan 2004) Vol.1, No.1.

3.1 A Standpoint: Rule 110 71

[Fig. 3.3] 2D cellular automata are a primary tool for studying complex systems.

Cellular automata are simple models in computational mathematics that consist of a

grid of cells, each of which can be in one of a finite number of states. The state of each cell

in the grid is updated at each moment in time according to a set of rules that depend on the

states of neighboring cells.

In the 1950s, renowned American mathematician John von Neumann, who is often

hailed as the progenitor of computing, devised a model predicated on a chessboard-square

array of cells, inspired by his exploration of biological cells. Each cell in this grid

transitions between states over time, but is usually limited to two distinct states. The

transformation of each cell’s state is determined exclusively by the influence of its adjacent

cells and its own prior state. The rules governing these transitions are manifold,

meticulously crafted by researchers to align with their specific investigatory needs, laying

the groundwork for what is known as cellular automata (Fig. 3.3).

A hallmark of this model is its initiation from individual components. Each cell

alternates between two states—black and white—impacted solely by the states of its

adjacent cells and itself. The number of neighbors is contingent upon the automaton’s

spatial dimensionality; one-dimensional automata are flanked by two neighbors, two-

72 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

dimensional by eight, and three-dimensional by 26. The transformation processes, termed

rules, fundamentally encapsulate the dynamics between components, with modifications

to these rules engendering diverse overarching patterns. Thus, OCAs emerge through

“interaction between parts,” rather than as a collective whole. Celebrated for their elaborate

mathematical frameworks and their profound resonance with nonlinear dynamics, cellular

automata have a deep resonance within the scientific community.

Notably, Stephen Wolfram has classified certain rules within OCAs as complex,

evidencing their shared attributes with a particular form of complexity across multiple

realms.

3.1.3 Stephen Wolfram’s Rule 110

Due to their simple characteristics in low dimensions, all of their possibilities can be easily

calculated. There are a total of 256 possibilities. In 1981, Stephen Wolfram listed all these

possibilities by hand and classified them into four categories: class I: homogeneous; class

II periodic; class III chaotic; and class IV: complex (Fig. 3.4). They are known as

Wolfram’s Classification (WC).

[Fig. 3.4] The four classes of Wolfram’s Classification.

Among all the rules, 110 is a unique entity. (The mirror image of Rule 110 is Rule

124, the complement is Rule 137, and the mirrored complement is Rule 193.) The

description of this rule is still very simple: take the new color of a cell to be black in every

case except when the previous colors of the cell and its two neighbors were all the same,

or when the left neighbor was black and the cell and its right neighbor were both white

(Fig. 3.5).

[Fig. 3.5] Rule 110.

Waldrop, Complexity, p225.

3.1 A Standpoint: Rule 110 73

[Fig. 3.6] Rule 110 from a single initial condition in 20 and 100 steps.

Unlike most other rules, Rule 110 creates a unique impression on its own (Fig. 3.6).

First, it defies our expectations that simple rules lead to simple outcomes. The pattern it

reveals is indescribably complex, a complexity that becomes even more evident on a larger

scale (Fig. 3.7).

Secondly, attempting to describe the overall pattern of this figure precisely can be

challenging. While we can attempt to piece together its “entirety” using simple language,

here are some characteristics that may be summarized through observation:

1. Simplicity. All patterns can be described in a simple sentence.

2. Simplicity can lead to complexity. Stephen Wolfram claimed that the basic

phenomenon that can be observed in these patterns “is ultimately responsible for most

of the ‘complexity’ that we see in nature.”

Simple rules result in “patterns that are

Wolfram, A New Kind of Science, p28.

74 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

difficult to describe simply.” However, simplicity does not always lead to complexity.

In most cases, simplicity merely results in simplicity.

[Fig. 3.7] Rule 110 from a random initial condition.

3. The whole is formed by the interaction of parts. They are all generative and are

generated from bottom to top, meaning that the formation of the whole relies on local

information.

4. A large number of constituents. These consist of many small cells.

5. Fractal and self-similar features. Triangles can be observed at many different scales.

6. A self-organized overall pattern. Not just the triangles, but some underlying non-trivial

structures are self-organized—leading to another important, yet famous concept:

emergence.

Apart from the graphic for “Equilibrium,” all the other graphics of the FGO are generated by the model

“CA 1D Elementary” in Netlogo Software. Wilensky, U. (1999). NetLogo.

http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling,

Northwestern University, Evanston, IL.

3.1 A Standpoint: Rule 110 75

7. Emergence. The emergence of triangles, structures formed by triangles, or more

sophisticated structures formed by structures, occurs without explicit instructions in

their generation rules. They all deviate from their origin—the rules.

8. Centerlessness/No Central Control. No central point can be found in the overall pattern

of Rule 110. Moreover, the absence of a center is related to self-organization, meaning

there is no central control. Every single cell has its own control. The control logic in

OCA is dispersive and scattered.

9. Ambiguity. The overall pattern is “difficult to describe.” And, without knowing the

specific rules of formation, drawing this pattern is problematic. Thus, the ambiguity

stems partly from the inability to simply describe the overall pattern and partly from

the origins of the pattern, or how it emerged.

10. There is no boundary, but there is density. There are no clear boundaries between

different orders within the overall pattern; they merge gradually. However, this gradient

does not feel uniform—there is rhythm and density.

11. Randomness. Although Rule 110 is entirely deterministic, predicting future states

without computing them is challenging due to the complexity it generates. This

unpredictability is characteristic of randomness, indicating that entirely deterministic

systems can produce complex and unpredictable behavior. The randomness in Rule 110

also manifests in its sensitivity to initial conditions: even minor changes in the initial

state can lead to vastly different long-term behaviors, making it challenging to predict

long-term behavior due to its extreme sensitivity to the initial state of each cell.

12. Coexistence of order and disorder. First, in the development of Rule 110, one can notice

the presence of local organized structures, like repeating sequences or stable forms,

amidst overarching chaos. These entities exhibit movement or interaction within the

grid of the cellular automaton, demonstrating a semblance of order. Nevertheless, these

pockets of organization are often set against a backdrop of greater chaos and apparent

randomness, presenting a global level of disorder. Here order and disorder coexist.

Secondly, from the perspective of deterministic rules and overall patterns, if the former

(specific rules) are considered orderly and the latter (overall patterns) disorderly, Rule

110 also represents a coexistence of order and disorder, where the cause is orderly, but

the result is disorderly. Thirdly, the Turing completeness of Rule 110 signifies the

embodiment of the dual nature of computation itself: it is both a precise, orderly, and

logical process and a tool capable of producing and interpreting complex, variable

phenomena. Here, too, is a coexistence of order and disorder.

This classification is a broad description, and a simple comparison will reveal that

Fujimoto’s discourse and works encompass all the above features.

76 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

3.1.4 Comparing Rule 110 with Sou Fujimoto

In this section, Rule 110 will be compared with Fujimoto’s architectural philosophy. The

features of Rule 110 that can be observed with the naked eye exhibit similarities with

various aspects of Fujimoto’s discourse and works.

[Fig. 3.8] Overview of Fujimoto’s works (for comparison with Rule 110).

3.1 A Standpoint: Rule 110 77

Architecture of Parts

In “Architecture of Parts,” published in Japan Architect in 2001, Fujimoto states:

I begin by thinking, not of the overall, but of the relationship between the parts. If

indeed architectural design provides some kind of order to space, I strive to achieve

this by overlaying order established between the parts, instead of defining an overall

order in the architecture. I call this way of thinking of architecture and the architecture

that results an “architecture of parts.”

With regards to this statement, he gives three of his projects as examples: Design

Competition for the Aomori Prefectural Art Museum (1999-2000); Seidai Hospital New

Ward (1998-1999); M Hospital Day-Care Wing (2000) (Fig. 3.9).

[Fig. 3.9] Left: Design Competition for the Aomori Prefectural Art Museum (1999-2000). Middle: Seidai

Hospital New Ward (1998-1999). Right: M Hospital Day-Care Wing (2000).

In Seidai Hospital New Ward (1998-1999), the building is “a cluster of parts.” The

corridor and main hall—spaces which have traditionally carried connotations of central

control—have been removed. Rooms, as parts, are attached to one another directly.

Similarly, the plan of M Hospital Day-Care Wing (2000) is also decided by “adjacent mass

and space,” like, says Fujimoto, the “Go Stones game,” which evolves according to the

state of parts. Along with the Design Competition for the Aomori Prefectural Art Museum

(1999-2000), all three projects “start, not from overall order, but from ‘parts’.” All three of

them maintain an overall coherence through the relationships of their parts. The “whole”

is only vaguely determined and, according to Fujimoto, the aim is to achieve “diverse

spaces” and a sense of randomness.

In fact, Fujimoto emphasizes this approach in many places, claiming that “a certain

sense of complexity” can be achieved by adopting this method. For example, in two articles

in The Birth of Architecture, entitled “The New Order Formed by the Relationship Between

Parts” and “The Architecture of Parts,” Fujimoto mentions the concept of “a new order

formed from the relationship between parts that leads to the overall structure.” As can be

seen in (Fig. 3.2), most of Fujimoto’s early architecture was composed of individual “parts,”

ranging from materials such as slender steel pipes (Serpentine Gallery [2013]),

bookshelves (Musashino Art University Library [2010]), rooms (Seidai Hospital New

Sosuke Fujimoto, “Architecture of parts,” The Japan Architect, 2001, Vol.43, p10.

78 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

Ward), individual boxes (Children’s Centre for Psychiatric Rehabilitation [2006]), to

buildings (Tokyo Apartment). They are indeed as Fujimoto describes: proceeding not from

the overall order, but from the parts. The relationships between the parts maintain the

overall coherence, and the whole exhibits a state of looseness.

On this basis, Fujimoto developed a series of concepts, such as “weak architecture.”

Let’s take another look at this concept. Weak architecture is “not making architecture from

an overall order but from the relationships between each of the parts” and, as a result, “an

order can be made that incorporates uncertainty or disorder.”

As one can see from the above, “weak architecture” and the “architecture of parts” are

identical. In the overall pattern of complexity, there is an indescribable “uncertainty.” It is

obviously looser than the homogeneous pattern, which is at least one reason why Fujimoto

calls it “weak.”

“The order of the forest” is another concept that runs parallel to “weakness.” In Design

Competition for the Aomori Prefectural Art Museum (1999-2000), Fujimoto claimed that

the architecture abandoned its own order and has instead applied the order of the forest.

What is the order of the forest?

[Fig. 3.10] A partial map of a tropical rainforest beautifully illustrates one of the orders of the forest in

Fujimoto’s mind. This is a 50-hectare Barro Colorado Island rainforest in Panama. Barro Colorado is a

protected area of tropical rainforest located in the middle of the Panama Canal. Over the past few decades,

thousands of types of vegetation in this area have been identified, marked, and measured. The rich and

detailed data converges into a knowledge map of this area. The figure above is a top view of Barro Colorado.

When the treetops are below 20 meters, they are displayed as black. The figure shows the distribution of gaps

between trees.

In the forest, (Fig. 3.10) the formation of gaps between tree canopies is caused by the

death and collapse of trees. Often, when trees die in the rainforest, they do not fall over but

rather remain upright and in place, and so their deaths do not have much impact on their

neighbors. However, once they collapse, they can sometimes cause a chain reaction of

Ito, “Casting off ‘Weak Architecture’,” p9.

3.1 A Standpoint: Rule 110 79

continuous collapse, resulting in damage to adjacent trees. Therefore, large gaps are often

created. When this happens, black areas appear on the figure.

[Fig. 3.11] Forest fire simulation. Fire is transmitted through “parts.”

In addition, the competition for sunlight is also a vital condition for the survival of

plants. If the plants in an area are too dense, this will inevitably affect the survival of the

surrounding plants, which will begin to wither and collapse, forming new gaps. The

formation of new gaps creates new opportunities for obtaining sunlight and uncontested,

nutrient-rich soil, and thus makes way for new life.

Equally, once a forest fire breaks out, the burning starts from a specific location and

spreads through neighboring plants (Fig. 3.11). Therefore, in the forest, it is indeed the

local plants that begin to produce effects and changes. The forest that is produced through

local impact and interaction is the order of the forest. It is still a result of interactions in

parts.

Another similar remark of Fujimoto that is often mentioned is “Musical Notes

Without Staves.” Fujimoto believed that the grid-like staves stand for the “homogeneous

space” of modern architecture, which can be removed. To rely solely on the local

relationships between musical notes would not only mean that the music would not become

chaotic, but it would also create a “dynamic and gentle order,” which is “precisely the order

for 21st century architecture.” What Fujimoto wants to convey here is clear. That is, he

advocates for a consideration of the relationship between parts and wholes, and a

generative approach from bottom up.

Under Rule 110, such a connection becomes clear and direct. One can easily relate

Fujimoto’s randomness, uncertainty, and disorder to complexity.

80 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

A Large Number of Constituents

It can be seen that the smallest unit used in Rule 110 is a single square. The whole is

composed of a large number of squares.

Fujimoto once used the title “Density created by an infinite collection of small

matters”

to describe House NA. In this work, the delicate steel structures, transparent

glass, furnishings, plants, and a multitude of small elements work to compose a “home.”

In fact, “quantity” consistently plays an obvious role in Fujimoto’s early works (Fig. 3.8).

These works are often composed of a large number of small units: the small “parts” directly

form the “whole” of his buildings.

[Fig. 3.12] Left: “The Game of Life 3D.” “Life” is a famous 2D cellular automata model invented in 1970

by John Conway. This is the 3D version of it.

[Fig. 3.13] Middle: Sou Fujimoto stacks aluminum boxes to form a “nomadic” house installation in Paris for

the FIAC art fair.

[Fig. 3.14] Right: Sou Fujimoto’s Final Wooden House (2008).

Some of these “parts” are cell-like units (Tokyo Apartment), some are rooms, some

floors (Primitive Future House), some furniture (The Musashino Art University Library),

some roofs, and some simply materials (Serpentine Gallery). Some of them even bear a

close resemblance to 3D cellular automata (Fig. 3.13).

Cloud-like, Nebulous

[Fig. 3.15] Left. Abstraction of Clouds as engendered spaces.

[Fig. 3.16] Right. Geometric Forest – Solo Houses (2011).

Sou Fujimoto, Sou Fujimoto Architecture Works 1995-2015 (Tokyo: TOTO Shuppan, 2015), p174.

3.1 A Standpoint: Rule 110 81

[Fig. 3.17] Louisiana Cloud. [Fig. 3.18] LA Small house.

[Fig. 3.19] Floating Stone House. [Fig. 3.20] Floating Stone House.

A good, everyday example of a whole created by a large number of individual parts is a

“cloud.” According to Fujimoto, cloud-like architecture represents the ideal state of

architecture (Fig. 3.15). He even constructed a cloud-like structure himself. In the

Serpentine Pavilion project, Fujimoto used slender, white-painted steel pipes and glass to

assemble a structure that merges into the background. There are no strong separations or

boundaries, but different “densities” are created. The materiality of the architecture is

removed to the greatest extent possible, leaving only human activity.

82 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

Similarly, the architect sometimes uses the word “nebulous” to replace “cloud”:

“When one thinks of architecture’s origin, one can imagine it to be a ‘nebulous field’

derived from various densities of chiaroscuros.”

Creating cloud-like environments is another common theme for Fujimoto. In 2000,

shortly after his debut, Fujimoto proposed Day-Care Center (Hokkaido, 2000)—a

conceptual heir to the Aomori Museum of Art proposal—which was centered around the

theme of the “nebulous,” emphasizing this idea “not as enclosure but as something more

like a territory” which also has “density.” Following this concept, Fujimoto introduced a

series of designs themed around “clouds”: Louisiana Cloud (2011) (Fig. 3.17); Geometric

Forest-SOLO Houses Project (SAPIN 2011) (Fig. 3.16); LA Small House (California 2010)

(Fig. 3.18); Floating Stone House. (Fig. 3.19; Fig. 3.20) These projects all revolved around

his exploration of creating environments akin to clouds.

Gradation/ Boundary/ In-between/ Interval/ Density/ Inside-Outside

[Fig. 3.21] “There is an infinite degree of gray between black and white, just as there are innumerable values

between 0 and 1.” A picture commonly used by Fujimoto to express “Gradation.”

An important feature of clouds is their different gradations, and this is another frequent

topic of Fujimoto’s: “Ideal architecture is analogous to a ‘nebulous territory’. It is a place

where interiority and exteriority coalesce.”

The concepts of clouds and gradation are

intrinsically linked. Other similar concepts related to gradation include: boundaries, in-

between, and inside-outside. These are all logically connected inasmuch as they are not

divided by rigid boundaries, but by density. In Rule 110, different densities can be observed.

The nature of the order shown in this diagram is similar to that of clouds, nebulas, and

stages of water vapor, etc. If we acknowledge that a building is a matter that separates

things, then this matter needs a way to exist in the form of a boundary. Fujimoto does not

want this boundary to be strictly black and white, but between black and white, inside and

outside, house and city, 0 and 1, private and public, matter and space, morning and night,

Fujimoto, Primitive Future, p74.

Sou Fujimoto, El Croquis 151, 2000, p206.

3.1 A Standpoint: Rule 110 83

etc. Such a spatial form is a symbolic presence in Fujimoto’s architecture and throughout

Japan as a whole. It is a common pursuit for Japanese architects.

When all qualitative changes become gradations, a natural result is an environment

that is like a cloud. In this environment, there is no longer a distinction between indoor and

outdoor, between home and city. Everything coalesces into one.

[Fig. 3.22] House N.

The House N project (Fig. 3.22) is the best illustration of this idea. Fujimoto nested

three boxes inside one another, each decreasing in size, creating a multilayered nested

structure. What’s more, each box was punctuated by immense apertures. This manipulation

through “digging holes” means that the relationship between the boxes is no longer a

simple nesting relationship like a “Russian doll,” as Fujimoto described it. From the

innermost box, one can also feel the external environment on the street, not directly but

rather indirectly, through a series of progressively “in-between” spaces. Light and shadow

from outside the building enter through multiple layers of windows, not just through typical

windows.

“A box within another box, ad infinitum, produces diverse gradations.” Fujimoto

states that “life in his house resembles living among the clouds. A distinct boundary is

nowhere to be found, except for a gradual change in the domain.”

Fujimoto’s spatial

concept of “gradation,” as with his “cloud,” is therefore related to Rule 110.

Fractals/ Self-similarity/ Box-in-a-box/ Telescopic Nesting

In the House N project, another important concept alongside that of “in-betweenness” is

fractals. Although Fujimoto uses “telescopic nesting,” what we can clearly observe is “self-

similarity,” which is a striking feature of Rule 110.

Fujimoto, El Croquis 151, p206.

84 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

As we can see, although the various boxes are referred to as nested, they are actually

created to be similar. The roof and walls have no discernible differences, and white paint

covers all identifiable information. The material properties of the building, such as door

frames, window frames, and structural relationships, are deliberately eliminated by the

architect, and the only distinction between the different boxes is their size.

In Rule 110, one can also observe a clear structure of self-similarity, with triangles of

many different sizes. Nesting and complexity may not be related, but self-similarity and

complexity are.

First, self-similarity is closely related to fractals. One could compare it with the classic

example of “self-similarity”: the Koch curve. The symmetrical properties of these curves

are called self-similarity. They exhibit similar forms at different scales.

Behind this kind of similarity is an “in-between” dimension that lies between one and

two dimensions: 1.5 dimensions. Many examples of this can be found, such as the coastline

dimension of 1.2, the cloud surface dimension of 2.35, and the protein surface dimension

of 2.4.

Their common feature is that they are not integers but rather lie in some “in-

between” position of an integer dimension. This understanding immediately leads us to the

“gradations” diagram in the previous discussion of Fujimoto’s ideas.

The creator of the concept of fractals, Benoit Mandelbrot, proposed the concept in his

1967 article “How Long is the Coast of Britain?” published in the journal Science. The

coast of Britain is a kind of fractal with a dimension of 1.2, lying between certain integers.

Therefore, self-similarity is related to what we have just discussed—“gradation.”

Secondly, the appearance of fractals implies the appearance of chaos,

which brings

another further concept into the conversation. Fractal geometry is used to describe chaos.

This concept was born in 1975 and is the main research direction of the second phase of

complexity science, characterized by chaos theory and nonlinear science. Chaos, fractals,

and nonlinearity are often intertwined. One might see statements such as the following:

fractals are the spatial expression of chaos, while chaos is the temporal fractal; chaos

systems have fractal characteristics, and fractal methods can be used to analyze chaotic

systems; chaos focuses on the process of forming a dynamical system, that is, how

attractors are formed, while fractals focus on the results of the dynamical system, that is,

the attractors themselves; chaos focuses on the process, while fractals focus on the result.

Therefore, the relationship between the two is very close.

Friedrich Cramer, Chaos and Order: The Complex Structure of Living Systems, trans. Zhiyang Ke, Tong

Wu (Shanghai: Shanghai Scientific & Technological Education Publishing House, 2018), p163.

Cramer, Chaos and Order, p165.

3.1 A Standpoint: Rule 110 85

[Fig. 3.23] House N.

[Fig. 3.24] The self-similarity is evident in the image to the right.

The relationship between chaos and complexity is also intricate. As mentioned in

section 2.1.4, chaos is also understood as complexity in some contexts. In general, self-

similarity is a major characteristic of fractals. The appearance of fractals implies the

appearance of chaos, and complexity often includes chaos. Therefore, there is a relationship

between self-similarity and complexity.

This relationship may seem very indirect. However, from the perspective of

philosophical classification, fractals are often considered to be objective—as a form of

“structural complexity.” This refers to the internal structure of the system having multiple

levels and parts, and also interconnectedness, nesting, and recursion

Therefore, in certain

cases, fractals and complexity also have direct connections, for there are often

characteristic attributes that appear alongside complexity.

Overall, Fujimoto’s concept of “telescopic nesting” is very similar to the self-

similarity exhibited by Rule 110.

Architecture without Architects/ Self-organization

By adopting the method of designing an “architecture of parts” or thinking of the

relationships between the parts […] architects may be able to build this naturally

developed architecture that has been known as “architecture without architects.”

Fujimoto believes that “architecture without architects” is achievable by adopting his

method of “architecture of parts.” Using Guggenheim Museum Bilbao (1997) as an

example, Fujimoto states:

When examining the photographs of Bilbao, one realizes that it is similar to, for

example, medieval Italian cities on hillsides or communities that were developed

Wu, “Objective Complexity,” p45.

Fujimoto, “Architecture of parts,” p10.

86 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

naturally. It is also similar to the overlapping buildings in downtown Tokyo that at

first glance seem to have no order. What is important is that the similarity is not

limited to the surface, but extends to the way they stand and the way they are

constructed.

Fujimoto argues that the essence of Gary’s architectural forms is rooted in his focus on

individual components. Gary concentrates on shaping the three-dimensional curves of

these elements and merges them using a straightforward principle. Instead of beginning

with the overall form, his approach builds from these individual parts. This underlying

principle mirrors the evolutionary processes of ancient societies or the organic growth of

urban areas.

In addition, one can also discern the expectation of “architecture without architects”

from a consideration of Fujimoto’s Nest Vs Cave. (Fig. 3.25) Fujimoto compares his

“primitive future house” with Le Corbusier’s Dom-Ino. One does not need to read his annex

to understand that Le Corbusier’s Dom-Ino corresponds to the nest, and his primitive future

house is the cave. For the cave is a self-organizing natural object, while the nest implies

“artificial intervention.”

[Fig. 3.25] Nest Vs Cave.

“Architecture without architects” comes from an exhibition of the same name

organized by Bernard Rudofsky at the Museum of Modern Art in New York in 1964. This

was followed by the publication of the book Architecture Without Architects: A Short

Introduction to Non-Pedigreed Architecture. In its focus on non-pedigreed architecture,

this book criticizes Western architectural history as a “selected history” based on the “will

of the rulers,” reflecting particularly on modernism. It extensively documents the beauty

of “ordinary architecture” that is detached from the orthodox architectural history, using

keywords such as vernacular, anonymous, spontaneous, indigenous, and rural.

Rudofsky’s book appeared in an era of discontent with modernism, calling for history,

context, and humanistic spirit, and this naturally became the main direction of

interpretation. However, “architecture without architects” may be interpreted in another

way too, in accordance with the main theme of that time. In this light, we might say that it

Fujimoto, “Architecture of parts,” p10.

3.1 A Standpoint: Rule 110 87

emerged due to a dissatisfaction with what lay at the foundation of modernism—modern

science.

The absence of architects implies the absence of “control.” Thus, the emergence of

architecture in this way is, to some extent, self-organized. This may be the closest concept

of architecture to complex systems, which is what Fujimoto wants to express. In his books

such as Architecture o Part and The Birth of Architecture, Fujimoto repeatedly mentions

the rich spatial experience formed by the self-organization of ancient cities and villages,

and attempts to link the formation of Gary’s “whole” to self-organization.

“Other-organization” is the opposite of self-organization. As the name suggests, it is

organized from top to bottom through external commands. “Other-organization,” therefore

implies “modernism.” “Self-organization” has thus gained a “new” meaning in the eyes of

some architects because of its principle of bottom-up generation, which is different from

modernism.

In Rule 110, the appearance of non-trivial structure is the result of self-organization.

Clearly, there are no instructions for “forming structure” in the rules of generation, which

means that the system spontaneously organizes itself into this kind of structure without

central control. Therefore, the expression “architecture without architects,” once again

demonstrates the compatibility of Fujimoto’s ideas with Rule 110.

Centerlessness

The overall pattern of Rule 110 gives an impression of centerlessness. Centerlessness is a

common feature in Fujimoto’s architectural works, as seen in the Seidai Hospital Annex

project (Fig. 3.26). Ordinary architectural elements which “control” meaning, such as the

lobby, main entrance, and corridor, are completely eliminated. The lobby and corridors

tend to imply central control as the lobby is often the focal point of a plan, and the corridors

that lead from it serve to connect the various functional rooms.

[Fig. 3.26] Left: Layout of Seidai Hospital Annex.

[Fig. 3.27] Right: Axial view of Group Home in Noboribetsu.

88 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

In this building, the rooms are directly connected to each other. Users can only

determine their location and orientation by their current position and the adjacent rooms.

The usual traffic space and central space are completely excluded. The loss of centrality is

clear, and, according to Fujimoto, this can bring about a sense of ambiguity and vagueness.

A similar approach was used in the Group Home in Noboribetsu project. The entire

building is composed of rectangular rooms which connect to each other directly when

viewed from above. In the axial view (Fig. 3.27), this relationship is clearly shown: there

are no corridors, and the “parts” of the building, i.e., the spaces, are directly related. The

traditional way of connecting rooms through doors has also been abandoned here. Instead,

the rooms are connected by triangular slanted walls, which takes the ambiguity brought

about by this decentralization to the next level: the walls are like walls but not walls, and

the spaces appear to be connected, but are not completely so. The spaces as “parts” are

connected in an ambiguous manner.

In the previous section, it was mentioned that Fujimoto’s architecture often consists

of multiple individual units and also exhibits a lack of “unity” as a whole, which is also a

manifestation of the absence of a center. As illustrated in Fig. 3.12, it can be observed that

Fujimoto’s architecture generally lacks a clear center in its appearance. The whole seems

to be composed of loosely connected parts. The buildings do not have a so-called “front

façade” or a complete image. This is a value orientation that is often encountered in

Fujimoto’s architecture. Indeed, we have once again found a convergence between

Fujimoto’s architectural concepts and Rule 110.

The Coexistence of Order and Disorder

The roads in Rome stretch straight across all natural and artificial obstacles through

powerful construction methods. In contrast, roads in Japan wind and turn when they

encounter mountains and valleys, and stretch out in a curved manner. Although they

lack the strength of Roman roads, they are not without order. There is a natural, gentle

order to them. As a result, when we combine the multiple images, the word that

emerges is “weak.”

Similar descriptions of “weakness” can be found in the preface of the book Primitive

Future, written by Toyo Ito (section 3.1.1). “Weakness” clearly refers to the coexistence

of order and disorder.

The coexistence of order and disorder is evident in the architectural designs of

Fujimoto. The projects Design Competition for the Aomori Prefectural Art Museum (1999-

2000), Seidai Hospital New Ward (1998-1999), and M Hospital Day-Care Wing (2000)

feature the prominent juxtaposition of a “strict grid” against a “seemingly random layout.”

Notably, the Seidai Hospital New Ward presents a striking contrast between its orderly

square façade and the ensuing disorder caused by the absence of internal circulation spaces.

Fujimoto,

建筑诞生的时刻

, p116.

3.2 Pivotal Aspects for the Advent of Complexity 89

In the case of the Art Museum in Aomori project, Fujimoto himself describes the approach

as “the coexistence of order and disorder based on a grid,” a concept that he further evolved

and directly applied in subsequent projects, including the Shijima Lodge (NAGANO, 2002)

(Fig. 3.28), the M-hospital Day Care House (2000), and the Children’s Center for

Psychiatric Rehabilitation (2006) (Fig. 3.29)

[Fig. 3.28] Left: Shijima Lodge.

[Fig. 3.29] Middle: Children’s Center for Psychiatric Rehabilitation.

[Fig. 3.30] Right: Tokyo Apartment.

Additionally, Fujimoto’s emphasis on “randomness” demonstrates a deliberate

engagement with the coexistence of order and disorder, suggesting that a building must

inherently display some level of order in its appearance. This is akin to the human attraction

to the semblance of disorder in complexity when the underlying rules are unknown. The

attributes of being “seemingly random” and “irregular” frequently emerge in his works.

Consequently, we can also discern an alignment with Rule 110 in this respect.

These alignments, discernible to the observer, can essentially be categorized into two

parts: one establishes a connection between Fujimoto and the concept of complexity,

crucial for the emergence of complexity. The other begins to link Japan with the notion of

complexity.

3.2 Pivotal Aspects for the Advent of Complexity

A crucial point in the discussion of Rule 110 is the emergence of complexity. This also

hints at the relationship between Fujimoto and complexity.

3.2.1 Behind Rule 110

As introduced in section 2.1.5, the coexistence of order and disorder represents a common

perspective in defining complexity, relating to the transformation from order to disorder.

Whether it is through surface characteristics or underlying mechanisms, the coexistence of

order and disorder is a significant feature of Rule 110. This is one reason why it has been

Fujimoto, Sou Fujimoto Architecture Works, p32.

90 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

chosen to represent a broad category of complexity: it exemplifies a rare domain within the

entire spectrum of Cellular Automata (CA), where, amidst all 256 possible configurations,

only a fraction of which belong to Class IV. Moreover, Rule 110 stands out as the only one

to exhibit computationally universal behavior.

Class IV is characterized by its emergent and self-replicating capabilities. Rule 110

displays emergence, a concept often explored by complexity researchers in the 1980s and

a key feature of digital architecture. The “emergence of structure” observed in Rule 110

can accumulate in higher-dimensional expressions, such as the “Breeder” simulation,

which forms a third-order reproductive structure. However, this is still a small-scale

structure. In the world of cellular automata, structures can become significantly larger and

more varied, with the largest known translating structure, the “Caterpillar,” found in 2004,

containing at least 11,880,063 live cells and moving 17 cells up in 45 generations, nearing

“light speed” in the CA world.

Another notable structure is the “OTCA metapixel” (2005),

dubbed “life within life,” which simulates a single cell’s life activities within a 2048 x 2048

square area over 35,328 generations, demonstrating the recursive creation of infinitely

large structures, in a similar way to how molecules form cells, cells form tissues, and so

on.

Class IV represents a fascinating domain where rules neither result in frozen blocks

nor lead to complete chaos. They form coherent structures capable of wonderfully complex

behaviors in propagation, growth, division, and recombination, essentially never settling

into a static state.

Class IV also embodies an area of the unknown. In conventional dynamical systems

theory, nothing quite matches the behaviors seen in Class IV rules, which appear as a

unique manifestation of cellular automata behavior. The only way to determine a specific

rule’s class is through testing to see the behavior it generates.

Life, as it is considered,

exists within this dynamic realm.

Wolfram’s observation of Rule 110 suggests that many complex phenomena in nature

might stem from basic, discrete computational processes, not necessarily requiring

complex mathematical formulas for description. The reasons for this viewpoint are:

Computational universality is the ability of a computing system to perform any calculation or solve any

computational problem, given enough time and resources. In simple terms, if a system is computationally

universal, it can theoretically simulate or carry out any computation task. This concept means that any

computer can potentially complete the same tasks as any other computer, as long as it has the appropriate

programming and sufficient time and resources.

In the 1970s, the most famous moving structure was the Gosper Glider Gun. It always consists of five

chess pieces, which move one square to the lower right every four turns. Faster than this is an LWSS

(Lightweight Spacecraft), which moves two spaces to the right every four turns. This proved to be the fastest

speed in the “Game of Life.” It can be regarded as the "speed of light" in this virtual world.

Waldrop, Complexity, p226.

3.2 Pivotal Aspects for the Advent of Complexity 91

1. Universality of Complexity. Many natural phenomena exhibit highly complex

behaviors that are difficult to describe precisely using mathematical methods.

2. Discreteness in Nature. Many processes in nature are discrete rather than continuous,

contrasting with the continuous models in traditional mathematics. Wolfram believes

discrete computational models can better capture these phenomena.

3. Capability of Automata. Computational models, like cellular automata, possess a

strong ability to describe and simulate natural phenomena.

Wolfram emphasizes the importance of computation, discreteness, and automata,

suggesting that integrating computational science into the natural sciences could lead to

the replacement of traditional mathematical approaches in order to achieve better

simulations and understandings of complex natural phenomena. Thus, computational and

automata models are seen as better descriptors of complex phenomena in our world, not

just relying on traditional mathematical formulas.

The OCA is a microcosm that in a sense reflects the real world, with the four classes

remaining unchanged despite increasing complexity. For instance, adding a gray state

could exponentially increase possibilities, but according to Wolfram’s tests, it does not lead

to more complex overall behavior.

This viewpoint suggests that these four classes cover

most orders found in real life, and the same applies to increasing dimensions, such as the

well-known two-dimensional “Game of Life.” Research has also been conducted on a

three-dimensional version of the game, but overall, it does not introduce new types; they

all fall into Class IV.

3.2.2 The Significance of “Parts”

Why does Fujimoto place so much emphasis on the part? First of all, it should be pointed

out that the different attitudes toward parts and wholes are one of the fundamental

differences between contemporary science and complexity science.

The relationship between the whole and its parts has been a fundamental concept in

both philosophy and the realm of scientific exploration. Discussions on the interplay

between “parts” and “wholes” have been ongoing since the time of Aristotle. In the era

dominated by classical physics, it was posited that the whole could be understood simply

as the sum of its parts. However, with the advancement of systems science, it became

apparent that the whole surpasses the sum of its parts. Subsequently, with the advent of

fractal theory, a new understanding emerged that parts and wholes exhibit self-similarity.

The discourse on the dynamics between parts and wholes transcends time, reflecting a

continual evolution of thought.

Wolfram, A New Kind of Science, p62.

Tong Wu, “分形方法及其意义(Fractal Method and its Significance),” Journal of Inner Mongolia

University (Humanities and Social Sciences), Vol.31, No.4 (July 1999): p85.

92 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

Modern science believes that if a problem is too complex to be solved all at once, it

should be broken down into smaller parts which can then be solved separately. For example,

we can gain knowledge of life by dissecting it to understand the organs and tissues of the

organism. An understanding of the whole can be gained by breaking it down into individual

parts and studying them. This approach to the relationship between the whole and its parts

is also known as reductionist or analytical methodology. Some extreme reductionists even

believe that all biological and psychological phenomena can be gradually analyzed into

parts through reductionist analysis. Ultimately, all living and psychological phenomena

can be reduced to physical and chemical phenomena, and thus, in principle, biological laws

can be explained by physical and chemical laws.

However, complexity science challenges this perspective. Complexity scientists

believe that when life is dissected and destroyed, life as a whole no longer exists. As organs

are only part of the whole, they cannot provide all knowledge about the whole. In many

cases, the whole is not the sum of its parts. The whole is the whole, and many of the features

that it possesses cannot be obtained by simply adding up the parts. The detailed study of

parts does not necessarily provide effective knowledge of the whole. For example, no

matter how in-depth the study of cells is, it cannot explain consciousness. Complexity

science advocates starting from the whole, while observing the relationship between parts

and the whole; that is, how the parts are combined in such a way as to lead to the emergence

of the whole.

Secondly, as Fujimoto notes, complexity can only be approached from bottom up,

starting from the “parts.” A top-down approach cannot create complexity. This refers to

the way complex systems are generated, and is a common method of logical thinking that

is used in studying complex systems—reverse causality. Complex systems emerge layer

by layer. Basic particles form atoms, atoms form molecules, molecules form organelles,

organelles form cells, cells form tissues, tissues form organs, and finally, nine organ

systems form the whole bodies. Each “temporary” whole is generated by the “temporary”

parts of the previous level interacting in some way. This needs to evolve dynamically in

time and space. The whole is thus generated from the lowest level. Paying attention to the

“relationship” that is expressed by Rule 110 brings Fujimoto’s various discourses into

focus; one can discover that “weakness,” “forest order,” “Musical Notes Without Staves,”

and many other of Fujimoto’s design ideas are built on this point.

3.2.3 The Function of “Numerous Constituents”

In October and November 1984, two seminars on complexity attended by scholars from

various disciplines were held in Santa Fe. One of the common conclusions drawn at the

Xinrong Huang, Tong Wu, “从简单到复杂：复杂性范式的历史嬗变 (From Simplicity to Complexity:

The historical evolution of the complexity paradigm),” Journal of Jiangxi University of Finance and

Economics. 2005, No.5, Serial No.41. p81.

3.2 Pivotal Aspects for the Advent of Complexity 93

meetings was that the core of any disciplinary problem is a system composed of many,

many “agents.”

The primary precondition for a system to become a complex one is to have “a large

number of independent individual actions.” For example, the behavior trajectories between

three spheres are very chaotic and general mathematical methods cannot handle them,

resulting in chaos. However, the enormous quantity of gas molecules in a closed system

exhibits simplicity and consistency in macroscopic aspects such as temperature, pressure,

and density, such that their states can be easily calculated by statistics.

Similarly, a small number of individuals cannot affect the market or stock market, but

a large number of individuals can generate vaguely discernible collective behavior. A few

molecules cannot form a living organism; a few neurons cannot form a highly functional

brain; a few species cannot form an ecosystem; all these complex features depend on the

number of individuals, which needs to reach a certain scale.

Haken defines complexity from the perspective of self-organization, stating that

synergetics studies various systems composed of a large number of subsystems (such as

electrons, atoms, cells, neurons, mechanical elements, photons, organs, animals, and even

humans) of completely different natures, and investigates how these subsystems cooperate

to produce spatial, temporal, or functional structures at a macroscopic scale.

In general, the emergence of macroscopic patterns in a complex system depends on

the interactions of a large number of individuals at the microscopic level. Quantity is a key

factor in the formation of complexity.

3.2.4 The Metaphor of the Cloud

One does not need to dive into the details of the terms “nebulous” and “cloud” to

understand that both are neither as orderly as “homogeneity” nor as disorderly as

“equilibrium.” These concepts, which are favored by many Japanese architects, have a

metaphorical connotation:

With clouds replacing clocks, a revolution in thinking was under way, that can best be

understood by opposing it to the dominant world view, by contrasting the Post-Modern

sciences of complexity with the Modern sciences of simplicity.

Here Charles Jencks adeptly delineates the relationship between complexity science and

the concept of the cloud. This metaphor, far from being an abstract notion, is rooted in the

Waldrop, Complexity, p88.

Tong Wu, “论协同学理论方法——自组织动力学方法及其应用 (On the Methodology of Synergy—

Self-organizing Dynamics Method and its Application),” Inner Mongolia Social Sciences. 2000, Vol.124,

No.6. p19.

Jencks, The Architecture of The Jumping Universe, p31.

94 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

empirical observation of cloud systems, showcasing early investigations into the nature of

complexity.

At the outset, the “regularity” observed in cloud formations (Fig. 3.31) serves as a

gateway to understanding the underlying principles of fluid dynamics. This regularity,

particularly evident in the liquid manifestation of eddies, provides an intuitive glimpse into

the orderly patterns that emerge from fluid behavior.

[Fig. 3.31] The pattern of cloud. [Fig. 3.32] Eddies behind obstacle.

At their core, clouds, irrespective of their composition—be it air, water, or any

conventional fluid—exemplify fluid flow driven by the movement and interactions of

molecular particles. Their behavior underscores a universal characteristic of fluid dynamics,

revealing that, at a systemic level, the principles governing their macroscopic regularity

are remarkably consistent.

The phenomenon of turbulence, one of the most intricate aspects of fluid dynamics,

exemplifies this principle. The formation of eddies behind a stone in a stream, triggered by

differential flow speeds, illustrates a visible form of regularity (Fig. 3.32). As the flow

increases, these eddies elongate until a critical velocity is reached, at which point they

disintegrate, giving rise to a multitude of new eddies. (Fig. 3.33) This process unfolds a

complex yet discernible pattern of regularity, emblematic of the dynamic interplay between

order and chaos.

[Fig. 3.33] When a speed threshold is reached, a whole street of eddies is formed behind the object.

3.2 Pivotal Aspects for the Advent of Complexity 95

On the other hand, these molecules are discrete particles, each with its own

randomness. However, this micro-level randomness does not directly correlate with the

macro-level randomness observed, for example, in the dispersing forms of clouds. Stephen

Wolfram simulated this type of fluid turbulence using cellular automata (CA) and

concluded that the apparent randomness of clouds is not derived from micro-level

randomness but is an inherent systemic randomness. There is no direct link between

randomness at these two levels, implying that the “system” of the cloud inherently

generates macro-level randomness, and the seemingly random patterns are actually

complex. Wolfram noted that the behavior of Rule 225 (which exhibits another Class 4

behavior) is reminiscent of turbulent fluid flow,

further illustrating the complex interplay

between discrete elements and emergent, systemic properties.

3.2.5 The Nature of Telescopic Nesting

[Fig. 3.34] Left: New Library Museum of Musashino Art University.

[Fig. 3.35] Middle: House N.

[Fig. 3.36] Right: Spiral House Project.

In the New Library Museum of Musashino Art University and House N, Fujimoto

masterfully employs the principle of “Telescopic Nesting,” which has conceptual echoes

of the Russian Matryoshka doll, to weave a narrative of architectural harmony through

repetition and scale. This technique not only reveals a meticulous attention to structural

detail but also a profound engagement with the concept of self-similarity. Within these

spaces, whether through the stark uniformity of white boxes or the rhythmic continuity of

wooden shelves, Fujimoto achieves a seamless homogeneity. By stripping back nearly all

architectural detail, he allows the essence of form and function to speak volumes. The

deliberate perforations across both wall and rooftop surfaces further unify the architectural

experience, manifesting a visual and structural consistency that at its core exemplifies self-

similarity.

This architectural approach directly intersects with a foundational concern of

complexity theory: fractals. The synergy between fractals and complexity unveils a

fascinating exploration of how simple, iterative processes can give rise to patterns of

Wolfram, A New Kind of Science, p376.

96 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

intricate beauty and complexity, offering profound insights into both the natural world and

human societal structures. The study of fractals permits a deeper understanding of the very

nature of complexity, including its structural dynamics and evolutionary tendencies, and

positions fractals as a pivotal concept in the discourse of complexity science across various

fields.

Indeed, fractals serve not merely as metaphorical representations but as analytical

tools within specific contexts, offering a quantifiable measure of complexity. In the

discipline of architecture, the confluence of fractals and complexity has prompted studies

that either equate the two or employ fractal analysis as a method for assessing architectural

complexity.

While the concepts of telescopic nesting and self-similarity may encompass a broader

spectrum than fractals, the latter is distinguished by its mathematical precision and the

fascinating patterns it reveals through the application of simple, repetitive rules. Although

not every manifestation of self-similarity qualifies as a fractal in the strictest sense, their

deep-seated connection to the fabric of complexity cannot be overstated. These concepts,

crucial for describing intricate structures, have captivated scholarly attention across

disciplines since the 1970s, contributing significantly to the multifaceted portrait of

complexity science alongside theories of dissipative structures, synergetics, hypercycles,

and punctuated equilibria.

3.2.6 The Essence of Self-Organization

As introduced in 2.1.1, self-organization provides a definition of complexity.

Originally a concept in biology, self-organization has gradually expanded to

fundamental fields such as physics and chemistry, and even to economics, anthropology,

ecosystems, and stellar motion. It is a major research strand of complexity science and was

a key focus of research in the 1970s. The representatives of this field are the Brussels school

of Prigogine and the Synergetics of Haken. Prigogine’s dissipative structures focus on the

conditions for self-organization, while Haken’s Synergetics focus on the dynamics of self-

organizing structures.

These two schools make up the main body of self-organization

science. The Santa Fe Institute has always regarded self-organization as a central concept

of complexity theory. John H. Holland believes that self-organization is one of the core

features of complex adaptive systems (CAS). Gell-Mann locates the occurrence of self-

organization at “the edge of chaos.”

In the architectural discipline, self-organization also serves as a lens through which

architectural studies explore the myriad definitions of complexity. Moreover, the

emergence of structure, a natural outcome of self-organizing processes, inherently links

Tong Wu, “Outline for Self-organizing Methodology,” Journal of Systemic Dialectics. 2001, Vol.9, No.2.

p8.

3.2 Pivotal Aspects for the Advent of Complexity 97

self-organization with the principle of emergence, further solidifying its role as a

foundational concept within complexity theory.

This reveals that Fujimoto’s architectural philosophies, particularly his advocacy for

“architecture without architects” and his fascination with the organic randomness of Italian

hill towns, are deeply rooted in the narrative of complexity.

3.2.7 The Role of Randomness

While not a prerequisite for complexity, randomness acts as a vital catalyst within many

complex systems. It introduces a layer of uncertainty and diversity essential for the

evolution of complex patterns and structures. From the genetic mutations that drive

biological evolution to the stochastic behaviors that shape social and economic structures,

randomness is a fundamental force that underpins the dynamic and multifaceted nature of

complex systems.

Furthermore, randomness influences nonlinear feedback loops, amplifying minor

variations into significant systemic changes. This sensitivity to initial conditions can lead

to unpredictably complex behaviors and structural formations.

In the quest for optimization and exploration, randomness transcends local optima,

guiding systems toward more efficient or diverse solutions. Whether through genetic

algorithms or complex adaptive systems, randomness fosters an environment where

exploration and adaptation thrive, facilitating the emergence of complexity in physical,

chemical, biological, and social systems.

Through this lens, Fujimoto’s architectural endeavors can be seen as a microcosm of

the broader, intricate dance between order and chaos, structure and fluidity, that defines

the pursuit of understanding in complexity science.

3.2.8 The Perception of Centerlessness

Centerlessness is an important characteristic of complexity. The concept of “centerlessness”

can be understood from two aspects. One is from the perspective of the process, which

manifests as lack of central control, as discussed in the previous section on self-

organization.

In nature, it is neither feasible nor effective for organization to be upheld by

centralized control. Instead, order is achieved and sustained through the principle of self-

organization. Such systems are capable of adapting to standard environmental conditions,

responding to alterations in their surroundings via thermodynamic processes. This adaptive

response grants these systems remarkable flexibility and resilience, enabling them to

withstand external disruptions.

Christof K Biebracher, Gregoire Nicolis, and Peter Schuster. “Self-Organization in the Physicochemical

and Life Sciences,” Report No.EUR 16546 (European Commission, 1995), p1.

98 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

In a simple system, control often concentrates in one or a few local areas. In a complex

system, the control is usually diffuse, as if there is a control center, and the actual control

and power are spread out in a decentralized structure, which produces the particular

behavior of the system through the union of certain units.

Such characteristics provide

complex systems with a certain adaptability and resilience. As there is no single point of

failure, the system can continue to function even if parts of it fail. This distributed nature

helps in managing complexity by allowing local adaptations that can better respond to local

conditions or challenges.

The other aspect is from the perspective of the result, where the final overall pattern

presents a state of central loss. This centerlessness is a more subjective and vague concept.

For example, in living organisms, we can often observe symmetries, or “centers” such as

“trunks.” In economic concepts, we can also clearly understand that certain economies are

often regarded as “centers” because of their greater influence. Such a centerless overall

model is also shown in Rule 110, yet clearly this still has some “content” that might be

regarded as a kind of “central” feature. However, any judgment here requires “subjective”

participation. The reason for this situation is the coexistence of order and disorder.

3.2.9 The Symbol of the Co-existence of Order and Disorder

As introduced in 2.1.7, this phenomenon—which can be observed during the transition

between phases—has always fascinated scientists. The coexistence of order and disorder

is considered by many to be a sign of complexity.

For example, in their book Signs of Life, Solé and Goodwin describe it as follows:

Ecosystems show well-defined regularities, but populations often fluctuate wildly.

The brain stores extraordinary amounts of information, but its activity, as revealed by

an electroencephalogram, is far from regular. Our cities are large-scale structures with

a long history, but their growth is often almost organic […] Thus complexity is neither

complete order nor complete disorder.

Immediately after this description, the authors introduce complexity, using three pictures

to explain it:

The structure is neither totally random nor completely ordered. We observe triangles

of many different sizes, and in between we can see domains of disorder. We perceive

some underlying structure at many different scales. This pattern is complex.

Here, the authors’ assessment of complexity is based on the coexistence of order and

disorder.

Wu, “Objective Complexity in the View of Philosophy of Science,” p46.

Solé and Goodwin, Signs of Life, p33.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 99

Morin also discusses complexity from the perspective of order and disorder. He

believes that it is meaningless to discuss these two concepts separately because they are

both very rich in meaning and can even be interchangeable in many cases. Neither is more

or less important than the other, and they cannot simply be separated from each other

because they are always intertwined: “A deterministic universe and a completely random

universe are both impossible.”

It is only by combining order and disorder that the world

can be formed and life can appear and evolve.

The definitions of “effective complexity” by Gell-Mann and “the edge of chaos” by

Langton, and even Wolfram’s definitions of complexity, are all based on this common

perspective of the relationship between order and disorder. Although the definition of

complexity is not uniform, there is a general similarity within one type of complexity. This

type of definition assumes that complexity lies somewhere in the middle between order

and disorder. The coexistence of order and disorder is therefore closely related to the

emergence of complexity.

In general, the above points are key to the emergence of complexity and are central

to complexity research. Fujimoto emphasizes so many key points at once that it is clear

that he is referring to this kind of complexity.

3.3 Connecting with “Nihonteki na mono” (Japaneseness)

In the previous section, the conversation shifted toward complexity. However, if one traces

these different points back through the history of Japanese architecture, it becomes

apparent that they are not novel. They have been discussed repeatedly over history, each

with a distinct origin. Some can even be traced back to the roots of pre-war modern

Japanese architecture, which have been cultivated by generations. The integration of these

elements occurred around the year 2000. This implies that Japanese architects’ attention to

these aspects was not driven by an interest in scientific theories but rather by a focus on

what defines Japanese architecture. They are considered “Nihonteki na mono,” rather than

being understood in terms of “complexity.”

What is “Nihonteki na mono”？This concept has been known by various terms across

different eras. Before the war, it was referred to as Japonism,

and afterwards it was called

Japonica (which was almost synonymous with Japonism). The notion of “Japaneseness”

within architecture (“Kenchiku ni okeru, Nihonteki na mono”) can be traced back to

Architectural Style Essays (1932) (

建筑样式论叢

), edited by Sutemi Horiguchi and

including his papers “The Ideological Background and Composition of the Tea Room” (茶

Edgar Morin, Science avec conscience, trans. Yizhuang Chen (Beijing: Peking University Press, 2001),

p159.

The term mainly denotes the fascination with Japanese art that swept through Europe and America during

the latter half of the nineteenth century. Included in this artistic wave were Ukiyo-e prints, Buddhist statuary,

the tea ceremony, and architectural styles.

100 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

室的思想背景与其构成) and “On the Japanese Taste Revealed in Modern Architecture”

(关于现代建筑所显现的日本趣味). Arata Isozaki regarded this as the origin of the usage

of “Nihonteki na mono” in Japanese architectural studies, meaning a focus on “things

Japanese.”

In the 1980s and 1990s, a collection of essays by Arata Isozaki continued the exploration

of “Nihonteki na mono” in architecture, which was translated into English in 2003 under

[Fig. 3.37] The features delineated in Rule 110 are deeply rooted: each can be traced back to specific aspects

of Japanese history.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 101

the title Japan-ness in Architecture (Kenchiku ni okeru, Nihonteki na mono), with

“Nihonteki na mono” translated as “Japan-ness.”

There have been numerous discussions of “Japaneseness” throughout Japanese

history, with its content and direction constantly evolving. To describe this concept

succinctly, this dissertation borrows Fumihiko’s words: “Japanese” refers to “unique

phenomena that can only be found in Japan,”

representing the efforts and explorations of

Japanese architects in “bridging modern and national styles.”

The focus of this concept

varies across different periods. For ease of discussion, this dissertation adopts the more

neutral term “Japaneseness” to collectively describe the varying aspects of “Nihonteki na

mono” through different times.

3.3.1 “Architecture of Parts” in Japan

In the previous section, the research introduced the pivotal topic of “the relationship

between parts and the whole.” This theme is exemplified in both the Sendai Mediatheque

and House SA.

As previously discussed in the section on the research background, the Sendai

Mediatheque is a significant architectural achievement dating from the turn of the century.

The Sendai Mediatheque also demonstrates a focus on “parts.” In a lecture at Harvard

university titled “New Innocents,” Fujimoto stated that the columns in the Sendai

Mediatheque were reduced in size from their original solid form, resulting in a surprisingly

unique environment. He then mentioned that his own “stairs” were inspired by Sendai

Mediatheque, with the floorboards also reduced in size. Thus, the primary elements of the

two houses, columns and floorboards, were logically and similarly reduced in size,

resulting in two works which seem different but actually demonstrate a similar approach.

Fujimoto refers to this approach as “successfully changing the object to space.” Here, the

Sendai Mediatheque’s “columns” and Fujimoto’s “floorboards” are further divided into

“parts” (Fig. 3.38) (Fig. 3.39).

Similarly, in the House SA, the fragmented “parts” are prominent both in the

appearance of the building and the experience of the space. Each element in architecture—

roof, enclosure, site, structure—acts according to its own purpose, as Sakamoto himself

explains:

Through this composition, each component responds to external conditions

independently based on its own purpose rather than being hierarchical or unified. Each

Taro, Nihon Kenchiku Nyumon, p138.

Arata Isozaki, Japan-ness in Architecture, ed. David B. Stewart, trans.Sabu Kohso (The MIT Press, 2006),

p261.

102 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

part forms a relationship of parallel and coexistence, creating a fragmented and non-

conclusive space.

This arrangement is similar to that of individuals in a complex system—without central

control—and the whole is formed by the actions of individuals. This approach has resulted

in the overall form of the architecture and its aesthetic considerations being ignored.

[Fig. 3.38] Left: Sendai Mediatheque.

[Fig. 3.39] Right: Primitive Future House.

Moreover, the broken spiral structure conforms to the shape of the site. In this way,

the “spiral structure” itself, together with other elements of the building, becomes a “part”

that is somewhat independent yet also interconnected. A “clear and distinct” composition

is avoided, resulting in an “ambiguous” feeling of opposition and confrontation. This

“ambiguous” feeling arises from a bottom-up approach to the “parts” of the building.

[Fig. 3.40] House in Sanda. [Fig. 3.41] Machiya in Minase.

Shunsuke Kurakata, The Poetics in Architecture. Dialogue with Kazunari Sakamoto, ed. Guo Yimi (Nan

Jin: Southeast university Press. 2011), p82.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 103

Fujimoto’s concept of a “box-in-a-box” in House N is also an exploration of the

relationship between parts. However, this idea was used extensively by Kazunari Sakamoto

over a long period of time during the 1970s. Back then, in Sakamoto’s early career, the

“box-in-a-box” was his signature design philosophy. House in Sanda (1969), (Fig. 3.40)

his debut, was designed on the basis of this idea.

At that time, due to the oil crisis, and various problems caused by the rapid

development of urban modernization, such as pollution, noise, environmental degradation,

and social security, Japanese architects began to create “closed boxes” that isolated

themselves from the outside world, forming an internal “utopia.”

In House in Sanda, the entire building is based on a large box, with small boxes

embedded inside as functional rooms. This constitutes the form of the “box-in-a-box.”

Some of these boxes have functional rooms, while others are embedded “protruding

windows” with “openness” implied. Guo Yimin explains that the “closed box” isolates the

outside world, and the new relationship formed between the composition of the small box

placed inside and the blank space creates an ambiguity between “inside and outside.” The

superimposed structure of the simultaneous presence of visual form (visually confirmed

existence) and perceptual form (objective existence that cannot be visually confirmed, such

as one’s own head) makes time concretize.

As has already been introduced in 2.4.2, creating closed boxes and forming internal

“utopias” was common practice in Japan in the 1970s. However, the practice of the “box-

in-a-box” is mainly attributed to Kazunari Sakamoto. Later, Sakamoto designed Machiya

in Minase (1970) (Fig. 3.41), Kumono-Nagareyama House in Yunono-Ryuzan (1973), and

House in Nago (1978), all of which formed closed spaces using the “box-in-a-box”

composition.

Kazunari Sakamoto emphasizes the significance of the relationship between parts and

wholes:

Within these contemporary types of spaces, the space I am most interested in, as noted

above, is that which continues through a chaining of parts […] The space formed by

this sort of composition is where the parts are articulated against the whole. Rather

than making the uniform or consistent space the dominant, this is space that is linked

and spread out. The whole is not homogeneous, but is a space that eliminates wholes

by having parts—or by being partitioned—and this can be thought of as open-form

space.

Yimin Guo, “对话概述——‘架构’-材料/形式-现实,” in The Poetics in Architecture. Dialogue with

Kazunari Sakamoto. edited by Guo Yimi (Nan Jin: Southeast university Press. 2011), p14.

Sakamoto, House: Poetics in the ordinary, p241.

104 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

[Fig. 3.42] Sakamoto’s “spatial arrangement construction methods.”

[Fig. 3.43] Sakamoto’s “box-in-a-box” arrangement.

[Fig. 3.44] Christopher Alexander’s semi-lattice versus a tree. A similarity can be seen between this image

and Sakamoto’s conceptual drawings, (Fig. 3.43) as well as Fujimoto’s House N. In Sakamoto’s three works,

the concept of the box expresses “closedness” and has no connection with fractals. According to Fujimoto’s

description, his “box-in-a-box” is related to telescopic nesting. Fujimoto describes imagining “nesting from

the palm-sized box, to furniture, to rooms, to buildings, to cities [...] all the way to the entire world,” and a

tendency toward “openness” is clearly manifested in the outcomes of this.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 105

Sakamoto’s comments here were echoed in Fujimoto’s words some decades ago. In the

section titled “The whole and the part in architecture—architecture as a spatial

arrangement,” Sakamoto even proposes a set of “spatial arrangement construction methods”

(Fig. 3.42) to elaborate on how he generates the whole by connecting the “parts.”

According to Sakamoto, his “spatial arrangement construction methods” apply not only to

architecture but also to the relationship between architecture and the city. Furthermore,

there is a deep connection between the non-homogeneous and non-integral space formed

by connecting the parts and the “open space” commonly seen in Japan. “The relationship

between parts” is so crucial to Sakamoto that he even describes it as “the most important

and even the root metaphor of spatial composition in architecture.”

If one continues to trace back, one can find that these two were not the first to

demonstrate an interest in “parts.” The 1972 Nakagin Capsule Tower was implemented

with the concept of “aggregation of parts into a whole.” This “aggregation of parts,” in the

words of Kisho Kurokawa, a major member of the Metabolist movement, is related to the

concept of capsules, which is also related to the Ise Shrine, in that it is movable, replaceable,

and renewable. However, this work is likely to have had a more direct connection with

Kurokawa’s visit to the Soviet Union in 1959 to visit prefabricated housing and factories.

According to Toyokawa Saikaku, Kurokawa was shocked by the degree of automation in

the housing industry during his visit to the Soviet Union and drafted the “Box-shaped

Prefabricated Apartment Plan” (箱式预制公寓计划) in his own office in 1962. He also

published a paper entitled “Mass-Produced Design Methodology” (量产设计方法论).

Soon afterwards, in 1970, Kurokawa designed the Takara Beautilion Pavilion, which

suspended capsules directly on a steel frame, for the Osaka World Expo.

During this period, Kurokawa did not widely promote the concept of “parts.” It was

not until the 1980s that the relationship between parts and wholes actually occupied a core

position in his thinking. His “philosophy of symbiosis,” “dissolution of binary oppositions,”

“Two-faced God Janus,” etc., discuss the relationship between parts and wholes. In 1986,

Kurokawa explicitly expressed that the relationship between parts and wholes as the central

issue of architecture in the new era, and that the “soft structure” generated by the

connection of “parts” can be found in the midst of chaos and is different from the design

ideas dominated by Newtonian physics.

Yoshinobu Ashihara also places the relationship between parts and wholes in a

prominent position. In his book Hidden Order, Ashihara compares Paris and Tokyo from

the perspective of “the relationship between wholes and parts,” pointing out that:

Paris is a city divided with foresight into parts “cut” from the whole, while Tokyo

follows the sense of the whole enveloping all its various parts […] Its (Paris’s)

Toyokawa, Tange Kenzo, p229.

Kurokawa, “An Architecture of Symbiosis: The Two-faced God Janus,” p42.

106 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

masonry architecture makes it, in a way, a static and inorganic monument of the past.

Tokyo, however, remains a synchronic whole, tenaciously surviving by rather an

amoebic adaptability.

Obviously, Ashihara was influenced by complexity science at that time.

Hiroshi Hara recognizes the importance of the relationship between parts and wholes.

In the article “Interview with Hiroshi Hara: Mathematics, Discreteness, Architecture,”

Hara uses the relationship between parts and wholes to explain his iconic concept of

“modality.”

The article explores the relationship between discreteness in mathematics

and architecture. Hara points out that, from the perspective of discreteness, there is an

inherent connection between mathematics and architecture. In mathematics, discreteness

refers to objects or concepts that can be decomposed into a finite number of discrete parts.

In architecture, discreteness is manifested in space being divided into discrete modules or

units, which are then combined, arranged, and transformed to construct architectural forms.

Thus, both fields share a focus on how parts form a whole. Furthermore, the article’s

extensive use of key words such as “discreteness,” “topology,” and “ordered” also implies

Harai’s interest in the relationship between parts and wholes.

It is evident that the relationship between “the parts and the whole,” a topic crucial to

complexity, was placed at the center of discussions in Japan from the beginning. Moreover,

at least initially, it was less related to the theory of complexity and more connected to what

is quintessentially “Japanese.” By slightly altering the concept of “the parts,” we can segue

into the next topic—“in-betweenness,” which, likewise, is distinctively Japanese.

3.3.2 “Gradation” in Japan

[Fig. 3.45] The variations of “in-between.”

Ashihara, The Hidden Order, p63.

Hiroshi Hara, “Mathematics, Discreteness, Architecture,” The Japan Architect, No.78. (Summer 2010),

p14.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 107

In the 1970s, a time marked by the collective enquiry of several leading architects, the

discourse converged on a singularly captivating concept: Fujimoto’s “in-betweenness”

(Fig. 3.45).

This topic, which is deeply intertwined with fractals, coincidentally aligns with

significant temporal markers: it emerged in 1977, just two years after a year of paramount

importance to chaos theory. Despite the absence of direct evidence linking it to the

prevailing scientific theories of that era, the underlying motivation for its exploration was

identical: to delve into the essence of what constitutes “Japaneseness.”

Kisho Kurokawa began by proposing the concept of “Rikyu Grey” (Fig. 3.46). Rikyu

Grey is a Japanese word pronounced as “りきゅうねず” or “りきゅうねずみ” and

translated as “Rikyu Mouse.” It is a shade of grey with a slight greenish tinge. In his book

Culture of Grey: The “Edge” of Japanese Space (灰调的文化——作为日式空间的”边

缘”), published in 1977, Kurokawa writes:

Rikyu Grey is a continuous state of coexistence or a non-sensory state formed by

conflicting and canceling multiple elements. Rikyu attempted to freeze time and space

temporarily through the color perception called Rikyu Grey, creating a two-

dimensional, flat world.

Kurokawa’s main point regards the dissolution of binary opposition; the coexistence of two

seemingly opposing elements rather than a black-and-white dichotomy. This idea is similar

to Robert Venturi’s contemporary “embrace of opposing elements” and provided the basis

for Kurokawa’s later “Symbiosis.”

[Fig. 3.46] Rikyu Grey. [Fig. 3.47] Inwardness (okusei).

One year after the publication of Culture of Grey, Arata Isozaki held an exhibition

called “MA.” MA is the Romanized spelling of the Japanese word for “gap.” The term

“MA” originally referred to the distance between two objects. However, what interests

Taro, Nihon Kenchiku Nyumon, p133.

108 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

Isozaki is the concept of “MA” in the expression of time and space, as well as in various

fields such as music, painting, gardening, architecture, comedy, and dance, where the idea

is highly valued. From this perspective, the concept of “MA” has been extended to the

context of Japanese words such as “Suki” (gap), “Yami” (darkness), “Utsuroi” (transience),

and “Sabi” (solitude), and has developed into an attempt to connect classical forms of

various artistic fields with modern Japanese art.

This exhibition is Isozaki’s introduction

to the roots of what he considers to be Japanese art to the Western world.

Around the same time, Fumihiko Maki published City of Veiled and Unveiled (1980)

(

若隐若现的城市

) and The City and Inner Space, introducing the terms “Interstice,”

“inner space” (Fig. 3.47), “folding and pleating,” etc. to express the layered Japanese space.

Maki also compared the cities of Europe and Japan, and described the outline of European

cities as being clearly defined, which is a Gestalt switch—a relationship of either/or. In

contrast, the boundaries of Japanese cities are ambiguous and intertwined, with a complex

and difficult to distinguish web of relationships between them:

If we use a bold line to represent an object that completely separates inside and outside,

then the boundaries in Japan can be understood as a collection of dashed lines or

multiple thin lines. In other words, the domains do not play a role in clearly dividing

inside and outside or left and right. The areas that should be clearly divided become

ambiguous due to the simultaneous existence of left and right and inside and outside.

The plan of Japanese houses, which already makes use of eaves, projecting eaves, and

paper sliding doors, shares this overlapping of inside and outside environments. In

this sense, it is not surprising that one may have a similar sense of boundaries or

marginality in a broader urban environment.

Yoshinobu Ashihara held the same opinion of “in-betweenness.” In his The Hidden

Order: Tokyo Through the Twentieth Century, Ashihara criticized Western dualistic

thought, and claimed that Westerners, since the time of the Greek philosophers, had been

reluctant to deal with intermediate territory. Japan, on the other hand, celebrated and

embraced this ambiguity and incompleteness.

Another concept related to “in-betweenness” at that time was that of the “square.”

Like “in-betweenness,” it focused on boundaries and continued the pursuit of

“Japaneseness.” Architects at the time noted that the squares of Europe and the streets of

Japan constituted the main difference between the two regions. Kurokawa once remarked:

“Oriental cities have no squares, and Western European cities have no roads.” Kurokawa

recognized the road, which was originally an external space, as an architectural space—an

Toyokawa, Tange Kenzo, p218.

Taro, Nihon Kenchiku Nyumon, p138.

Ashihara, The Hidden Order, p54.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 109

internal space—in order to revitalize the street (narrow alley) and create the architecture of

street.

Similar expressions can be found at the entrance of the Museum of Modern Art

Saitama, where architects used a geometric framework similar to the building itself to

create a transitional space from indoors to outdoors. Yoshinobu Ashihara’s series of works

on “external space design,” including Cityscape Aesthetics and Exterior Design in

Architecture, also originated from this period. They can all be seen as explorations of

Japanese space from the perspective of “in-betweenness.”

Thus, Fujimoto’s concepts of “in-betweenness,” “gradations,” “inside-outside,” and

so on, are not at all new, but rather identical to the notions mentioned above. As a matter

of fact, even Kurokawa was not the first to identify this difference between Japan and the

West—all these concepts can be traced back to 1933, when Junichiro Tanizaki’s In Praise

of Shadows was published. In this book, traditional Japanese aesthetics is contrasted with

Western cultures, and the discussion of “layered tones of various kinds of shadows” in

particular has been widely circulated among Japanese architects. All of these texts identify

the same thing: the unique space of Japan is different from Western Europe (or transcends

Western Europe). They all share a desire to remove explicit boundaries. They are all the

result of architects’ search for “Japaneseness” at that time. The pursuit of localism can be

traced back to this period, when Japan explored its own strand of modernism, which was

demonstrated by a unified and consistent output.

Embarking from the granularity of parts, we transition toward the idea of “gradation.”

Should the entirety be woven from these gradations, we encounter a further abstraction—

“clouds.”

3.3.3 “Clouds” in Japan

This motif, deeply embedded within the Japanese aesthetic, resonates widely across its

architectural landscape.

Early in 1986, Hiroshi Hara explored the concept of “steam.” Hara aimed to strip away

materiality in the representation of objects, crafting an ambiance akin to “steam.” In his

quest for an image resembling “steam” within nature, he found that it could be observed in

phenomena such as clouds, fog, rainbows, and mirages. These natural manifestations are

not only translucent but are also constantly evolving. At their core, their shapes and

meanings are formless and indistinct, as are their boundaries.

Similarly, in three

consecutive articles—“Dissolution of objects and evasion of the city,” “Relativity of

materials,” and “Particle on horizontal plane”—Kengo Kuma uses the concept of the

“rainbow.” Kuma believes that the most perfect state of architecture is like a rainbow. He

Taro, Nihon Kenchiku Nyumon, p135.

Hiroshi Hara, “On the ‘Drifting Space’ and the Architectural Forms,” The Japan Architect, No.11 (Autumn

1993-3) p26-31.

110 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

states: “My goal is not to create architectural works that are like particles; I want to create

an environment that is itself ambiguous and indistinct, like floating particles. The best

representation of this state is a rainbow.” Here, “particulate” and “miniaturize” have the

same meaning. Kuma’s explanation is that traditional Japanese architecture uses very small

elements as building materials: wood, paper, and sometimes stone. Generally, there is

space between these small elements that allows the building to breathe. If the materials are

broken down into particles, they will become livelier and change in an instant, just like a

rainbow. Sometimes they behave like real objects, but with changes in light, they may

disappear like clouds or dissolve like mist. Junya Ishigami also favors the concept of

“clouds.” Discussing the “Tables for a restaurant” project, (Fig. 3.48) Ishigami notes:

“What came to mind was something gentle, almost like a cloud.” In this small restaurant,

Ishigami designed five large tables filled with potted plants, while people were arranged in

one corner of the table. The entire space is divided by plants of different densities. The

tables and plants serve to delineate different areas.

[Fig. 3.48] Tables for a Restaurant by Junya Ishigami.

[Fig. 3.49] Left: New Mercedes Benz Museum Competition (2002).

[Fig. 3.50] Middle: Christian Dior Building Omotesando (2003).

[Fig. 3.51] Right: Extension of the IVAM Competition (2002).

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 111

[Fig. 3.52] Left: Fukita Pavilion in Shodoshima (2012-2013).

[Fig. 3.53] Right: Teshima Art Museum (2010).

The concept of “clouds,” as seen in the literature, appears frequently in Japanese

architecture, (Fig. 3.49; Fig. 3.50; Fig. 3.51) and is said to have originated from the

reflections on modernism in the 1960s. Riichi Miyake also highlights that a core principle

of modernism is the notion that the world exhibits a consistent homogeneity, as seen in

Mies’s creations. Yet, among the newer wave of architects, this perspective is evolving.

These innovators are striving to introduce varied densities, diverging from the uniformity

that characterizes modernism. Japanese architects, in particular, have shown a preference

for clouds, which naturally embody non-homogeneous and fluctuating densities. This

inclination is deeply intertwined with the “Japaneseness” that defines architects who draw

inspiration from their indigenous culture.

3.3.4 “Centerlessness” in Japan

“Centerlessness” is another common motif in Japan; clearly, one of the main features of

clouds is their lack of a center.

Many of the characteristics exhibited by Japanese architecture during the late 1980s

have determined some of the values held in contemporary Japan, and “centerlessness” is

one of them. As early as 1981, Toyo Ito’s House in Kasama exhibited a multi-centered

space.

The building inserts one long rectangular shape abruptly into another. It is difficult

to identify the center of the building from the plan, as it is composed of multiple centers

working together.

In 1988, House F (Fig. 3.54), designed by Kazunari Sakamoto, exhibited an even

more pronounced feature of centerlessness. House F is the first work from Sakamoto’s

third period (the first two periods being “closed box” and “house type”). In this private

residence, all the building elements have a strong tendency to “do their own thing.” The

roof, structure, enclosure, and site are all determined according to their respective “needs.”

The combination of these scattered parts creates a fragmented form lacking in unity or

overall shape. There is no main facade, and there is no absolute center in the space:

Riichi Miyake, “Initiation to Nature,” The Japan Architect, no.363 (July 1987): p7.

112 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

centerlessness is manifested in its appearance as a lack of totality, which is also known as

fragmentation, miniaturization, or an anti-object aesthetic.

In addition, by comparing House F with another of Sakamoto’s early works, Sanda

House, one can also see the architect’s approach to dispersing the center. Sanda House is

a house with a “center-seeking” attitude. Only one pillar stands in the center of the house,

which has a strong symbolic meaning. House F, on the other hand, is composed of many

scattered pillars, and its center is cancelled, as the architect’s focus is not on emphasizing

the house, but rather on creating freedom in the vertical dimension.

In the subsequent House SA, (Fig. 3.55) Sakamoto’s decentralized approach became

even more apparent. Shunsuke Kurakata comments that:

No matter where you are, you don’t feel the center of the space, and every space is

swaying [...] The folded ceiling is determined by the position of the OM SOLAR solar

panel system, while the arrangement of the floor and shelves reflects the requirements

of structure and function. No design basis occupies a dominant position, However,

the interrelationship between them is not lost

[Fig. 3.54] House F. [Fig. 3.55] House SA.

During this period, the social and public aspects of architecture were commonly

discussed in literature. As is shown in Sakamoto’s work at this time—in contrast to his

work in the 1960s—architects began to open up buildings, engage with the city, and shift

the focus of design from residential to public buildings. This series of changes is often seen

as an “open” trend occurring around the 1980s.

Yimin Guo, “Dialogue with China: ‘Architecture’- Material/ Form-Reality,” in The Poetics in Architecture.

Dialogue with Kazunari Sakamoto, p23.

Shunsuke Kurakata, “The Modernist Poetics That Did Not Appear Suddenly,” in The Poetics in

Architecture. Dialogue with Kazunari Sakamoto, p91.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 113

[Fig. 3.56] House in China (2003) by SANAA. The plan is similar to Fujimoto’s Seidai Hospital Annex

project (Fig. 3.26), with no traffic space or central control.

However, it should be noted that the topic of decentralization is not only related to

complexity, but also has a significant overlap with the destructive side of postmodernism.

Words like “decomposition,” “fragmentation,” “deconstruction,” “dislocation,” and

“dissolution of integrated entity” played a crucial role in Japanese architectural discourse

during this period. Sakamoto himself explained that in his early “house-type” works, the

scattered arrangement of certain elements was influenced by postmodernism. However,

when it came to House F, this influence became something from which Sakamoto

deliberately tried to distance himself.

Returning to the concept of “centerlessness,” it also implies “equivalence of space.”

This was most clearly demonstrated in the completion of the Sendai Mediatheque in 2000,

where not only was the center of each floor avoided as much as possible, but even the

center in a vertical sense was deliberately eliminated by the architect. Sakamoto comments:

the feeling of quickly passing through each thin layer of floor in the meshy elevator.

In this way, the places on each floor alternate quickly, and the resulting space makes

one not feel the existence of the building element: floor.

The different floors in the building are therefore equivalent and decentralized. This

decentralization in both horizontal and vertical directions clearly produces a certain

ambiguity, which is another popular idea in Japanese architecture.

Yimin Guo, “Dialogue with China: ‘Architecture’- Material/ Form-Reality,” in The Poetics in Architecture.

Dialogue with Kazunari Sakamoto, p16.

Kazunari Sakamoto, “Conversation with Toyo Ito: Institutions/ Consumption/ Symbols,” in The Poetics in

Architecture. Dialogue with Kazunari Sakamoto, p61.

114 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

3.3.5 The Evolution of “Japaneseness”

It is evident that there exists a logical inference among the aforementioned points:

proceeding from parts leads to gradients, and if the entirety is formed by gradients, clouds

are produced. Consequently, clouds, by nature, are centerless—a consequence of beginning

with parts.

“Parts” is a key topic and the notion of the “particular” is inherently “Japanese”

because Japanese cities are developed on the basis of “parts.”

As mentioned earlier, with the slowdown of the economy and the contraction of

capital, architects gradually awakened from the “happiness” of the 1960s and began to

think calmly about reality. This period, according to most historians, was when the idea of

utopia began to collapse, which was marked by Expo’70. The so-called “reality” of the

time was, in one respect, the catastrophic nature of Japan.

As has been mentioned, Japan is a country with frequent earthquakes, and major

earthquakes have had a profound impact on the Japanese architectural industry. These

disasters have brought about enormous changes in Japanese architecture and have led to an

increased sense on the part of Japanese architects of Japan’s catastrophic nature. The ideas

of modernism completely ignored Japan’s problems. Japanese cities have been plagued by

disasters since ancient times, with frequent earthquakes and fires, often requiring large-

scale reconstruction. This phenomenon has not changed since the Meiji period and, coupled

with the bombing of the Allied forces during World War II, means that urban

reconstruction has often appeared as a form of partial renewal, resembling a forest fire.

However, modernism imagined entire cities in a top-down way, ignoring the locality and

chaos of Japanese cities. Modernism failed to understand Japanese cities, which did not

undergo modernization in the same way as the West. Modernism did not simply arise for

Japanese cities, it was born in the soil of Europe, and its methodological framework could

not regulate the chaos and conflict in Japanese cities.

On the other hand, Japan’s urban environment underwent tremendous changes during

rapid modernization. After the Meiji Restoration in 1868, Edo was renamed Tokyo and

became the capital. A series of events followed, including the collapse of shogunate legacy

and the disappearance of feudal monarchy. The relationship between the ground and

architecture was destroyed. Following physiocratic ideology, gardens were converted into

agricultural land. Ways of using land changed constantly, and the rapid development of the

city under a program of total Westernization brought about environmental problems.

Combined with the fires and earthquakes mentioned earlier, as well as the atomic bombing

of Hiroshima and Nagasaki during World War II, each of these events had the potential to

completely reshape the city. Even beyond the Meiji era, Tokyo’s cycle of destruction and

reconstruction persisted. Tokyo underwent frequent phases of ruin and renewal, on a scale

unparalleled elsewhere. The approach to modern city planning in Tokyo failed to offer a

holistic understanding of the city’s inherent cycle of transformation. It is apparent that

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 115

Japanese cities are perpetually renewed from the “parts,” akin to the “forest” mentioned in

section 3.1.4.

The Ise Shrine achieves permanence through the replacement of parts, a concept

regarded by Japanese architects as inherently “Japanese.” This principle of part

replacement, embraced by the Metabolist movement, originates from there. The “Shikinen

Sengu,” a ritual reconstruction every twenty years, not only maintains the shrine’s purity

but also reflects the Japanese cultural understanding of nature and life. Whether it is Kisho

Kurokawa’s Nakagin Capsule Tower or Kiyonori Kikutake’s own residence, there is a

focused attention on “parts.”

Thus, the thread of “Japaneseness” comes into view. Upon exploring what constitutes

“Japaneseness,” it can be seen that its characteristics vary across different periods, and

while they are not necessarily related to the complexity explored in natural sciences, they

bear striking similarities.

The post-war era: Junichiro Tanizaki and Sutemi Horiguchi

This era’s understanding of “Japaneseness” bore no direct ties to complexity theory, yet

the discussions ventured into the heart of complexity. As previously mentioned, Sutemi

Horiguchi’s Architectural Style Essays”(1932), which featured an essay by Horiguchi,

marks the genesis of “things Japanese.” In this period, under the guidance of Riki Sano

from the Tokyo University Structural School, there was an initiative to rationalize Western

elements through a scientific lens, emphasizing earthquake and fire resistance, which then

became the architectural orthodoxy. Conversely, Sutemi adopted a markedly different,

even conflicting, stance, departing from orthodoxy with Eastern and Japanese styles.

Simultaneously, Junichiro Tanizaki’s In Praise of Shadows (1933) depicted

Japaneseness through the lens of shadow and subtlety, embodying a broader spectrum of

perception, experience, and culture akin to a collective unconscious. In his 1944 essay “On

the Issue of a National Architectural Style for Japan” (日本国民建筑样式的问题),

Ryuichi Hamaguchi, a peer of Kenzo Tange, highlighted the Japanese predilection for

action and space over the Western inclination toward objects and construction. Arata

Isozaki lauded this as “a nuanced modernist interpretation of Japan.”

Therefore, in this timeframe, “things Japanese” included tea rooms and sukiya-style

architecture, which epitomized a particular style and stance. Between the 1930s and 1940s,

Japanese identity and complexity theory seemed disparate, yet the dialogue on the former

broached a subject central to complexity’s goal: the interplay of behavior and perception—

a theme that remains a focal point for Japanese architects.

Isozaki, History of Japanese Architectural Thought, p107.

116 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

1950s-1960s: Kenzo Tange and Metabolism

During these decades, the dialogue between Japaneseness and complexity was nuanced and

occasionally paradoxical, with Japaneseness at its core. This era spotlighted certain temples

as archetypes of Japanese architecture, from which Japanese architects derived ideas

resonant with complexity’s essence: life.

This epoch in Japanese architectural philosophy showcased two dominant narratives:

the influence of information theory and cybernetics in Tange’s work, and the Metabolist

movement’s “Declaration of Life,” both of which were reflective of a cognitive shift.

Nonetheless, “complexity theory’s” influence on Japan was minimal and somewhat

contradictory.

Kenzo Tange emerged as a pivotal figure, with modernism reigning as the prevailing

philosophy in Japanese architectural thought. Modernist architecture, rooted in the classical

science worldview, was mechanical, reducible, centrally controlled, deterministic, and

predictable—precisely the concepts “complexity” thinking sought to challenge. Despite his

staunch modernism, Tange was among the first to elevate information theory, a key facet

of complexity science, thus demonstrating the most direct engagement with “complexity”

science in Japan at the time.

However, complexity thinking seemed to resonate with the Metabolists—through

both their moniker and philosophies—yet a direct connection to complexity at a

foundational level remained elusive.

In his graduation thesis of 1928, Bertalanffy describes the system of organic organisms

which awakened modern scientific interest in complexity. According to George Cowan,

Bertalanffy’s work marked the birth of complexity science.

In his General Systems

Theory, Bertalanffy states that living organisms are maintained by the constant exchange

of components, and the fundamental characteristic of a living system is metabolism.

can be said that complexity science was born in the field of organic organisms. Life has

always been a typical problem of complexity. The original meaning of “metabolism” is

intimately connected with complexity science. Schrödinger defined life from the

perspective of metabolism.

However, when one examines the naming of the “Metabolist

Cowan was the first president of the Santa Fe Institute.

Cowan. George A D. Pines & D. Elliott Meltzer. Complexity: Metaphors, Models, and Reality. MA:

Addison-Wesley Publishing Company. 1994. 2; Huang, Xinrong. “贝塔朗菲与复杂性范式的兴起

(Bertalanffy and the rise of the complexity paradigm),” Science, Technology and Dialectics. 2004, 8, Vol.21,

No.4. p11-14.

L.V. Bertalanffy, General System Theory, trans. Lin Kangyi et al (Beijing: Tsinghua University Press,

1987), p116.

E Schrödinger, What is Life?, (Cambridge: Cambridge University Press, 1945).

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 117

movement,” one can find connections to Marxism,

the Wachsmann Seminar,

the Ise

Grand Shrine, and the Katsura Imperial Villa,

but not to complexity in natural science.

When one considers the origins of Metabolist philosophy, one can see a resistance to

the “permanence” of architecture due to the occurrence of “disasters.” One can appreciate

how the Collapse of CIAM shocked the members of the Metabolist movement. Influences

from prefabricated buildings in the Soviet Union, Buddhist thought, and Shinto Japan may

also be witnessed, but it is still difficult to find traces of “complexity” thinking.

In addition, the main achievement of the Metabolists, “megastructures,” contradicts

their advocacy of an understanding of life promoted by Metabolism, including such

features as replaceability, growability, movability, etc., but still reflects a top-down

perspective. This top-down perspective is, from the point view of methodology, clearly

closer to modernism and contrary to complexity thinking. A contradiction is also reflected

in the debate about whether Metabolism belongs to the modernist movement or the

postmodern movement in general. For example, Arata Isozaki has always believed that

Metabolism is a modernist movement. Koolhaas has also referred to it as the last avant-

garde movement. However, Taro Igarashi believes that Metabolism should belong to the

broad movement of postmodernism. This debate is not confusing if viewed from the

perspective of “cognitive change.”

However, the common thread between the two dominant narratives lies in their quest

to define the Japanese essence. In 1955, Tange sparked a conversation about “Japanese

tradition,”

amidst a critical reassessment of Functionalism. Challenging the era’s

Rem Koolhaas, Hans Ulrich Obrist. Project Japan: Metabolist talks (New York: Taschen, 2011), p301. It

might be argued that Noboru Kawazoe, one of the leaders of the movement, who brought together various

different ideas and gave the avant-garde movement a common name, was the first person to use this term in

the context of architecture. However, according to Kawazoe, the name originated from Friedrich Engels’s

Dialectics of Nature: “There’s a line that says something to the effect of ‘one of the most essential features

of living things is shinchintaisha [metabolism].’ That’s where I got the term.” The name is therefore related

to Marxism rather than the “complexity” in natural sciences at that time.

Another event that led to the Metabolism movement was the 1955 Wachsmann Seminar. Although it was

mainly influenced by Team X, the seminar, held in 1955, was later referred to as the “seed of Metabolism.”

15 years after the seminar, Konrad Wachsmann, a structural expert, directly applied his space truss structure

approach to the Osaka Expo '70. Wachsmann was famous for the small prefabricated houses that he designed

with Walter Gropius in the 1940s, which could be assembled in nine hours using only a hammer as a tool.

Wachsmann's approach was temporary and practical, which completely opposed Corbusier's pursuit of

elegance and eternity at that time, but was in line with the spirit of Ise. However, there was still no direct

connection to complexity research.

The Ise Grand Shrine, which has been rebuilt every 20 years on adjacent sites since 690 CE, is considered

the prototype of Japanese architecture. The question of originality was not important to Japanese culture. The

Shrine conforms to Japan's understanding of the eternal. The materials in the building, like the cells that make

up life, are constantly replaced through metabolism. However, life remains unchanged, and so does

architecture. It was therefore named “metabolism,” meaning that all solid things can be dissolved, and all

fixed things can disappear. Everything that is considered eternal is actually fragmented, and nature is believed

to be a cycle that constantly repeats itself. Looking at it this way, the term “metabolism” is related to Japanese

tradition, though still not to complexity science.

Isozaki, History of Japanese Architectural Thought, p124.

118 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

unassailable allegiance to Functionalism, Tange elegantly argued that “only that which is

beautiful is functional,” subverting conventional wisdom and countering Le Corbusier’s

axiom that functionality begets beauty.

Tange’s journey was a relentless pursuit of a distinctly Japanese modernism, with a

deep reverence for “the local” at its core. The 1950s were marked by the seminal “debate

between Jomon and Yayoi,”

with Tange in the spotlight. This era spotlighted the Jomon

culture within archaeology and fine arts, framing Jomon and Yayoi as contrasting

paradigms. Inspired by Taro Okamoto’s The Theory of Jomon Pottery (绳纹土器论) in

1952, Noboru Kawazoe led the vibrant debate, positioning Tange as the emblem of Yayoi

and Seiichi Shirai as the advocate for Jomon. This ignited a discourse that spanned nearly

a decade. Tange’s collaboration with Yasuhiro Ishimoto in 1960 on “Katsura,” and the

subsequent articulation of “Ise Theory” by Arata Isozaki, are not merely examples of

architectural critique but profound explorations of Japanese culture, highlighting the

intricate interplay between Jomon and Yayoi, with Ise standing poignantly at the crossroads

of these historical narratives.

On the other hand, Tange was a pioneer in exploring “Japaneseness.” Together with

Noboru Kawazoe, Tange completed “Ise: Prototype of Japanese Architecture” in 1965. In

the literature, it can be seen that a group of architects, including Sutemi Horiguchi, found

these two “prototypes” in the journey of exploring “Japaneseness.” As a contrast with the

Metabolism movement, Tange had previously taken Katsura Imperial Villa and Ise Shrine

as reference points, and used them in his design for the Hiroshima Peace Park project.

Although Tange’s design was based on modernist thinking, the prototypes the architect

conceived were the same as those of the Metabolism movement. Particularly when dealing

with the pillars of the main hall and the overall proportion of the east hall in this project,

Tange referred to the Ise Shrine and Katsura Imperial Villa, creating the intention of

“standing up from the ruins” in a way similar to the ground-floor pillars of Le Corbusier’s

Marseille Apartment, although with some changes. The Hiroshima Peace Memorial

Museum, particularly in the concrete construction of its main building, mirrors the aesthetic

of traditional Japanese timber architecture. Noboru Kawazoe describes the Peace

Memorial Museum as being reminiscent of “Shinden-zukuri.”

Saikaku Toyokawa

remarks that: “at this point, his practice has surpassed mere input and imitation of modern

The Jomon period lasted roughly from around 14,000 BC to 300 BC. It is known for its distinctive pottery,

which is referred to as “cord-marked ware” due to the rough cord-like patterns often found on the pottery.

The Yayoi period followed the Jomon period, spanning from around 300 BC to AD 300. During the Yayoi

period, there was a significant shift in pottery production and decoration, with the use of more refined pottery-

making techniques and more intricate surface decorations. The core of the debate revolves around the

transition between the Jomon and Yayoi periods. Some archaeologists argue that there was a clear break

between these two periods, suggesting that Yayoi culture was introduced from outside Japan.

Isozaki, History of Japanese Architectural Thought, p151.

Isozaki, History of Japanese Architectural Thought, p129.

3.3 Connecting with “Nihonteki na mono” (Japaneseness) 119

architecture and is attempting to derive modern architectural principles applicable to

himself from the non-Western historical context of Japan.”

This exploration should be framed within the broader historical milieu, as

demonstrating the architectural community’s reflection on modernism’s penchant for

diminishing cultural distinctions. It attempts to integrate “local” perspectives into a

paradigm of modernism that was then considered normative, as well as reflecting on the

essence of Japaneseness.

Broadly speaking, the era under consideration reveals a fragile nexus between

“Japaneseness” and complexity theory. Despite the influence of complexity (systems

theory) on Japanese architecture at the time, Japaneseness remained the core focus.

1970s: Renewed Investigations into Japaneseness

The 1970s marked the beginning of a period of intricate interplay between Japaneseness

and complexity, which can be discerned by taking a chronological view. As seminal

“prototypes” like Ise and Katsura were explored exhaustively, the architectural community

began to question the label of Japaneseness, thus embarking on a quest for a novel

interpretation of this identity—one which would ultimately eschew Ise and Katsura.

Coinciding with this era, as detailed in section 2.4, was a major breakthrough in

complexity research regarding chaos. Merely two years later, Kisho Kurokawa introduced

the notion of “intermediate space,” which was subsequently echoed by numerous architects

with similar ideas. These concepts were inherently tied to the notion of “in-betweenness.”

The period’s Japaneseness was in fact characterized by this “in-between” state, which was

epitomized by Arata Isozaki’s interpretation of Japan-ness during the 1970s.

The Late 1980s: A Direct Correlation Between Japaneseness and Complexity

While the idea of Japaneseness continued to be upheld in the 1970s, there was an evident

inclination toward deviating from tradition. By the late 1980s, the term itself began to fall

out of favor. Architects of this time refrained from direct discussions of Japaneseness.

Yoichi Iijima

observes:

Japanese architects are apt to display oversensitivity to any characterization of their

work as “Japanese.” An architect who claims to be avant-garde will practically never

admit that his or her work has a “Japanese” aspect to any great extent. In Japan, to be

avant-garde or experimental automatically means being “un-Japanese.”

Arata Isozaki is a case in point. This distinguished architect, associated with

postmodernism for his 1980s Tsukuba Center projects, did not challenge the label but

Toyokawa, Tange Kenzo, p23.

Iijima is a critic and an Assistant Professor at Tama Art University.

Yoichi Iijima, “Toward Japanesenes,” The Japan Architect, No.18 (Summer 1995-2). KISHO

KUROKAWA issue, p28.

120 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

expressed reluctance and dissatisfaction when he became internationally recognized as a

symbol of Japaneseness. This stance is particularly intriguing given that he authored a book

entitled “Japan-ness.”

This dissertation posits that the distancing from “Japaneseness” does not signify a

detachment from Japan per se, but rather from Japaneseness as it was widely understood

at the time. This entails a deliberate sidestepping of the topic to probe into an alternative

Japaneseness, seemingly detached from conventional perceptions. Given the close

connection between complexity discussions and Japaneseness at this juncture, there was

an ideal opportunity for the emergence of complexity as a central theme. And indeed,

“complexity” made a timely appearance. During this peak period of influence for

complexity science, a plethora of architects started engaging directly with complexity

theory. Furthermore, the era’s dominant themes—lightness, ephemerality, consumer

culture, openness, chaos, non-linearity, and postmodernism—all resonate with the concept

of complexity (as referenced in section 2.4.3).

Post-2000: The Integration of Japaneseness

This phase, identified as the integration era in section 2.4.4, indicates a period where

elements historically understood in terms of Japaneseness start to merge and abstract, with

Sendai Mediatheque often cited as an example. This era is characterized by an intentional

detachment from “tradition,” a notion frequently articulated through the lens of “weakness”

by Sou Fujimoto and others, who use terms such as cutting off, undermining, negating, and

distancing. Here, “tradition” spans a wide array of phenomena, from temples and materials

to physical properties, architectural principles, societal norms, and even experiential and a

priori knowledge. The residual abstraction—order—emerges as the contemporary

embodiment of Japaneseness. Fujimoto, in particular, presents this concept by interpreting

Japanese elements through complexity, deeming the core idea to be “weakness.” His

portrayal of weakness fully encapsulates a Japanese narrative, with an intricate melding of

complexity and Japaneseness in his works.

A comprehensive review of the interplay between complexity science and Japanese

architectural history reveals that the pivotal elements identified through the comparison

between Rule 110 and Fujimoto’s approaches relate not merely to “complexity” but

inherently to Japaneseness. Japanese architects have long explored various facets that

contribute to the emergence of complexity, inadvertently crafting core architectural

philosophies that have been the collective endeavor of multiple generations. These

philosophies create a coherent lineage which, although not explicitly named as complexity,

is undeniably Japanese.

Initially, this lineage seemed unrelated to complexity theory, yet especially notable in

the 1930s, with the influence of Sutemi Horiguchi and the secession movement on Japanese

culture, was a focus akin to that of complexity. From the 1950s to the 1960s, the era

dominated by Kenzo Tange, the synergy between Japaneseness and complexity theory was

3.4 Summary 121

notably weak, despite the apparent influences of complexity theory. It was approximately

around 1975, with the increasing influence of complexity theory, that Japanese architects

started to acknowledge the synergy between complexity and Japan-ness, and they

subsequently began to apply complexity theory to refine Japaneseness. It was not until the

dawn of the new century, particularly through the work of Sou Fujimoto, that complexity

and Japaneseness exhibited their most profound integration. The quest to define “what is

Japanese” has always been a driving force in the evolution of Japanese architecture.

Japaneseness, while independent from the research in complexity science, is influenced by

it. The scientific exploration of complexity, due to its alignment with Japaneseness, served

primarily to refine and deepen the understanding of Japaneseness, rather than define it.

3.4 Summary

This chapter has focused on Fujimoto’s discourse on complexity, using a single image to

draw connections between Japan and complexity from a historical viewpoint. It suggests

the foundational potential and applicability of Rule 110, though not without leaving some

questions unanswered.

Those with a basic understanding of chaos theory will quickly recognize that the

characteristics listed in section 3.2 are also inherent to chaos. Chaos stems from the

interactions among parts of a system, often in varied and nonlinear ways. This nonlinearity,

coupled with the complex interactions within, fosters unpredictable behavior in the system,

exemplified by the well-known butterfly effect.

Chaos encompasses a multitude of individual actors; for instance, meteorology, the

birthplace of chaos theory, views atmospheric systems as composed of innumerable

interacting parts. These nonlinear interactions lead to the chaotic behavior of weather

systems, which complicates weather forecasting. Thus, chaos possesses qualities akin to

“clouds”—it is characterized by “density” and “gradient,” and exhibits a “centerless”

nature.

Fractals and self-similarity are more closely related to chaos than complexity. These

concepts are central to chaos theory and the field of nonlinear dynamical systems.

Chaos theory also studies the coexistence of order and disorder within systems that

seem entirely random and unpredictable, highlighting an intrinsic order beneath the surface

chaos. This aligns with Fujimoto’s frequent references to randomness.

Chaos is a recurring theme in Fujimoto’s discussions. The background research

indicates a historical “embrace of chaos” in Japan, with many prominent architects

employing chaos to articulate architectural concepts. Indeed, the connection between Japan

and “chaos” is profound. Notably, Lorenz unveiled his discovery of chaos in Tokyo in 1960.

The following year, the American architecture magazine “PA” hosted a symposium on

“The Age of Chaos,” coinciding with the early years of the Metabolism movement. Various

122 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

factors have led Japanese architects to perceive cities in Japan as “chaotic,” a stark contrast

to the “order” of modernism, thus blurring the distinction further.

A crucial distinction between chaos and complexity is “emergence,” a primary focus

of “emergence architecture” that is not given significant expression or emphasis by

Fujimoto or within the Japanese context. This raises questions about the accuracy of

attributing Fujimoto’s discussions solely to complexity and, by extension, about the

relationship between Japan and complexity. Clearly, this connection cannot be fully

explained by these discussions alone.

In addition, a comparison of timelines reveals another issue. Concepts like chaos and

nonlinearity emerged from theories in the 1970s, and by the 1980s, especially after the

establishment of the Santa Fe Institute in 1984, a plethora of new theories had emerged.

However, in the latter half of the 1980s and even into the 1990s, Japan continued to

emphasize “outdated” theories such as chaos and nonlinearity. This raises questions about

why Japan did not experience a “emergence” similar to that seen in the West, and how their

expression differed. Furthermore, as Jörg Gleiter pointed out, despite digital parametric

architecture becoming standard everywhere, Japan remained unaffected.

Was there a key

turning point or event that led Japan to choose a different path? Does Japan truly lack an

expression of “emergence”?

This dissertation posits that these questions stem from the ambiguity of concepts and

are a flawed basis for judgment. For any feature of complexity, strictly speaking, represents

just one aspect of complexity. Even combining all known features cannot fully encapsulate

the rich and diverse connotations of complexity.

Take “emergence,” for example. In the Encyclopedia Britannica’s description of

complexity in systems science, the attributes include: emergence, unpredictability,

connectivity, decentralized control, indivisibility, singularity, instability, and

incalculability. Similarly, in Tong Wu’s Objective Complexity, features of complexity

include: instability, multi-connectivity, decentralized control, indivisibility, emergence,

and the diversity and capacity of the evolutionary process. In Wei Hongsen’s proposal of

complex characteristics, emergence is also just one of many, and is mentioned alongside

instability, differentiation, interaction between order and disorder, randomness,

nonlinearity, non-additivity, self-organization, chaos, fractals, the counter-intuitiveness of

causality, emergence, bifurcation, and so forth.

It is evident that emergence is just one characteristic of complexity among many.

There are numerous other “indicative” concepts of complexity, such as bifurcation points,

symmetry breaking, departure from equilibrium, hierarchy, long-range correlations, and

Jörg H. Gleiter, “The most extreme aesthetic The Architecture of Sou Fujimoto,” In Sou Fujimoto:

Futurospective Architecture, ed. Friedrich Meschede (Köln: Walther König, 2013), p329.

Wei, “Complexity Research and Systematic Thinking Approach,” p8.

3.4 Summary 123

more. These concepts may be less well known but are equally crucial, as they are common

to most complex systems.

Furthermore, not everyone accepts the concept of emergence. The concept of

dissipative structures, for example, does not include emergence. There is no place for

emergence in the European school dominated by Prigogine and Haken. Prigogine and

Haken began to accept the concept of emergence in the 1990s, but used it only occasionally

and did not integrate it as an organic part of their respective theoretical frameworks.

Emergence was first introduced into systems science by Bertalanffy, and was further

elucidated by William R. Ashby and Peter Checkland, but it was only systematically

expounded by researchers in Santa Fe in the 1980s, The term “emergence,” long shrouded

in mystery, eventually gained its modern scientific connotations, becoming a fundamental

concept in systems science and complexity research, widely accepted by other schools

worldwide.

Only then was it translated into architecture.

The situation in complexity science remains the same: researchers are still working

on a jigsaw puzzle, trying to piece together the “complex” whole through continuous

identification. Individually, the pieces cannot be called complexity but merely represent

particular corners of it.

Scholars in this field are often engaged in identifying and delineating specific areas.

The discipline is still relatively undeveloped. The challenge of complex problems lies in

the lack of clear definitions, unclear environments, and changes that are unknown.

The interpretation of complex attributes, for the time being, is inexhaustible. It is

impossible to prove that a particular architect possesses complex thinking by exhaustively

listing all features. Conversely, even if an architect discusses or uses features in different

places or works that cover all the attributes of complexity, it cannot be said that they

possess complex thinking, or that their architectural works are complex systems.

Therefore, as the research questions at the beginning indicate, in the current situation,

discussing complexity requires context. When architects translate theories or

understandings of the real world into architecture, they inevitably choose to express certain

specific attributes. Understanding the complexity of Fujimoto and Japanese architecture

requires tailor-made “design.”

Overall, through an examination of the history of complexity research, the influence

of complexity theory on architecture, and the interaction between Japanese architecture and

complexity theory in history, this chapter has found that Stephen Wolfram’s Rule 110 is

most suitable as a basis for connecting Fujimoto and complexity. It is a suitable starting

point because when the description of an object is unclear, a feasible method is to list its

Miao, “The Achievements and Vexation of the Complexity Studies,” Journal of Systems Science. 2009,

Vol.17, No.1. p1-5.

Wu, “On Relationships between Complexity and Randomicity,” p22.

124 3 Rule 110 as a Foothold: Fujimoto’s Complexity Under One Graphic

features to obtain a comprehensive understanding. However, discussing Fujimoto and

complexity in this way will inevitably involve listing a large number of definitions and

metaphors. There is potential, therefore, in the graphical approach. Compared to other

definitions, it is purer, more intuitive and efficient, and less artificial. It does not place any

mathematical demands on the reader. Simply by observing a graph with the naked eye, and

without the need to enter any definitions or mathematical formulas, it can narrow down

Fujimoto’s complexity to a certain type of complexity and clearly delineate the architect’s

thoughts into various points. It corresponds to micro-properties of complexity and

establishes preliminary connections with “Japaneseness.” However, relying solely on Rule

110 is not enough. It merely provides a quick focus for the problem and exposes some

issues. What complexity actually is still remains unexplained. All Rule 110 offers is a

collection of certain features, and more work is needed to advance the discussion further.

4 The Nexus Between “Japaneseness” and

“Complexity” under the FGO

This chapter introduces another four graphics of order which, alongside Rule 110, form a

tool that can be referred to in discussions about order. These five graphics enable us to

better define order and interpret the complexity of Sou Fujimoto, thus aiding in discussions

about the relationship between “Japaneseness” and “complexity.”

4.1 What is the FGO?

All five graphics are generated on the basis of the “CA 1D Elementary” model

in NetLogo

software.

In addition to Rule 110, the selection, according to Wolfram’s Classification,

includes: Rule 254, representing homogeneity; Rule 67, representing periodicity; and Rule

30, representing chaos. The last image, which is not within Wolfram’s Classification, is

also generated by OCA. The generation method involves using the software’s built-in

random generator, representing equilibrium. The five images are arranged in a particular

order, abbreviated as FGO.

4.1.1 The Other Three Graphics

Rule 254: Homogeneity

In Wolfram’s Classification, this type of pattern (Class I) leads to a very simple, and almost

uniform final state. All cells become black or white quickly, and so this is called a

homogeneous state—no changes ever remain. Wolfram also refers to this as the

“Doomsday Rule.” In dynamical systems terminology, this rule has a single “attractor

point.”

A typical rule is Rule 254, which can be described in one sentence: when both

neighbors of a cell are white, its next state will be white; otherwise, it will be black. This

description can be illustrated by the following diagram (Fig. 4.1).

Wilensky, U. (1998). NetLogo CA 1D Elementary model.

http://ccl.northwestern.edu/netlogo/models/CA1DElementary. Center for Connected Learning and

Computer-Based Modeling, Northwestern University, Evanston, IL.

Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and

Computer-Based Modeling, Northwestern University, Evanston, IL.

In the terminology of dynamical systems, a “single attractor point” refers to a point in the phase space

toward which trajectories of the system tend to converge over time, regardless of the initial conditions of the

system. This concept is integral to the study of stable equilibrium states in mathematical models of physical,

biological, and social systems. An attractor can be thought of as a state toward which a system naturally

evolves. A "single attractor point," specifically, means that the system will settle into a steady state

characterized by this single point after sufficient time has passed. This behavior contrasts with other types of

attractors, such as limit cycles (where the system oscillates in a repeating cycle) or strange attractors (which

are associated with chaotic dynamics). In essence, a single attractor point signifies a stable equilibrium to

which, despite potential disturbances, the system will return, due to its inherent dynamics. This concept is

widely used in various fields to analyze and predict the long-term behavior of complex systems.

126 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

[Fig. 4.1] Rule icon of Rule 254.

[Fig. 4.2] Left: Rule 254 in 20 and 100 steps from single initial condition.

[Fig. 4.3] Right: Rule 254 from random initial condition.

Rule 67: Periodicity

Compared to Class I, Class II has a bit more “vigor” to it, but still gives a sense of

“frozenness” and “deadlock.” Patterns are composed of specific simple structures that

either remain constant indefinitely or recur periodically after a few steps. In short, patterns

became repetitive. Rule 67 is a typical rule (Fig. 4.4). The specific rule is as follows:

[Fig. 4.5] Rule 67 from single initial condition. [Fig. 4.6] Rule 67 from random initial condition.

4.1 What is the FGO? 127

[Fig. 4.4] Rule icon of Rule 67.

As one can see, the generated results have some interesting variations. However, they

still exhibit a clear and recognizable pattern. Compared to the previous homogeneous case,

Rule 67, which represents periodicity, shows two diagonal lines in a black-and-white

alternating background.

Rule 30: Chaos

The simple appearance of the first two patterns is produced by very simple rules, which is

not surprising. However, Class III, represented by Rule 30 exhibits unexpected patterns,

but still relies solely on very simple rules. First, look at each cell and its right-hand neighbor.

If both of these were white on the previous step, then take the new color of the cell to be

whatever the previous color of its left-hand neighbor was. Otherwise, take the new color

to be the opposite of that (Fig. 4.7).

The cellular automata produce a pattern that seems extremely irregular (Fig. 4.8; Fig.

4.9). In this pattern, first, one can observe triangles and other small-scale structures of

different sizes. Secondly, in the case of a black cell initial start, one can clearly see that, on

the left side, different layers of small-scale structures develop along the edges of the

triangles in a very stable manner. But on the right side, there are different-sized triangles

that appear to be randomly distributed in many ways. Thirdly, the order on the left side and

the randomness on the right side melt into each other in a certain area in the middle. This

area is not a simple and obvious line and it is not easily identifiable. The entire pattern is

no longer a simple repetition and nor is it entirely lacking in order. In a way, order and

disorder coexist within this pattern.

In the case of random initial points, the clear “order” previously observed on the left

side of the single starting point disappears, and the entire pattern appears to be replaced by

patterns from the right side. Let’s try to describe this image. We observe many triangles at

different scales. In-between those triangles, we can find something indescribable,

something like a mirrored L shape. There seems to be no discernible pattern in the relation

between these triangles, nor in the things between the triangles. Overall, it is hard to say

whether it is ordered or disordered. It still looks as if order and disorder coexist.

Let’s pause for now on the introduction of these three images and take a look at the

last image, an order that does not exist within Wolfram’s Classification.

[Fig. 4.7] Rule icon of Rule 30.

128 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

[Fig. 4.8] Left: Rule 30 from single initial condition.

[Fig. 4.9] Right: Rule 30 from random initial condition.

4.1.2 The Addition of Equilibrium State

[Fig. 4.10] Terms to describe these states are varied: disorder; chaos; complete chaos; complete randomness;

microscopic chaos; Kolmogorov maximum complexity; irregularity; maximum entropy; maximum

possibility; attractor; unconditional chaos; disorganized complexity; death; AIC; fundamental complexity.

In the last section, the article introduced three graphics which, alongside the previously

mentioned Rule 110, represent complexity. There are a total of four types of order, each

representing one of the four classes in Wolfram’s Classification. This dissertation argues

that, to discuss the complexity of Sou Fujimoto, another type of order needs to be added.

This order, which is crucial for understanding complexity, is equilibrium.

The graphic for equilibrium is also created by Netlogo software.

4.1 What is the FGO? 129

WC is based on elementary cellular automata, the basic feature of which is the

evolution of time and space. Equilibrium, however, is the so-called final state, which no

longer has the dynamics to evolve without external force. Therefore, equilibrium is not

within WC, but it is a natural phenomenon and an important concept in a complex system,

as well as in understanding Fujimoto’s work. In this research, equilibrium (Fig. 4.10) is

used to describe the above graphic as the fifth order.

Equilibrium itself doesn’t mean much, because nothing has happened. But how things

tend towards equilibrium is a very interesting question. The moment when a living

organism is closest to a state of equilibrium is death. In contrast, how a living

organism died is much more interesting than just the fact that it died, which is a

prerequisite for the popularity of detective novels or mystery murder stories.

The equilibrium to which Gribbin refers is precisely the state of this order. It also represents

a common order. In Chambers Encyclopedic English Dictionary, the definition of disorder

has only three meanings: 1) lack of order; confusion or disturbance; 2) unruly or riotous

behavior; 3) a disease or illness.

Among these, “lack of order” can describe this state. It

has no discernible structure that is visible to the naked eye. In this case, the absence of

order is its order. However, given the richness and importance of its meaning, such a

description seems somewhat arbitrary. For example, a gas in a container is in this state after

reaching stability. But in many cases, this state is also called chaos. As a matter of fact, it

goes by many names: complete disorder, randomness, microscopic chaos, stochasticity,

irregularity, chance, and so on. The name given to this state depends on the author’s

preference, understanding, and context. One can therefore imagine how many concepts of

order would be overlooked without it.

[Fig. 4.11] A schematic diagram of Boltzmann’s maximum entropy calculation principle. The upper: four

balls in the same container with only one possibility. The lower: if four balls are evenly distributed into two

containers, there are six possibilities.

Translated by author. Gribbin, Deep Simplicity, p119.

“Disorder,” in Chambers encyclopedic English dictionary, ed. Robert Allen. (Edinburgh: Chambers, 1994),

p368.

130 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

On the meaning of disorder, Haken writes: “The disorder in physics has to do with the

large number of different possibilities where objects can be found.”

This statement can

be explained by the Boltzmann distribution diagram (Fig. 4.11).

Assuming that there are four molecules, the possible distribution of these molecules

in a sealed box with a partition in the middle is as follows: there is only one possibility

where all four molecules are on the left side, while there are six possibilities where two

molecules are on the left side and the other two are on the right side. With only one

possibility versus six possibilities, the six possibility states win. Therefore, the state with

the greatest possibility is the equilibrium state.

The figure above is a schematic diagram used by Austrian physicist Ludwig Eduard

Boltzmann (1844-1906) to calculate the maximum entropy rule. Boltzmann developed

statistical mechanics and, based on statistical concepts, explained the second law of

thermodynamics, thus inventing entropy. This description brings us back to the topic of

entropy.

The equilibrium state corresponds to the state where the system entropy is at its

maximum. The state with the maximum entropy is the most disordered state of the system.

Imagine a drop of slightly warm red water dripping into a cup of colder water. This drop

of hot water will spread out in in the water beautifully and eventually disappear. The change

in the cup as a whole is that it becomes slightly hotter and slightly redder than before. What

remains unchanged is the overall water temperature. This process involves a transformation

from order to disorder. The initial state of the separated red water droplets and the cup of

water is an ordered state, as its energy has a more uniform degree of freedom and its entropy

is at its lowest level in the system. The final state is called the disordered state, as the degree

of freedom of the red water droplets is distributed to a lower level of freedom, and there is

less heat dissipated into the environment, resulting in the highest entropy for this system.

In any case, the intermediate state of the water droplets spreading out in the water is more

beautiful and fascinating. The final state is the most boring state, also known as the

equilibrium state. It is the most disordered state and has the highest entropy.

The equilibrium state is the ultimate state, a state of death, also called an “attractor.”

The second law of thermodynamics states that the system, when left to itself, will change

to a condition of maximum probability. It is a force that attracts the system to move toward

it, hence the name “attractor.” The famous heat death theory

is a speculation based on

Hermann Haken, Erfolgsgeheimnisse der Natur. Synergetik: Die Lehre vom Zusammenwirken, trans.

Fuhua Lin (Shanghai: Shanghai Translation Publishing House, 2018), p13.

This is a hypothesis about the ultimate fate of the universe. It was first proposed by William Thomson in

1850 and later developed by Hermann von Helmholtz. The hypothesis is mainly based on the first and second

laws of thermodynamics and their application to the universe. According to the second law of

thermodynamics, the energy in the universe will eventually reach a state of thermal equilibrium, similar to a

heated iron rod. At this point, the entropy and disorder of the universe will be at their maximum, and there

4.1 What is the FGO? 131

this state. After entering this state, the system will no longer have energy flow, so there

will be no further changes, hence it is also called the state of death.

The equilibrium state is a critical “driving force.” Morin’s most important view relates

to the perception of disorder. He posits that disorder plays a dual role: it serves as a

foundational element of social order by contributing to diversity, variability, flexibility,

and complexity, while simultaneously representing chaos and posing a risk to structural

cohesion. Moreover, the perpetual challenge posed by disorder imbues society with a

unique form of complexity and dynamism: a constant state of reorganization.

Morin’s

disorder is actually a “force” derived from the equilibrium state. It constantly pulls and

urges the system to move toward this state.

It is the ultimate state, a death state, and an attractor of maximum complexity, referred

to as Kolmogorov complexity. It is also what is referred to as Cramer’s fundamental

complexity. As introduced in section 2.1.3, Kolmogorov complexity refers to the minimum

resources required to describe a system. In this state, the minimum resource required to

describe the system is the whole system itself. If 1 represents black and 0 represents white,

the program needs to list the status of each square (such as

011010010101101101001110111010101...) in order to describe it. As discussed in the

previous section, this is also why it does not exist in the WC: it cannot be described in a

simple language, and nor can it be obtained through partial interactions. In this state, there

are no long-range correlations

as it loses the “power” of mutual influence among parts:

the system is in a “dead” state.

The discussion above offers some descriptions of this state. Although it does not

appear in the WC, it is indeed a common order in nature. The connotation of the order it

encompasses is crucial and rich, and its existence is significant for locating the concept of

various orders and understanding the complexity of Fujimoto’s work. Its existence allows

the complete story of the whole order. This dissertation refers to it as the equilibrium state.

will be no more energy flow or life. The entire universe will be in a state of static equilibrium, with no further

changes.

Morin,

迷失的范式

人性研究

, p29.

Ilya Prigogine, Isabelle Stengers. The End of Certainty: Time, Chaos, and the New Laws of Nature, trans.

Min Zhan (Shanghai: Shanghai Scientific & Technological Education Publishing House, 2009), p53.

132 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

4.1.3 The Order of the Orders

[Fig. 4.12] The images above are arranged from left to right according to the degree of their orderliness.

The five images above are arranged from left to right on the basis of their respective degrees

of orderliness. In fact, their degrees of orderliness can be ordered simply with the naked

eye.

The first graphic, of random initial conditions, quickly transitions to a homogeneous

state after a few steps, ultimately becoming a single white color (becoming monochrome).

Regardless of the starting point, it would always quickly move to a homogeneous state. It

is the most ordered. The second image, of random initial conditions, exhibits several

diagonal lines. Compared to the “homogeneous” white-out, it appears slightly more

dynamic, displaying periodic variations. Its level of orderliness decreases slightly.

Nevertheless, the presence of “order” can still be observed. From the third image onwards,

it is difficult to describe them as “ordered.” However, it is still quite easy to make

judgments: the complex image is more ordered than the chaotic one because it possesses

structure. Equilibrium, on the other hand, is the most complete state of randomness and

evidently has the lowest degree of orderliness. Therefore, the images are ordered from left

to right based on their degrees of orderliness.

The greatest controversy in such ordering may arise regarding the positions of

complexity and chaos. In these instances, Langton’s “edge of chaos” provides theoretical

support for such ordering.

Wolfram’s system only classifies one-dimensional cellular automata, and the

categories are not related to each other. Langton’s concept of “the edge of chaos,” however,

actually studies the relationship between the categories.

In everyday life, one can observe the evolution sequence of such orderliness. The

leaky faucet, for example, is a much-studied problem, and is recognized as a prototypical

nonlinear dynamical system. In daily life, one can observe that a faucet can produce a

steady leaking within a certain range. But at some point, the dripping will suddenly become

4.2 First Step: Locating the Orders 133

irregular. The same phenomenon can also be found in phase transitions. For example, when

a magnet is heated, its magnetic force disappears. At this point, there is complete disorder,

with each magnetic atom randomly oriented, resulting in a zero magnetic force exhibited

by the entire magnetic field due to the mutual cancellation of atoms. When measuring the

magnetic force of a magnet that is gradually cooled, it can be found that the magnetic force

suddenly recovers at a certain point as the temperature decreases. Both of these phenomena

jump directly from order to chaos (or vice versa). So where does complexity appear?

Langton addresses the problem directly and, by chance, stumbles upon his famous λ

parameter value (approximately 0.273), which happens to be situated between Class 2 and

Class 3.

Langton’s research identifies a challenging transition in dynamical systems: Order →

Complexity → Chaos. Complexity is located precisely at “a moment just before chaos

occurs.”

4.2 First Step: Locating the Orders

Each order has its own place. The FGO locates five orders, which clarifies most concepts

of order, and therefore to some extent alleviates the confusion about them.

The status of complexity within these five orders is immediately clear. Thus, when

architects talk about order, they now have a clearer direction for what they truly mean.

Identifying each order is a necessary first step before discussing complexity. Particularly

in the absence of a clear, strict definition of the concepts of order, graphics serve as a good

point of reference.

4.2.1 Forms of Difference

What do architects mean when they delve into concepts like order, disorder, chaos,

complexity, equilibrium, randomness, and nonlinearity?

Three Complexities

[Fig. 4.13] FGO covers four types of “complexity.”

There are actually three types of “complexity” and one type of “compound” (or

complicate) (Fig. 4.13).

134 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

The compound is represented by the periodic graph. It is a type of complexity at the

level of everyday language, which means that it looks messy and disorganized. The other

three types are frequently used in the language of natural sciences: complexity, chaos, and

equilibrium. They are all considered complex in some timeframe or context.

First there is the compound represented by the periodic graph. The introduction of the

compound is a common “opening statement” used in many studies to quickly exclude them

from the discussion. It is easy to distinguish complexity from everyday language. With a

single starting point, the graph presents two diagonal lines on a black and white striped

background. With a random starting point, the lines seem to simply overlap. The “parts”

of the graph are independent of each other, and the sum of the attributes of the parts is

equal to the attributes of the whole.

For example, a pile of randomly stacked wood is compound. Taking out a few pieces

will only cause linear changes in the whole system, without any qualitative changes.

Therefore, the relationship between the parts is simple addition, i.e., 1+1=2. In this system,

the individual parts are independent of each other, so even when put together, the whole

can be understood and predicted by understanding the individual pieces of wood as “parts,”

including the total mass and buoyancy of the wood.

But a large tree is complex. The relationship between the parts of a tree is not a

straightforward “additive” relationship, but rather they depend on one another. At the same

time, the tree also exhibits a certain “stability” and a “profound connectivity” at different

levels. For example, cutting off large branches of a tree will not affect its life, but cutting

off the bark can easily kill it.

Similarly, both a pile of wood and a large tree are made of wood, but a pile of wood

stacked together is just a pile of wood, while a large tree connected through certain

relationships exhibits vitality. In this case, 1+1>2.

This chapter will now introduce the three types of complexity contained in the five

figures. The first is equilibrium. As mentioned earlier, a large amount of “complexity” has

been defined on the basis of Kolmogorov complexity. Also known as computational

complexity, it is defined by measuring the number of computational resources required to

solve a problem. The emergence of this definition is due to the attempt to quantify

“complexity.” To do this, computer experts use the length of the information string of a

computer program to describe things, and the basic idea is that the length of the description

defines the complexity of the description. Therefore, when the computational resources

required to describe a problem are as large as the problem itself, the complexity of the

problem reaches its peak. Logical depth, Algorithm Information Content, Algorithm

Complexity, and Friedrich Cramer’s “fundamental complexity” are all based on

Kolmogorov complexity.

4.2 First Step: Locating the Orders 135

Under their definition, the more random something is, the longer its description length,

and the information represented by equilibrium cannot be compressed in any way.

Therefore, the description of equilibrium is equivalent to describing the object itself, and

equilibrium is thus equivalent to the maximum computational complexity. Equilibrium is

therefore a type of complexity.

The second type is chaos, a popular term that has long been synonymous with

complexity. From some perspectives, they are indeed similar and even interchangeable. E.

Lorenz uses chaos as a definition of complexity. To this day, the relationship between this

word and complexity is still widely confused in many fields. This dissertation contends

that the root of such misconceptions lies not within the confines of cognition, but in the

inadequacy of scholarly terms, which leads to misinterpretations. Furthermore, it reveals

that beneath their apparent disarray, an intrinsic “order” prevails.

The final type is complexity in the FGO, which is also the complexity defined by

Wolfram.

This type of complexity is the mainstream form of complexity. It shares a core

defining perspective with many others: the relationship between order and disorder.

Langton’s “edge of chaos,” Gell-Mann’s “effective complexity,” “emergence,” Herbert

Alexander Simon’s “hierarchy,” and the “complexity” relied on by the Western “emergent

school” etc., are all related to this type of complexity.

Three Types of Randomness

The concept of “randomness” was discussed in section 2.1 of this dissertation. The FGO

contains three types of randomness, which provides a certain degree of clarification. In the

FGO, complexity, chaos and equilibrium all contain randomness, but each has its own

distinguishing characteristics.

First, equilibrium represents a type of randomness that is different from chaotic

randomness. It refers to the randomness of individual movements at the micro level. It

describes a state where the behavior of an object or objects is highly irregular and cannot

be compressed into any regular pattern.

Next is the randomness in the chaos graphic. The chaos graph used here is Rule 30,

classified as Class 3 by Wolfram. Wolfram also sometimes calls Rule 30 random.

Chaos

Wolfram did not give a clear definition of complexity. In the “Defining Complexity” section of his book

New Kind of Science, Wolfram merely points out that complexity is related to perception and analysis. It

usually means that a simple description of something cannot be found.

Wolfram believes that Rule 30 exhibits “true randomness” in the central column under a single starting

point, as the changes in cell states show completely unpredictable and patternless random variations without

any observable periodicity. Wolfram has proven this to be the case for at least one million steps. To this end,

he once offered a prize of $300,000 to prove that the central column will never exhibit periodic changes. In

addition, the ratio of black and white cells in the central column shows a pattern that tends toward 1 from

2.3333, starting from the tenth step. This is another problem in the $300,000 prize challenge, which asks

whether the ratio of black and white cells will reach equality in some future step. By this criterion, the central

column of Rule 30 is considered truly random. The purpose of discussing randomness here is to point out

what architects mean when they talk about the concept.

136 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

is actually a seemingly random phenomenon that appears in deterministic nonlinear

systems. The beauty of chaos lies in unifying two previously unrelated things: determinism

and randomness. The founder of chaos theory, Lorenz, states: “I used the term chaos to

refer to processes which look random but are actually governed by precise laws [...] a

chaotic system is one which is highly sensitive to initial conditions and undergoes internal

changes.”

One can therefore view it as “seemingly random.” It is a result of pseudo-

randomness generated by a process that is actually a deterministic process, but the outcome

is very disorderly.

Finally, there is also randomness in complexity. What needs to be pointed out is that

the complexity here is caused by deterministic rules. That is, its pattern is difficult to predict

without doing all the calculations. But it is still “seemingly random.”

Most of the complexity in real life is precipitated by true randomness. The randomness

displayed by such complexity naturally also contains elements of it. From this point of

view, equilibrium, chaos, and complexity should correspond to the three types of

randomness mentioned in 2.1: complete randomness (note that the generation method of

equilibrium in this dissertation is the random generator inside the software, which is still

the result of calculation, so strictly speaking does not represent true randomness—it is only

used to demonstrate and understand the concept of randomness); the randomness of the

result; comprehensive randomness (note that in Rule 110, this is excluded and a

phenomenon outside of true randomness is shown; here, Rule 110 is simply used to

understand the position of comprehensive randomness).

One can see this type of randomness (namely, randomness in complexity) as a

combination of the other two types (randomness in chaos and equilibrium), where the

outcome and the process both contribute to the randomness. True randomness is the result

of the joint effect of outcome and process randomness.

Complexity contains randomness because true randomness is required for complexity

to exist: “All the complexity we see around us can emerge from simple rules and a little

randomness.”

However, complexity is not the same as randomness, but rather surpasses

it.

Therefore, randomness cannot be used as a standard to judge whether something is

complex, as randomness is only one attribute of complexity. “Randomness” cannot be used

casually, as at least three of the five images in this article have meanings related to

randomness.

Lorenz, The Essence of Chaos, p20.

Wu, “On Relationships between Complexity and Randomicity,” p20.

Gribbin, Deep Simplicity, p106.

Wu, “On Relationships between Complexity and Randomicity,” p21.

4.2 First Step: Locating the Orders 137

Nonlinearity in the FGO

Complexity is indeed closely related to nonlinearity. Even in the fields of natural and

technological sciences, they are often considered as one and the same thing.

Some

scholars would say that “the most important intellectual revolution of the 21st century is

about complexity and nonlinear thinking.”

Some would use the term “nonlinear complex

system” directly. However, nonlinearity and complexity are not at all the same.

In 1984, Wolfram pointed out that cellular automata not only contain rich and diverse

mathematical structures, but also have profound similarities with nonlinear dynamics.

Both the Rule 110 and Rule 30 used by the FGO have nonlinear dynamic characteristics,

but they can be broken down into more specific mappings. These mappings are either linear

or nonlinear. Nonlinearity is not exclusive to any one rule. In addition to many mappings

in Class 3 and Class 4 rules, they also have non-linear characteristics. (When these rules

are not simple summations or linear functions, but are based on specific combinations of

states, then the neighbor dependency is nonlinear. These characteristics are key factors that

can create complexity in the overall patterns.) Therefore, a certain rule cannot simply be

judged as either linear or nonlinear. Conversely, not all nonlinear systems or equations

necessarily exhibit complex behaviors.

In FGO nonlinearity appears as it should indeed be understood—as not even a type of

order. The distinction between nonlinearity and complexity can be summarized as follows:

1. From a definitional standpoint, complexity is defined in relation to simplicity, while

nonlinearity is defined in relation to linearity. Their names relate to that which they are

defined against. Complexity and nonlinearity are common problems in different fields of

natural sciences and engineering and technology sciences, and research on them is

conducted in various fields.

2. Complexity reflects the overall characteristics of a system, while nonlinearity

represents the mechanism of interaction among individual components within the system.

Complexity refers to the external connections and surface features of a specific structure

Wu, “Review of Complexity, nonlinear research and their philosophical issues,” p31.

Tong Wu, “20 世纪未竟的革命和思想遗产—复杂性认识 (The Unfinished Revolution and Ideological

Legacy of the 20th Century—Complexity Understanding),” Journal of Inner Mongolia University

(Humanities and Social Sciences). Vol.32, No.3. (May 2000), p1.

This concept is particularly likely to be misunderstood in certain contexts. In the preface of Deep

Simplicity: Chaos, Complexity and the Emergence of Life, Ma Ziheng refers sarcastically to “postmodernists”

along these lines: “But if you raise your value by using scientific jargon that you only half-understand, create

theories, and set the tone, it makes people uneasy [...] Postmodernists sometimes even use special

mathematical terms like ‘nonlinear’. As stated clearly in this book, the ‘nonlinearity’ in chaos theory refers

to the properties of a certain mathematical function, nothing more and nothing less.”

Waldrop, Complexity, p225.

Wu, “Review of Complexity, nonlinear research and their philosophical issues,” p32.

138 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

Class 1

Class 2

Class 4

Class 3

None

Order (general classification)

Complex

Disorder

Compound

Complex

Ordered

Disordered

Random

Stochastic

Fractal-like

Contains Homogeneous

Contains all

Contains Periodic and

Homogeneous

High Dimensional

Chaos

Low Dimensional Chaos

Complete Chaos

Microscopic Chaos

Nonlinear Dynamics

Effective Complexity

Logical Depth

Kolmogorov

Complexity

AIC

Algorithm Complexity

Fundamental

Complexity

Self-Organization

Dissipative Structure

Edge of Chaos

Minimum Entropy

Energy High

Highly Structured

Frozen/ Starting State

Multiple Steady States

Competing Area

Structure Emerged

Life/ Balanced

Unsettling

Turbulence

Maximum Entropy

Energy Low

No Structure

Death/ Final State

[Fig. 4.14] The cluster of concepts that fit under the broad umbrella of FGO.

4.2 First Step: Locating the Orders 139

of things, and is the external manifestation of things. Nonlinearity refers to the internal

connections and fundamental properties of a specific structure of things.

3. Nonlinearity is the root of complexity or, in other words, nonlinearity and

complexity have a causal relationship. However, nonlinearity alone does not guarantee the

emergence of complexity. For example, as Xuefeng Song summarizes, it is generally

believed that nonlinearity is a necessary condition for generating complexity. Without

nonlinearity, there would be no complexity. Complex systems are all nonlinear dynamic

systems.

4. Complexity and chaos have in common the property of nonlinearity. Practically

every nonlinear system is chaotic some of the time, which means that complexity implies

the presence of chaos. But the reverse is not true.

Nonlinear systems are not 100%

chaotic, let alone complex. In fact, the topic of nonlinearity is much larger than that of

complexity. In natural science, there are at least three classes of nonlinearity: solitons,

chaos, and fractals.

Particularly in the field of mathematics, research related to

nonlinearity and the fields it involves is much broader in scope than that of complexity.

5. In terms of methodology, there are also differences between the research methods

of nonlinear and complex systems.

6. Nonlinear science is a discipline with a precise scientific field, while it is still a

matter of debate whether complexity science can be called a discipline.

It is therefore quite controversial to equate complexity with nonlinearity in

architectural research on complexity. The formation mechanism of FGO can simply

demonstrate the relationship between nonlinearity and complexity: nonlinearity is not order,

but a necessary and insufficient condition for the formation of complexity. If one has to

connect them, the relationship between nonlinearity and chaos may become closer. Based

on this analysis, it is not particularly appropriate to equate nonlinearity with complexity.

When viewed in this manner, FGO organizes and delineates many confusing concepts

in an intuitive way and so prepares the ground for an explanation of complexity. Three

types of complexity and three types of randomness all compete on the same stage,

alongside nonlinearity, chaos, fractals, and a series of other concepts, and so must be

clearly distinguished and compared in terms of their differences and similarities. (Fig. 2.13)

The FGO is a small cosmos, in which there are only five orders. However, this is

enough to reflect the orders in the real world. It serves the role of a “ruler,” a foundation to

Jianming Gao, Zhaogang Sun. “On the Interrelation between Complexity and Non-linearity,” Journal of

Systemic Dialectics. Vol.10, No.4. (Oct. 2002): p36.

Song, “Complexity, Complex System, and the Science of Complexity,” p263.

Michel Baranger, “Chaos, Complexity, and Entropy. A physics talk for non-physicists,” England Complex

Systems Institute, Cambridge, 2000.

Chaohao Gu, “非线性现象的个性和共性(The Individuality and Commonality of Nonlinear

Phenomena),”

科学

(Science). 1992(3): 10-12.

140 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

which one can refer when one talks about order. In the FGO, Rule 250 represents

homogeneity; Rule 67 periodicity; Rule 110 complexity; and Rule 30 chaos. Equilibrium

is not within WC and is generated in a completely random manner.

The FGO is visual in nature. It does not rely on a specific, complex definition. It omits

a lot of text and represents order primarily on the logic of the graphics themselves.

The FGO is simple and concise. Complexity is complex enough. Yet while a certain

degree of simplicity is helpful for discussing “complexity,” simplification should not result

in the loss of its essence. The FGO does not simplify the essence that needs to be discussed.

The characteristics it presents are sufficient for organizing discussions about Fujimoto.

4.2.2 Complexity or Chaos?

The preceding section outlined the positioning of various concepts of order and

complexity’s role was vividly illustrated through diagrams. This section aims to clarify the

question posed in 3.4: in his discussions, does Fujimoto (Japan) speak of chaos or

complexity? Importantly, as the FGO’s comparisons make clear, these are distinct concepts

and should not be used interchangeably.

[Fig. 4.15] This image represents common understanding of the difference between complexity and chaos:

the emergence of structure, which is often referred to as simply “emergence.” In the figure for complexity,

emergence is expressed as the appearance of non-trivial structures. The triangular pattern seems to be across

the whole of the black grid, but the triangles together form a larger structure. As discussed earlier, a visible

difference between the two orders of complexity and chaos is that chaos has a strong sense of “noise.”

However, in the complex figure, a certain structure clearly appears. The structure, which is composed of

triangles, interacts with periodic patterns in a very complex manner.

4.2 First Step: Locating the Orders 141

Complexity, as depicted in FGO, exhibits greater “stability” than chaos. Chaos lacks

emergent characteristics. As depicted in Fig. 4.15, the chaotic pattern produces a feeling of

instability: it is excessively “lively.” Conversely, complexity not only shares many traits

with chaos but, in contrast to the latter, it also “starts settling down.” Coherent structures

“visible to the naked eye” are formed. These structures interact with each other and travel

along the evolution, which is usually interpreted as “emergence.” Chaos does not exhibit

emergent properties—it is a characteristic unique to a complex system.

First, the appearance of each level in a complex system is emergent, meaning that the

structure spans several scales. Let’s take the human body as an example. The human body

is composed of molecules, which form various protein molecules that constitute organelles;

organelles form cells, cells form tissues, tissues form organs, and organs form organ

systems, with the nine organ systems together forming the human body. Each stage sees

the emergence of new structures, which then settle down. Each settled structure can emerge

into more complex structures. Each emergence generates a new level of structure and is

accompanied by new behaviors. These emergent properties cannot be seen in systems that

exhibit merely chaotic behavior.

Second, in the FGO, the complex and the chaotic have different positions. Complexity

arises in the instant just before chaos emerges,

as is seen in the graph of complexity

located in the FGO, which is what Langton’s “edge of chaos” is trying to convey. This is

something that one can observe in many places. Dripping faucets, turbulence, the Benard

convection, phase transitions—all of these phenomena suggest the spatial relationships

between chaos and complexity.

Third, in FGO, complexity occupies a dominant position. It is easy to understand that

periodicity contains homogeneity since homogeneity itself is a single periodic expression.

It is also easy to understand that chaos contains periodicity, as the article that gave chaos

its name—Tien-Yien Li’s “Period Three Implies Chaos”—explains how chaos enters

through periodic doubling. The most confusing and controversial aspect is that complexity

contains chaos. This is obvious in the FGO, and there is some theoretical support for the

relationship.

Generally speaking, complexity is a bigger topic than chaos and contains many ideas

that have nothing to do with chaos. Chaos is a purely mathematical concept, while

complexity is more extensive and includes a broader range of topics. For example, some

researchers use dimensionality to describe the relationship between chaos and complexity,

where complexity is high-dimensional chaos. The domain of chaos represents a minor

segment within the broader scope of complexity, which encompasses both chaotic and

orderly interactions. Both complexity and chaos share the characteristic of nonlinearity,

with almost every nonlinear system exhibiting chaotic behavior at times. This suggests that

Gribbin, Deep Simplicity, p122.

142 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

chaos is inherent in complexity. However, the converse does not hold true.

This can also

be understood as a relationship of inclusion. Secondly, chaos, nonlinearity, fractals,

bifurcation, randomness, irreversibility, and cyclical nesting are usually considered to be

the basic attributes of complexity.

[Fig. 4.16] One can tell which is the most “complex” with the naked eye. In the figure above, one can clearly

observe the existence of the other three types of order in the graphic for complexity. They have a relationship

of inclusion, where periodicity contains homogeneity, chaos contains periodicity, and complexity contains

them all.

From a philosophical perspective, complexity holds a dominant position, as from an

ontological and epistemological standpoint, complexity represents the opposite of

simplicity in classical science. Complexity is an objectively essential attribute of this world,

and it is a more macroscopic term. For example, nonlinearity is usually considered as the

dynamic mechanism for the emergence and evolution of complexity. Chaos and fractals

are the spatial and temporal characteristics of complexity, respectively. That is, chaos

represents spatial complexity, while fractals represent temporal complexity. Fluctuations

and mutations are the intrinsic characteristics of complex evolution that cannot be

externally encoded. Randomness and contingency are manifestations of complexity on the

path of its evolution.

These statements all imply that complexity has a dominant position.

Last but not least, one can also understand the difference between chaos and

complexity from a quantitative perspective. Chaos refers to the unpredictable behavior of

a small number of individuals, while complexity requires a large number of individuals.

Put perhaps too simply, chaos can be thought of as complicated behavior from simple

systems, like the three body problem, whereas complexity science can be thought of as

addressing systems that are very complicated (with billions of “three bodies”) but have

simple behavior.

Baranger, “Chaos, Complexity, and Entropy,” p10.

Wu, “The Some Philosophical Problems in the Research of ‘Complexity’,” p6-10.

4.2 First Step: Locating the Orders 143

To summarize, these two words clearly have completely different meanings and

implications, and should not be used interchangeably.

4.2.3 Why does Fujimoto Use “Chaos”?

In the FGO, the juxtaposition of the two diagrams illustrates not only the difference but

also the connection between chaos and complexity. This is crucial for clarifying whether

Fujimoto and the Japanese discourse are discussing chaos or complexity. Both Fujimoto’s

and the historical Japanese usage of the term “chaos” stem from the shared characteristics

between complexity and chaos.

In a similar way to complexity, chaos theory stands as an antidote to modernism,

emerging as a pivotal theoretical innovation amidst a shift in intellectual paradigms. When

viewed through a macro lens, the exploration of chaos is intrinsically linked to the

investigation of complexity. Both concepts, born out of a critical examination of classical

science, confront a common adversary. They transcend the limitations of mechanical

reductionism, drawing from a singular philosophical wellspring and embracing a collective

holistic vision. This shared perspective underpins both chaos and complexity, underscoring

why chaos theory is an integral element of the science of complexity. Engaging with

themes of “disorder” and “uncertainty,” they employ non-reductionist methodologies and

throw a spotlight on realms neglected by the scientific discourse of their time. The

distinction between them is primarily a matter of the linguistic expressions chosen to

navigate the evolving human comprehension of the cosmos. Their ultimate aims converge.

The prevalent invocation of “chaos” by Japanese architects of this period reflects an affinity

with this holistic viewpoint, harmonizing with both the Japanese essence and a broader

conceptual unity. This leads us to another topic: density.

The literature indicates that, from 1960 onwards, Japanese architects have engaged in

an uninterrupted reflection on modernism. Among the plethora of reflective points, one

particular aspect produced a remarkable consensus: a resistance against the homogeneity

of modernist space. Whether it is Kisho Kurokawa’s concept of “homogeneous

satisfaction,”

Hiroshi Hara’s idea of “Universalism,”

or Kazuo Shinohara’s

discussions on “homogeneity,”

Japanese architects have offered a persistent critique of

Kisho Kurokawa articulates “homogeneous satisfaction” as the uniform happiness derived from the era of

machine production. He argues that the notion of homogeneity is a product of European civilization,

embodying a quintessential feature of the mechanical era. This notion, stretching from Ancient Greece and

Rome to contemporary times, forms the bedrock of Western ideology. Intriguingly, the term “Catholic”

encapsulates the idea of the “universal.” The convergence of identity and universality with the mechanical

era is no mere coincidence. Kurokawa labels the machine age as the epoch of the European spirit—an era

dominated by uniformity.

“Modality: Central Concept of Contemporary Architecture,” published in 1986 in The Japan Architect.

Hiroshi Hara used “Universalism” to summarize the characteristics of Gropius, Mies van der Rohe, and Le

Corbusier’s works.

Similarly, Kazuo Shinohara employs the term “homogeneity” to critique the ambition among numerous

Japanese architects to conceive of a Japanese iteration of the Villa Savoye. He highlights the infeasibility of

144 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

this notion since the post-war era. Their arguments often incorporate a broad spectrum of

references, and at times they even provide critique from the perspective of ancient Greek

philosophy. The architectural discourse covers topics such as functionalism, frontality,

symmetry, the machine age, relationships, art, religion, and beyond. Yet, architects

uniformly converge on the theme of chaos. Chaos, in spatial terms, offers an alternative to

the homogeneity of modernism: it embodies disorder yet harbors order. It distinguishes but

does not disconnect; it flows yet is not homogeneous.

Riichi Miyake has noted that a fundamental tenet of modernism is the belief in a world

characterized by uniform homogeneity. This mindset, however, has started to shift within

the newer generation of architects, who endeavor to create spaces of varied densities.

The second reason is that chaos also springs from “parts.” As previously discussed, it

“originates from ‘parts’,” thus embodying a distinctly Japanese characteristic. Like

complexity, chaos too is derived from “parts.” The formation of chaos relies heavily on the

long-range correlations that emerge from local information, marking a pivotal area of study

within chaotic systems. This insight allows us to grasp how internal system interactions

impact the system’s overall behavior on various scales. The concept of sensitivity to initial

conditions in chaos—denoting the nonlinear interactions among system components—

highlights how slight variations can manifest as significant disparities in overarching

patterns. There exists an intimate linkage between individual system components (like

initial conditions) and the aggregate (such as long-term dynamics).

The third reason is that order underlies chaos. In the modern understanding, chaos has

become a dominant descriptor, indicating the identification of order amidst perceived

disarray. The presence of order within chaos grants it the essence of “beauty.”

The objective of scientific endeavor is to decipher patterns. The absence of pattern

relegates a subject outside the scope of scientific study. Historically, chaos and randomness

were often lumped together as inscrutable and uncontrollable from a perceptual and

analogical standpoint. Yet, by the mid-1970s, scientific progress appeared to render them

controllable and understandable, igniting widespread fascination. This unveils the human

longing for control and a renewed comprehension of controllability. The book titles of

esteemed authors in the field of complexity (Fig. 4.17) reveal a recurring insight: David J.

Bohm’s Wholeness and the Implicate Order; John H. Holland’s Hidden Order: How

Adaptation Builds Complexity and Emergence: From Chaos to Order; Yoshinobu

Ashihara’s Hidden Order: Tokyo through the Twentieth Century; Friedrich Cramer’s

Chaos and Order: The Complex Structure of Living System; Ilya Prigogine and Isabelle

Stengers’s Order out of Chaos: Man’s New Dialogue with Nature; M. Mitchell Waldrop’s

Complexity: The Emerging Science at the Edge of Order and Chaos, and so on. This list—

their vision for a unified, homogeneous Japanese city grounded in modernist principles. Contemporary space

was, for Mies van der Rohe, universal space. His approach was to dismantle and to dissolve this universal

space. Miyake, Riichi. “Deconstructivists in architecture,” The Japan Architect. No.362 (June1987): p6-9.

4.2 First Step: Locating the Orders 145

which is by no means exhaustive—hints at a pervasive theme: the presence of order amidst

chaos. This underlying order is further illuminated through “simplicity,” as articulated by

John Gribbin in Deep Simplicity: “Complex systems, it turns out, can be generated or

described by applying a simple rule repetitively.”

This conviction is widely held among

complexity scientists, where complexity is seen as an evolution from the minimal to the

vast, from the diminutive to the grand. For example, Holland equates the concept of rules

in phenomena from the OCA to Newton’s laws and Maxwell’s equations. He contends that

complexity arises from the accumulation of simple, small beginnings, and our

comprehension of the material world is fundamentally rooted in a handful of basic

equations, centered around the principles of Newton and Maxwell. These laws and

equations serve as the “rules” for this framework.

Holland’s analogy with physical laws

suggests that the world’s essence is simplicity, masked by less visible “rules.” Despite their

inherent simplicity, Newton’s laws and Maxwell’s equations facilitate the emergence of

complexity from simplicity.

Stephen Wolfram concurs, arguing that simple local rules adequately explain the

myriad complex phenomena observable in our surroundings. As shown by the OCA,

complex patterns are indeed born from simple rules.

[Fig. 4.17] “The hidden order” emerged as a common expression during this era. Upon initial observation,

the phrase intuitively conveys that there is an underlying pattern or regularity behind elements that seem

chaotic or haphazard. Intrinsically, this expression intentionally masks the subject of “disorder.”

In this period, the quest for order within chaos paralleled Newton’s pursuit to uncover

unified principles that elucidate the structural rules underpinning interactive behaviors. The

Gribbin, Deep Simplicity, p105.

John H. Holland, Emergence: From Chaos to Order (New York: Basic Books. 1999), p2.

146 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

intersection of these scholarly advancements and the contemporary Japanese context meant

that Japan’s dramatic reassessment of “chaos” was entirely expected. Japan was grappling

with “chaos” on various fronts: urban environmental decay, a predisposition toward

disasters, challenges brought on by rapid modernization, and sudden societal shifts.

Concurrently, there was a burgeoning critique of modernism from within Japan. Chaos,

therefore, was naturally perceived as an intrinsic aspect of Japanese identity and received

widespread acclaim. It fulfilled the aspirations of numerous Japanese architects, which

explains their preference for it.

However, to focus solely on chaos is futile, as chaos in itself lacks substantive

meaning. By comparison, complexity conveys a far more significant message.

First and foremost, chaos fails to establish meaningful structures. This lack of

structure is starkly evident in the FGO (Fig. 4.15, left)—it presents density without detail.

In contrast, the structural dynamics within complexity (Fig. 4.15, right) allow for

accumulation, leading to an emergence of finer details. This process mirrors the

mechanisms of life.

By the early 1980s, chaos theory had hit the point of stagnation, and its leading

researchers had grown disillusioned with its limitations.

It fell short of helping to

elucidate further phenomena. On the other hand, complexity carries inherent meaning: it is

rich in detail and embodies life’s order. The Chinese translation of Deep Simplicity: Chaos,

Complexity and the Emergence of Life bears a telling sentence on its cover: “Chaos breeds

complexity, and complexity heralds the genesis of life.” This statement reflects Gribbin’s

perspective on the evolution of human insight as the transition from chaos to the discovery

of complexity. It underscores the notion that complexity represents an advanced stage of

human understanding, which will be a prominent theme in the forthcoming exploration on

Western architectural interpretations of complexity.

Here, the research quotes Doyne Farmer, whose attitude was recorded in Complexity: “‘After a while,

though, I got pretty bored with chaos,’ says Farmer, ‘I felt So what? The basic theory had already been fleshed

out. So, there wasn’t that excitement of being on the frontier, where things aren’t understood.’ Besides, he

says, chaos theory by itself didn’t go far enough. It told you a lot about how certain simple rules of behavior

could give rise to astonishingly complicated dynamic. But despite all the beautiful pictures of fractals and

such, chaos theory actually had very little to say about the fundamental principles of living systems or of

evolution. It didn’t explain how system’s starting out in a state of random nothingness could then organize

themselves into complex whole. Most important, it didn’t answer his old question about the inexorable

growth of order and structure in the universe.” Paul Cilliers has also expressed a similar attitude. In

Complexity and Postmodernism: Understanding Complex Systems (1998), Cilliers states: “it is necessary to

say something about the relationship between complexity and chaos theory. The hype created by chaos theory

has abated somewhat, but the perception that it has an important role to play in the study of complex systems

is still widespread. Although I would not deny that chaos theory could contribute to the study of complexity,

I do feel that its contribution would be extremely limited.”

4.3 “Complexity” Under the Evolution of Order 147

Thus, in their exploration of fractals, self-similarity, chaos, and randomness, architects

are likely delving into the realm of complexity. Complexity encapsulates these notions,

offering a richer, more meaningful analysis.

In a word, complexity does not subtract, but rather enriches the “density” referred to

by Japanese architects with intricate details.

4.3 “Complexity” Under the Evolution of Order

The FGO serves as a demonstration of logical reasoning that underpins the progression of

many individuals. This reasoning offers an insight into complexity through the prism of

order transformation.

In this context, a renewed understanding is gained of three clichés within Japanese

architecture that highlight a key aspect of complex thinking: they afford us a second glance

at the familiar.

These clichés—ambiguity, dualism, and openness—are widely acknowledged and

represent the essence of Japanese architectural identity. They are particularly reflective of

Fujimoto’s designs. Each of these clichés holds a commanding presence, linking more

broadly to other prevalent concepts in Japanese architectural discourse. Viewed through

this lens, the three clichés achieve a further level of cohesion—all are tied to the concept

of the “in-between.” They are involved in the domain of “complexity,” and within this

framework they display their interrelations.

4.3.1 “Complexity” Under the FGO

The FGO offers a general perspective on order. In many cases, the exploration of

“complexity” in architecture is conducted separately and independently. This is another

reason why “complexity” is easily confused. The FGO does not emphasize “complexity,”

but rather treats the five orders equally, providing a more holistic perspective. The

boundaries between orders are not always black-and-white. To understand “complexity,”

it is necessary to approach it from an integrated view.

Introduced in section 4.1.2, the dispersion of ink droplets in water over time illustrates

a uniform spread throughout the entirety of the container. The converse, ink reconverging

into a droplet, remains unseen. Similarly, heating one end of a long slab quickly makes the

other end unbearably hot, and is a phenomenon where heat has never been observed to

spontaneously localize to one side. In the context of human consumption, not all ingested

food is fully converted into usable energy, with a portion being lost as heat. This directional

process is non-reversible, meaning neither physical work on the person nor heating can

restore the ingested food.

C.P. Snow, The Two Cultures and a Second Look (Cambridge: Cambridge University Press, 1965).

148 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

These phenomena are governed by the second law of thermodynamics, which asserts

the impossibility of such occurrences. The law underlines that disorder and randomness on

an atomic scale are inevitable and irreversible. Take, for example, a car converting fuel

into kinetic energy to move. In this process, heat is unavoidably generated by various parts

and released into the air—not all of the fuel energy is efficiently transformed into kinetic

energy for the car, and thus the universe is incrementally heated. However, applying heat

to the car fails to produce fuel, which would contravene the second law of thermodynamics.

The heat generated in the conversion process represents downgraded energy.

Therefore, if we envision the universe as an immense machine transforming heat into

work, we can see that this transformation inherently entails energy loss, and consequently

elevates the ambient temperature. Viewing this on a cosmic scale, the continual

downgrading (or loss) of energy during the conversion suggests that, eventually, all energy

within the universe will diminish to the lowest level of thermal energy.

[Fig. 4.18] The starting point and the end are determined, but the middle process is not.

The second law of thermodynamics, though described in numerous manners, can be

interpreted uniformly through the lens of “order”: in any closed system, there is a natural

progression toward maximal disorder. Hence, the second law is fundamentally about the

irreversible degradation of energy: it asserts that all organized systems are destined for

eventual dissolution. It conveys a compelling principle of inevitable decline within our

universe, characterizing it as a statute governing decay and degradation. It signifies that

our world is inexorably advancing toward decay. Order inherently follows an evolutionary

4.3 “Complexity” Under the Evolution of Order 149

path. If the graphic for equilibrium is perceived as the epitome of disorder within the

OCA’s miniature world, then this state acts as a magnet, pulling relentlessly (Fig. 4.19). It

resembles an invisible force—the force of disorder—guiding the system relentlessly

toward peak disorder.

[Fig. 4.19] The second law is like the little red man: it is the force of disorder.

This raises a crucial question: are we, and our Earth, among countless other life forms,

positioned precisely within the spectrum of complexity?

Imagine equilibrium as the ultimate destiny of the universe

and homogeneity as its

origin.

With the progression of macro-order, could it be that we are serendipitously

positioned at this evolutionary midpoint—the complex phase?

One encounters a profound contradiction here. If we are indeed in this phase, does it

suggest we have not yet progressed into a phase of chaos? Yet, the universe’s infancy was

marked by chaos. “Chaos,” in its original sense, refers to the universe’s formative state.

Setting aside the debate on the universe’s early conditions, there remains no proof of life’s

presence in the universe’s dawn, implying an absence of complexity, or to put it more

Based on conclusions drawn from the second law of thermodynamics, the universe can be likened to a

drop of ink diffusing in a cup of water, ultimately losing all distinction in color. There will cease to be any

change across the cosmos, and it will succumb to absolute silence. This concept is known as heat death.

Hermann von Helmholtz remarks: “Henceforth, the universe is doomed to an everlasting state of inertia.”

Consider the sequence of order changes from an energy standpoint. The peak energy condition is when

energy is in a clumped-up state, marked by homogeneity and orderliness. An example of this is the Big Bang

theory: the prevailing belief is that our universe originated from a Big Bang around 14 billion years ago.

Initially, the universe was a singularity characterized by an infinitesimally small volume and infinite mass,

density, temperature, and energy, akin to a “super-energy crystal” without any flaws or perturbations. Its

physical state was perfectly homogeneous and entirely free from defects.

150 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

accurately, an absence of order as sophisticated as our own. This indicates that we

originated from a state of chaos or, at the very least, a primitive state of complexity. Under

the second law of thermodynamics, it would seem logical for us to devolve into further

disorder, or evolve toward more chaotic or equilibrated states. How, then, did the order of

complexity arise? How were structured, meaningful constructs accumulated? How did life

emerge?

Contemplating this, one might consider examples of “order reversal” observed in

daily life, such as the condensation of water vapor into liquid upon cooling, further

transitioning into ice with additional cooling. Transitioning from gas to liquid, then to solid,

the system’s molecules gradually “calm down” as thermal energy diminishes, leading to

an increasingly “ordered” state, ultimately forming highly ordered ice crystals,

accompanied by a temperature decrease. Superconductivity

serves as a further example.

Yet, these instances still conform to the second law. The complexity observed on Earth

might merely represent a small “fluctuation” within the vast cosmos, contingent upon a

slight increase in “disorder” elsewhere in the universe. This is akin to observing gas

molecules in a container occasionally clustering to one side rather than spreading uniformly,

a scenario which, statistically speaking, is exceedingly rare.

This leads to a plausible conjecture: might there be an unseen force countering the

second law? A force capable of elevating the system’s degree of order, facilitating the

emergence and stabilization of structures, and allowing for the accumulation of complexity,

thereby enabling the origin of life?

According to current knowledge, there is no force that works entirely against the

second law, but there is one that can slow it down. This force can somehow simultaneously

affect both the system’s order and the second law.

This force was first described by the French scientist Henri Bénard in 1900. By

initiating convection through heating the fluid’s base and cooling its top, Bénard observed

a transformative phenomenon: at a specific critical temperature gradient, the fluid’s

movement spontaneously shifted from chaos to order. His experiment is known as

Rayleigh-Bénard Convection, or R-B convection. (Fig. 4.20)

In Synergetics, Haken articulates a quintessential question: “The consensus among most physicists is that

approximately 10 billion years ago, the universe originated from an intensely hot fireball during a ‘Big Bang’,

a state devoid of any prevailing order, implying the universe’s nascent state was one of chaos and absence of

structure. Given this, disorder is expected to have escalated, maximizing over time. How, then, is there space

for the emergence of orderly, significant structures, or even life?” Such enquiries resonate across numerous

publications by researchers in complexity.

The Dutch physicist Heike Kamerlingh Onnes pioneered the observation of superconductivity in a

laboratory setting. He noted that mercury's electrical resistance falls sharply to zero, not merely diminishing,

when cooled to 4.2K (-269°C). This phenomenon occurs as reducing the temperature significantly enhances

the orderliness of electron movement within specific metals.

4.3 “Complexity” Under the Evolution of Order 151

[Fig. 4.20] R-B convection. Envision this process in terms of observing the cross-section of a flat-bottomed

pan uniformly heated with liquid contained within. Hot (red) fluid rises from the bottom while cold (blue)

fluid falls down from the top. With continuous energy input, the mixture of hot and cold fluids becomes

exceedingly chaotic. Yet, when a critical threshold is reached, the equilibrium is disturbed, and the previously

uniform liquid surface abruptly transitions into hexagonal convection cells. With ongoing energy input, these

convection cells are perpetually disrupted and reassembled.

[Fig. 4.21] B-Z reaction. Discovered in the 1950s by the Russians Boris Belousov and Anatol Zhabotinsky,

this reaction demonstrates orderly periodic behavior—the cycling of oscillation—upon the addition of

reactants, a process that requires no external control. This signifies the spontaneous emergence of order

within the system.

152 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

Another pivotal experiment is the Belousov-Zhabotinsky, or B-Z, reaction (Fig. 4.21).

These experiments provide a vital insight into our existence: under specific conditions,

order can manifest spontaneously. Systems can evolve from disorder to order without any

external intervention.

Initially, these discoveries were met with skepticism from the scientific community,

where they were perceived as challenging established thermodynamic laws. The concept

of a spontaneous force of order was not yet recognized, with the prevailing belief being

that order could not emerge from disorder and that the progression toward order was

inherently unidirectional.

Yet, its profound implications were grasped by one individual. Two decades later,

leveraging these foundational experiments, he formulated a comprehensive theory, earning

the Nobel Prize for his contributions. This individual was Ilya Prigogine, and his pioneering

work introduced the theory of self-organization

—the force of order.

This dissertation began to explore self-organization in section 2.1.5. Within

architectural discourse, self-organization frequently conjures images of randomness, or the

concept of “architecture without an architect.” Yet, self-organization transcends the mere

provision of an aesthetic or feeling; it embodies a profound mechanism capable of

counteracting the forces of disorder, thereby decelerating the systemic march toward

entropy. It underlies the emergence of “structures” within our environment, the genesis of

life, and the preservation of structure in our world. It is the interplay of self-organizing

forces that transitions us from a state of chaos to complexity.

In summary, complexity discussions often hinge on specific definitions. The graphic

for complexity, for example, though it is indicative of structural emergence and is linked

metaphorically to life—with life indeed serving as an apt metaphor for complexity—has,

as we have acknowledged previously, self-organization as a facet of its complexity. Hence,

the advent of life and its inherent structure, as dissipative phenomena, are intricately linked

to complexity, making both life’s emergence and its essence fundamentally connected to

complexity.

As already discussed in section 2.1, self-organization describes the phenomenon where a system's internal

component interactions foster the development of ordered and complex structures and behavioral patterns,

all in the absence of external direction. Haken, an influential proponent of self-organization theory, delineates

“self-organization” thusly: a system is considered self-organizing if it attains spatial, temporal, or functional

structuration autonomously, devoid of any explicit external manipulation. Haken H. Information and Self-

Organization: A Macroscopic Approach to Complex System. (Berlin & New York: Springer-Verlag, 1988).

Not every system experiences a phase of “complexity.” Prigogine’s self-organization approach emphasizes

the prerequisites for self-organization, while Haken’s perspective delves into the dynamic aspects of self-

organizing processes.

In Complexity, Michell succinctly encapsulates it as a new second law that contradicts the second law of

thermodynamics. He posits that, though they are still nebulous, phenomena like emergence, adaptiveness,

and the brink of chaos have begun to delineate a preliminary framework for this novel principle. Waldrop,

Complexity, p288.

4.3 “Complexity” Under the Evolution of Order 153

[Fig. 4.22] The “force of order” counteracts the second law, delaying the system’s descent into disorder.

This perspective, however, offers a static view of complexity and life. Viewed through

a broader lens, complexity theory essentially probes the genesis of “life” from an orderly

perspective. As Waldrop notes:

For Kauffman, order is the key to unraveling the mystery of human existence,

elucidating our emergence and existence as sentient, living beings in a universe

ostensibly ruled by randomness, chaos, and blind natural laws [...] Darwin’s theory of

natural selection does not encompass the entirety of human existence. Darwin was

oblivious to the force of self-organization, the enduring power that molds itself into

progressively complex systems, even as they are subject to the perpetual force of

disintegration as outlined by the Second Law of Thermodynamics. Darwin was

unaware that the forces of order and self-organization are the architects of living

systems

Complexity emerges from the interplay of these forces, with the sustenance of life

structures advancing under their mutual influence. This represents an interpretation of life

through the prism of order, focusing on the dynamic evolution of structure formation,

accumulation, and collapse under these forces. It conceptualizes order as various states of

a unified whole, not as static, extant, or end-state phenomena (Fig. 4.22). Complexity,

therefore, cannot be dissected for isolated examination; order is comprehensive.

With this nuanced comprehension of complexity, we proceed to explore the three

clichés within Japanese architecture, beginning with further discussions of Fujimoto that

were not covered solely by Rule 110.

4.3.2 The Unity of Opposites

In Fujimoto’s architectural discourse, the “dissolution of binary oppositions” emerges as a

central and frequently revisited concept, embodying his approach and expectations. His

exploration of the inside-outside dynamic serves as a prime example, raising questions

such as: How can one inhabit inside and outside simultaneously? How can a structure

embody both home and city? How can division coexist with connection?

Waldrop, Complexity, p134.

154 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

A closer look at Fujimoto’s narratives reveals a pattern: the juxtaposition of two

apparently contradictory facets that hint at potential transformations (Fig. 4.23).

[Fig. 4.23] The oppositions explored regularly by Fujimoto.

Through Fujimoto’s lens, various themes are dissected, each revealing a deeper

dialogue. On the surface, the “nest or cave” discourse critiques functionalism by

distinguishing between the human-crafted nest and the naturally occurring cave, subtly

addressing the artificial versus natural dichotomy. However, its deeper pursuit lies in

harmonizing the artificial (nest) with the natural (cave). Discussions on gradations navigate

the spectrum between black and white, advocating for their mutual existence. The “city as

house—house as city” theme endeavors to meld the distinctions between urban and

domestic realms. “Inside out—outside in” seeks the dissolution of interior and exterior

dichotomies. The dialogue on “nature—forests” portrays forests as an interplay between

transparency and opacity, the coexistence of segmentation and totality, encapsulated in the

concept of “envelope—lack of envelope.” The “before differentiation” theme contemplates

Gestalt switches, embodying a departure from binary distinctions. The discourse spans

various dichotomies—houses and streets; matter and space; morning and night;

comprehensibility and incomprehensibility; dynamism and immobility; segmentation and

totality; interiority and exteriority; 0 and 1; one-dimensionality and two-dimensionality,

4.3 “Complexity” Under the Evolution of Order 155

among others. Each theme, rich in oppositions, converges on the notion of merging and

cohabiting, positioning itself in an “in-between” state.

Section 3.3 highlighted discussions among influential architects of the 1970s about

“in-betweenness,” a concept emblematic of that era’s “Japanese” aesthetic. Yet, its

interplay with complexity was only explored in a piecemeal fashion. Further insights from

the subsequent section offer a clearer perspective, illustrating how “in-betweenness” and

complexity are intimately connected.

This exploration reveals Fujimoto’s architectural narrative not just as a collection of

themes but as a cohesive enquiry into the essence of complexity, where the dissolution and

coexistence of binary oppositions forge a path toward an “in-between” realm of existence.

The emergence of complexity is delineated through the dynamics between two polar

forces: the entropic pull of disorder, symbolized by the second law, which draws everything

toward decay and dissolution, and the counteracting force of order, or self-organization,

which mitigates the relentless march toward entropy. Life’s intricate structures flourish

within this fraught yet fortuitous nexus, engaging in a perpetual cycle of energy

assimilation, decomposition, and reconstitution.

The imperative of order is undeniable, providing the foundation for structure and

accumulation, warding off an immediate lapse into disarray. However, the significance of

disorder is arguably paramount. Absent its influence, order would stagnate, crystalizing

into a static uniformity.

Morin’s concept of the “third look” captures this duality as a keen awareness of how

the generative forces of order and the erosive powers of disorder coexist, shaping our world

through a continuous flux between formation and breakdown. Morin’s discussion of this

subject sheds light on the intrinsic dynamism that defines our existence:

The intricate melding of order with disorder, and the dance between chance and

necessity (embodying a logic of dualities), lies at the heart of complexity. Complexus

denotes a richly interlaced fabric. Our experiential universe is an elaborate weave of

order, disorder, and organization, indissolubly bound together. These elements are

simultaneously complementary and, in the juxtaposition of order versus disorder,

confrontational, even paradoxical. This illuminates the notion that complexity is a

conceptual scaffold that weaves the singular with the plural into the complexus’s

unitas multiplex (a tapestry of diversity), melding complementarity and contradiction

into a harmonious duality of logic.

Order therefore emerges as an indispensable, unified whole. Complexity’s signature trait

is the enduring coexistence of contrasts. It is this interplay of forces that underscores

complexity’s pivotal role: a crucible for the dynamic interplay of varied forces. This

Morin, Edgar.

复杂思想：自觉的科学

(Science avec conscience), p170.

156 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

elucidation enables us to perceive all other forms of order within the graphic of complexity

(Fig. 4.16). Absent any one side, the system (life) would veer from the complexity domain,

precipitating a fall from grace.

This exposition invites a transformative shift in understanding: it was once presumed

that opposites within complexity simply coexisted. However, this refined interpretation

highlights their intrinsic interdependence. The interrelation of opposing forces undergoes

a complete inversion within the domain of complexity. This notion dovetails seamlessly

with Fujimoto’s previously discussed idea of “expectation.”

In our collective experiences, there lies a common desire: to share moments with our

loved ones—family, partners, friends—within the same spatial and temporal confines. Yet,

paradoxically, there arises a need for personal space to engage in work, contemplation, or

rest in solitude. How, then, can we navigate the balance between collective presence and

individual solitude? We seek to immerse ourselves in the outdoors, to breathe in the

freshness of the air, while simultaneously wishing for protection from its elements. How

do we achieve a state of being both indoors and outdoors? How can architecture be a

testament to both the archaic and the futuristic, embodying both the individual components

and the entirety? These dualisms, once perceived as contradictions, now find reconciliation

in the concept of complexity. The skin of an apple (or any living form), a paradigm of a

“complex” boundary, illustrates this beautifully. It achieves feats that are deceptively

simple, yet elusive in our current technological prowess: facilitating breathability while

preserving moisture.

Fujimoto’s architectural ventures seek to realize these very ambitions, potentially

marking his success. Jörg H. Gleiter’s observation about House N may very well capture

the essence of complexity—the vibrancy of life itself: “A strange tension fills the space; it

is a different kind of equilibrium, an almost feverish calm…”

This exploration of “dissolving binary oppositions” in Fujimoto’s work echoes a

longstanding tradition in Japanese architecture. Kisho Kurokawa’s philosophy of

symbiosis, particularly when viewed against the backdrop of its era, tends to symbolize a

“cultural symbiosis” which aims to confront the modernist agenda of “eradicating all

cultures.” Yet, the symbiosis discussed extends beyond mere cultural dialogue, advocating

for a harmonious coexistence of diverse entities.

Kisho Kurokawa, an architect profoundly influenced by complexity theory, was also

a fervent advocate of “Japaneseness.” Regardless of how the notion of “Japaneseness” has

been labeled or interpreted across different periods, his work, The Philosophy of Symbiosis,

makes a distinct argument for the idea that architects should be anchored firmly in their

own historical and cultural heritage. According to Kurokawa, one’s historical and cultural

Gleiter, “The most extreme aesthetic The Architecture of Sou Fujimoto,” p330.

4.3 “Complexity” Under the Evolution of Order 157

background is “the proof of [one’s] own identity.” Essentially, his book is a discourse on

Japan.

This nuanced comprehension of complexity lends a possible trajectory to the concept

of “in-betweenness,” fostering a dialogue between the complexity inherent in architecture

and the essence of “Japaneseness.”

4.3.3 Ambiguity

“Ambiguity” often emerges as a recurring motif within the realm of Japanese architecture.

Originally, this concept was invoked in response to the rigid “definitiveness” and “clarity”

of modernism, serving to extol the virtues of “Japanese” attributes. As architectural

discourse evolved, the application of ambiguity extended into myriad facets. The notion of

the in-between, layered or indistinct boundaries, disorderliness, and the absence of a central

focus all serve as catalysts for ambiguity. Phenomena such as clouds, fog, vapor, and

rainbows, which possess variable densities without clear demarcations, are quintessential

examples of ambiguous outcomes. The principle of self-similarity, shifts in scale, or their

negation, and the interplay between the internal and external realms, related to the

discourse on boundaries, all introduce elements of ambiguity. Self-organization, too, brings

forth ambiguity through a decentralized approach, underlining the ambiguous nature of

processes. Furthermore, the innovative manipulation of materials can instill a sense of

ambiguity. Kengo Kuma’s exploration of particle architecture, utilizing small,

transportable materials, aims to imbue spaces with an ambiguous aura. Kazunari

Sakamoto’s practice of painting over concrete or exquisite woods is another method of

introducing ambiguity, stripping away the “social significance” imbued in materials. This

concept is further illustrated in projects of his such as House F, with its stretching of

inherent relationships between architectural elements, or the dismantling of the spiral in

House SA, which disrupts conventional symbols to foster ambiguity. Junya Ishigami’s

deviation from the everyday, which resonates with Sakamoto’s ethos, finds its expression

in the Sendai Mediatheque, embodying ambiguity through the dissection of preconceived

notions.

These manifestations of ambiguity weave through the fabric of Japanese architectural

thought, binding together diverse yet prevalent strands within the architectural

philosophies of Japan and, by extension, Fujimoto, revealing a deep, unifying undercurrent.

At its essence, what encapsulates ambiguity?

Deliberation reveals a somewhat less “ambiguous” truth: the myriad expressions of

ambiguity converge on a singular necessity—the observer. Ambiguity, then, is born from

the observer’s interpretation, suggesting that ambiguity fundamentally denotes a form of

“perception.”

This realization enables a connection to a distinct “Japaneseness”; to particular human

actions and sensory experiences. This continuum spans the contemporary voices of

158 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

Fujimoto, Akihisa Hirata, and Junya Ishigami, reaches back to Kazuyo Sejima and Ryue

Nishizawa, to the innovative “wild samurai” like Toyo Ito and Kazunari Sakamoto,

navigates through the legacy of Kazuo Shinohara to Kenzo Tange and, ultimately, to

Sutemi Horiguchi. This lineage is united by its exploration of perception and corporeality,

a thread that has been woven through the narrative of modern Japanese architecture from

its outset.

In contrast, the realm of perception, intricately tied to consciousness, stands as a

hallmark of complexity. Its intricate web of considerations may well surpass the deepest

complexities found within life itself, presenting challenges that defy reductionist solutions.

When perception and action are distilled into the dynamics of stimulus and response, one

encounters one of the most fundamental simplifications prevalent in the exploration of

complex systems.

From this vantage point, the synergy between “Japaneseness” and “complexity”

emerges as inherently logical. However, this realization frames ambiguity merely as a

phenomenon of perception. The question deepens: what underlies the sensation of

ambiguity?

For the moment, avoiding a deep dive into semantics, let’s visually engage with a few

images from the FGO. The representations of complexity, chaos, and equilibrium within

the FGO evoke a distinctive sense of ambiguity. Does an intrinsic relationship exist

between the ambiguity found in Japanese architecture and these visual representations? If

so, which illustration aligns most closely?

The essence of ambiguity in equilibrium is derived from the sheer randomness of its

constituents. This randomness is perceived as ambiguity specifically when there is an intent

to delineate equilibrium accurately. Despite its disparate nature and the lack of any

discernible pattern, it is often reduced to a familiar analogy in human interpretations: the

snow of static on a television screen. The differentiation between complexity and chaos is

equally discernible. In contrast to the randomness and turbulence signified by chaos,

complexity offers a semblance of stability, presenting structures that elude straightforward

description. While chaos embodies a sense of unbridled disorder, complexity occupies a

more nuanced position, delicately locating itself between the realms of order and disorder.

Exploring the roots of this ambiguous sensation, one discovers that perception and

analysis are at play. The challenge arises in our cognitive efforts to dissect and understand

these phenomena, which is demonstrated in our struggle to offer succinct descriptions. It

is this very challenge that renders complexity, chaos, and equilibrium signs of an

ambiguous sentiment.

Within complex systems research, a specific type of system is identified as the Sensitive and Reactive

System (SAR). Furthermore, the relationship between stimulus and response can be effectively captured and

implemented in computer programming language, using the foundational “if...then...” statement.

4.3 “Complexity” Under the Evolution of Order 159

Let’s return to the concept of ambiguity. Describing something as ambiguous implies

that it inherently combines elements of both clarity and obscurity. The absence of either

characteristic would preclude its classification as ambiguous. Thus, ambiguity necessarily

entails the coexistence of clarity and obscurity. Accepting this premise allows us to equate

clarity with order and obscurity with disorder, leading to the interpretation of ambiguity as

the concurrent perception of order and disorder. This interpretation circles back to the

notion of complexity.

The efficacy of human visual perception in elucidating this concept cannot be

overstated. The human eye’s capacity to observe and express feelings remains unparalleled

by any scientific method or technological advancement, standing as the most effective

means of understanding.

Initially, the concept of homogeneity is straightforward and

unambiguous. Transitioning to periodicity introduces a slight increase in descriptive

complexity, necessitating a more elaborate narrative, yet it remains comprehensible. The

progression to complexity marks a zenith in descriptive challenge, highlighting a point

where visual perception struggles to distill a succinct overview. Advancing to chaos again

means a simplification in description, despite the persistence of significant randomness.

This stage is characterized by a consistent randomness across areas, offering a stark

contrast to the complexity stage, which lacks uniformity even on a macro scale. The

journey ends at equilibrium, where, despite complete randomness, description is simplified

once more.

This analysis aligns with direct observations, enabling the most fascinating forms of

ambiguity to be identified. Further contemplation reveals that periodicity offers a more

organized form of ambiguity, chaos introduces a more disordered form, and complexity

provides a balanced version, which makes it the quintessential representation of the term.

In essence, the discussion of ambiguity may well be a discourse on complexity.

Addressing potential objections highlights the subjective nature of perception, where

one person’s ambiguity might be another’s clarity; when viewed from the perspective of

generating chaos through iterative operations, chaos appears simple. However, when

attempting to predict the sequence of states or describe the generative properties of

emerging patterns, chaos becomes highly complex. This observation leads to the question

of whether there exists a universally recognized form of ambiguity—an objective

ambiguity. In the context of Rule 110, one finds an example of such objective ambiguity,

rooted in the concept of emergence. Emergence, by its very definition, carries an element

of surprise. The macro patterns and micro behaviors within emergent systems exhibit no

direct correlation, suggesting that without an “experiential” bridge, it is inherently

challenging to predict the connection between two levels. This gap, or “Hierarchy Jump,”

Wolfram remarks that “by far the most common way in which we determine levels of complexity is by

using our eyes and our powers of visual perception.” Wolfram, Stephen. A New Kind of Science. Wolfram

Media, 2002, p559.

160 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

introduces a form of ambiguity that transcends subjective interpretation, providing a

compelling example of objective ambiguity. This refined explanation underscores the

complex interplay between order and chaos, subjective perception, and the objective reality

of emergent patterns, inviting further contemplation on the nature of ambiguity and

complexity.

The enquiry into why ambiguity is appealing raises questions about the brain’s

preferences. Is clarity not more desirable to the brain, in a way akin to humanity’s early

reverence for the golden ratio? This belief posits that the eyes favor simple imagery, and

aligns with the notion of a “lazy” brain that equates simplicity with order. Christopher

Alexander, in his 1959 paper, challenged these conventional views by proposing that the

brain might in fact have a predilection for complexity.

Further contemplation reveals that this preference for complexity is not unexpected.

We are fascinated by literary works that represent characters performing actions that are

contradictory to their nature. The multifaceted nature of characters is incredibly alluring,

as true complexity transcends simplistic, black-and-white narratives. Similarly, while

simple forms and the golden ratio are pleasing, the aesthetic joy derived from experiencing

order amidst disorder and chaos should not be underestimated.

This suggests that the brain may indeed have a propensity toward embracing

complexity, challenging the traditional belief in a preference for simplicity. Wolfram writes:

And indeed I suspect that even below the level of conscious thought our brains have

a rather definite notion of complexity. For when we are presented with a complex

image, our eyes tend to dwell on it, presumably in an effort to give our brains a chance

to extract a simple description […] somehow the images that draw us in the most—

are those for which some features are simple for us to describe, but others have no

short description that can be found by any of our standard processes of visual

perception.

The allure of ambiguity might not necessarily be viewed as a weakness but rather an

enticement that humans are not predisposed to resist. This enticement is evident in designs

targeting human vulnerabilities, such as smartphones, video games, social media, and

consumerism. Seen through a critical lens, these are crafted to exploit human

susceptibilities, becoming irresistible temptations that familiarity does not diminish.

Conversely, from a more generous perspective, they are created to resonate with human

consciousness and intellect. Similarly, the built environment ought to identify and cater to

these human inclinations. Complexity, in this context, may hold such latent capability.

Christopher Alexander, Early and Unpublished Writings of Christopher Alexander: Thinking, Building,

Writing, ed. Howard Davis (Routledge, 2022), p5.

Wolfram, A New Kind of Science. p558.

4.3 “Complexity” Under the Evolution of Order 161

Ambiguity engenders a uniquely stimulating and interactive experience for the brain,

a technique that features prominently in Japanese architecture. The intentional omission of

“experience” is a hallmark of iconic designs such as Toyo Ito’s Sendai Mediatheque,

Kazunari Sakamoto’s silver-laced concrete, Junya Ishigami’s ethereal metal, and Ryue

Nishizawa’s Teshima Art Museum (Fig. 4.24). These designs feature a purposeful omission

of experiential elements. For instance, the Teshima Art Museum’s expansive exhibition

space is starkly white and pillarless, diluting the relationship between individual

components and the whole, and ruthlessly eliminating any associated information. Within

such spaces, individuals lose their capacity for judgment as the “experiences” and

architectural habits that guide daily actions abruptly disappear. Initially, this unfamiliarity

is challenging because of the brain’s unaccustomedness to such a lack of “connection.”

Over time, without external directives, people begin to forge these “connections”

themselves, which highlights the human brain’s remarkable ability to adapt by instinctively

seeking comfort and engaging with its surroundings.

[Fig. 4.24] Teshima Art Museum (2004-2010).

As Ryue Nishizawa observes:

During my prolonged engagement with observing diverse architectural forms, I’ve

noted how buildings are enlivened through human interaction, and conversely, how

some buildings are utilized in a rather routine manner. I’ve been drawn to spaces that

invoke a desire for engagement, as well as to those that repel it. This observation led

me to appreciate that engaging with space is a form of creative expression [...] What

162 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

then constitutes a space that beckons to be used? It prompted our sustained interest in

architecture that sparks the imagination of its users.”

Junya Ishigami’s work exemplifies this ethos. In his Table Project (Fig. 4.25), Ishigami

utilized prestressed bending correction to fashion a table with the remarkable dimensions

of 10000 × 2500 mm and a mere thickness of 3mm, challenging the limits of conventional

experience. This design not only provokes curiosity but fosters a dynamic interaction

between the object and its user. Through his Balloon project, Ishigami introduced a

voluminous “metal block” suspended in mid-air (Fig. 4.26), creating a stark contrast with

the typical perception that metal is heavy. This design challenges physicality by exposing

and fundamentally restructuring the complex constraints and assumptions that are often

accepted uncritically.

[Fig. 4.25] Table Project.

[Fig. 4.26] Balloon Project.

Ryue Nishizawa, “Dialogue: Approach to Architecture,” The Japan Architect, No.72 (Yearbook 2008)：

p4-7.

4.3 “Complexity” Under the Evolution of Order 163

If we revisit Fujimoto’s philosophy, we can see that a sense of randomness pervades

both his rhetoric and his architectural creations. Yet, it is essential to recognize that the

essence of randomness is inherently undifferentiable—the emotions evoked by true

randomness and pseudo-randomness are essentially the same. Within the FGO, three

figures exhibit this randomness. Should randomness be synonymous with ambiguity, then

the figure labeled equilibrium would epitomize randomness. This perception, much like its

previous classification as the peak of complexity, is devoid of architectural relevance.

Hence, with regard to the feeling of randomness, chaos and complexity are perceived

equally, which explains the historical Japanese use of “chaos.” Mere randomness or the

feeling thereof lacks significance. The key question is what lies beyond the randomness.

Moreover, randomness conveys a feeling of disorder. Compared to this, the sensation

of complexity is broader as it does not reject “order” but rather includes it. Adding

“disorder” into the mix poses a cognitive challenge, thereby enriching the experience.

The brain, then, might perceive both order and disorder concurrently, as existing in

an “in-between” space.

4.3.4 Openness

From the functional elegance of traditional sliding doors

and the cultural practice of

Sakura viewing

to the serene expanse of Shinto shrine spaces,

the motif of openness

is often cited as an exemplary cliché within discussions of Japanese architecture. Openness

has been an enduring and universally recognized emblem of Japanese architectural identity

throughout the ages. Importantly, the principle of openness is also profoundly intertwined

with the dynamics of complexity, especially when examined through the transformative

lens of order and structure.

This dissertation poses a fundamental question: Is the openness observed in Japanese

architecture indicative of a higher-level “emergence”? Can it be seen as an outcome

Fusuma, a staple in traditional Japanese residences, employs lightweight sliding doors to delineate

spaces—an enduring testament to the concept of “openness.” With Fusuma retracted, interior and exterior

realms seamlessly merge through a nuanced, layered progression.

Sakura viewing, a quintessential Japanese practice, exemplifies spatial delineation through ambience

rather than explicit barriers. Amidst nature, individuals demarcate their presence with merely a fabric under

blossoms. Toyo Ito remarks that: “this singular act forges a unique spatial experience. The mere deployment

of ‘fabric’ acts as a gentle divide, embodying a philosophy deeply rooted in Japanese culture, significantly

influencing my creative endeavors.”

The Japanese practice of defining spaces simply with pillars, as seen in Torii gates, symbolizes the

threshold to the divine. They signal to visitors the impending transition into sanctity, necessitating decorum.

Kiyonori Kikutake writes: “Columns set off space, the floor defines space.” This notion finds resonance in

the Sendai Mediatheque, where columns not only sculpt the spatial experience but also radiate vitality. The

Onbashira Festival, a venerable event in Nagano—Toyo Ito’s homeland—revolves around four wooden

pillars that sanctify the shrine’s perimeter. This ritual, observed every six years, involves the community in

the ceremonial selection and renewal of the pillars, believed to house divine spirits, thus perpetuating the

essence of the deities. The Mediatheque’s pillars mirror this embodiment of the spiritual, shaping and

energizing the architectural space.

164 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

independent of its initial causes? Or is it an inevitable aspect of a particular phase in societal

evolution?

Let us first consider the concept of “openness” in Japanese architecture from a

macroscopic viewpoint. Openness indeed spans multiple dimensions, with distinct

interpretations in fundamental science, social science, psychology, and ecology. The

evolving philosophical landscape within the history of Japanese architecture has charted a

course of progressive openness across these realms (as detailed in section 2.4).

The 1980s, for example, witnessed the rise of architecture marked by its “lightness,

thinness, and temporariness,” illustrating a variant of openness. Themes such as the public

domain, interaction with urban contexts, perceptual experiences, spatial diversity, and the

breakdown of enclosure began to permeate architectural discourse. Furthermore, the

postmodern current that emerged in the 1960s, challenging the dominance of modernist

ideology by highlighting cultural pluralism and decentralization, and by critiquing grand

narratives, represented another facet of openness—intellectual openness. By around 2000,

these dimensions of “openness” had morphed into a notion of “freedom” or “liberation,”

interpreted as a more sophisticated and encompassing iteration of openness.

This narrative of incremental “opening,” from the late 1960s rejection of chaos,

through the gradual unveiling of the 1970s (Fig. 4.27), to the mid-1980s embrace of

“openness,” culminating in the “liberation” of the post-2000 era, parallels a deepening

grasp of “complexity.”

To explore further, the expression of “openness” by individual architects merits

attention. Sou Fujimoto, while not often verbalizing the concept, infuses his designs with

the concept of openness. House N, for instance, centers around themes of nebulousness and

self-similarity, and includes nested structures. While these are established concepts within

architectural discourse, Fujimoto shifts the focus from form to spatial perception. The

nesting within his projects generates “in-betweens”; space is employed to delineate other

spaces, thus creating a “continuous sequence of ‘in-betweens’.” Upon initial observation,

the architecture appears to be constructed from white walls that are self-similar but vary in

scale. Fujimoto seems to fully embrace the “nesting” principle (Fig. 4.28), yet the

generation of “in-between” spaces is facilitated by strategically placed openings in these

walls—a distinctive strategy that sets his approach apart from traditional “Matryoshka

dolls,” which are completely enclosed. The charm of Matryoshka dolls lies in the intrigue

of uncovering dolls-within-dolls, which contrasts with Fujimoto’s aim to make the

innermost box visible.

4.3 “Complexity” Under the Evolution of Order 165

[Fig. 4.27] In the middle of the 1970s, Sakamoto’s work began to articulate an ethos of openness. The

Machiya in Daita (1976), emblematic of Sakamoto’s “house type” concept during his second phase, presents

an exterior that might deceive with its “closed” appearance. However, as Sakamoto reflects, this project

initiated a transformative approach by “relativizing the closed nature of box-in-box relationships [...]

inaugurating a design philosophy that facilitated the interplay of sightlines and pathways, effectively

‘unboxing’ the enclosed space into a continuum of openness.” Toyo Ito’s pioneering engagement with

openness is epitomized in his House in Kasama, conceived in 1981. Following this trajectory, Adele’s Dream,

completed in 1983, acts as an antecedent to Silver Hut, advancing the nuanced dialogue of ambiguity and

contrast established in the House in Kasama. The architectural narrative employs dual geometric forms for

the roof and diverges into a palette of varied colors for the walls, a stark contrast to previous monochromatic

tendencies. The liberal application of expansive windows and the addition of skylights underscores a

commitment to luminosity. Subsequent to this endeavor, Ito crafted Silver Hut, a seminal project that stands

in diametric opposition to White U, championing a philosophy of openness. Through these edifices, one

discerns the crucial juncture in Ito’s oeuvre, a deliberate transition from the introspective to the open.

[Fig. 4.28] Left: Ordos 100.

[Fig. 4.29] Right: House N. Subsequent to Fujimoto’s depiction of nebulousness, the usual continuation

involves two models distinguished by their expansive openings in white walls and the extensive tree planting

featured within.

166 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

The notion of self-similarity, while not inherently linked to openness, is explored by

Gribbin in the context of chaos through the lens of the Feigenbaum diagram’s period-

doubling—a structured chaos, yet not directly tied to openness or complexity.

architectural practice, self-similarity’s relation to openness is not straightforward, yet

Fujimoto’s implementation seems intrinsically connected to fostering openness.

This perspective extends to other Japanese architects, such as Toyo Ito and Kazunari

Sakamoto in the 1980s and 1990s, who challenged notions of “consumption,” “meaning,”

“symbolism,” and “systems” as forms of restriction. Contemporary architects, including

SANAA, Junya Ishigami, and Akihisa Hirata, exhibit a nuanced exploration within their

architectural vernacular. Their methodologies, though not explicitly aimed at openness or

the direct discussion of it, consistently reveal an essence of openness. Without directly

referencing complexity theory, their deep engagement with Japaneseness, focusing on

“parts,” “in-betweens,” and “clouds,” suggests that openness is a logical culmination of

their architectural exploration.

Thirdly, we engage with a theme ubiquitously woven into the fabric of Japanese

architecture: the essence of life. From the inception of the Metabolist movement in 1960,

the motif of life has frequently emerged in the discourse of Japanese architecture, notably

initiated by Kisho Kurokawa with the “Era of Life” slogan, leading to profound

architectural reflections.

What constitutes life? Introduced in section 4.3.1 were dissipative structures which

position life

as something akin to hexagonal foam as shown in Fig. 4.20.

In this

context, Friedrich Cramer’s analysis of life is particularly illuminating:

Eventually, life systems disintegrate, and all highly ordered structures face inevitable

decay and breakdown. Death represents the juncture where an organism ceases to be

supported by external energy inputs, leading to the collapse of its systems. A living

entity is thus characterized as a system that sustains or even enhances its organized

structure through the continuous absorption of external energy.

Here, life is interpreted as an archetypal dissipative structure. The dissipative structure

theory offers an essential paradigm for grasping life’s underlying principles.

Gribbin, Deep Simplicity, p93.

It is not only life that exhibits self-organization; our urban environments, economic systems, scientific

advancements, and societal frameworks also embody this principle. This ordering force pervades our

everyday existence, aligning with the definition that, without external intervention, these entities have

developed stable structures.

Prigogine’s theory defines dissipative structures as ordered configurations within open systems that

deviate significantly from equilibrium. Such structures sustain themselves via the interchange of matter and

energy with their surroundings. Given specific conditions, these systems can spontaneously transition into a

state of order, facilitating the emergence of novel and intricate structures.

Cramer, Chaos and Order, p21.

4.3 “Complexity” Under the Evolution of Order 167

Openness stands as the essential precondition for the genesis of dissipative structures.

Traditional research in physics has been anchored in the study of closed systems, which

posits that the field investigates outcomes based on closed system analyses. A closed

system, by definition, neither impacts nor is impacted by its external environment, and nor

does it permit the transfer of matter. The dynamics described by the second law of

thermodynamics are exclusive to such closed systems. Conversely, open systems (Fig. 5.6)

are characterized by their interaction with the external environment through the exchange

of matter and energy, fostering a non-equilibrium state conducive to self-organizing into

coherent structures. This notion of structure upon structure suggests that one ordered

framework can be established over another, contributing to a complex, macro-structural

view. In this landscape, a vast array of biochemical mechanisms and countless dissipative

structures amalgamate to craft the dissipative structure of the Earth’s biosphere—a

testament to complexity. This global structure, akin to the self-sustaining process seen in

the Belousov-Zhabotinsky (B-Z) reaction, continuously absorbs energy from the cosmos

to maintain its integrity.

Thus, openness is fundamental to the essence of being “alive.” The postponement of

structural demise necessitates the system’s openness, highlighting once more the profound

nexus between complexity and openness.

[Fig. 4.30] Life-like systems must exchange matter, energy, or

information with their surroundings in order to maintain the complexity

of the structure.

At the heart of the discourse on openness lies the indispensable concept of “boundaries”

(Fig. 4.30). Boundaries are pivotal in systems theory, demarcating the system from its

surrounding environment and its internal subsystems, thereby enabling distinct

classifications. It is the presence of boundaries that gives rise to qualitative differences,

which means that without boundaries, the discourse on openness would be moot.

Boundaries hold such critical importance that they are considered to be integral to the

168 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

system’s identity. The complexity inherent in open systems is often attributed to the

dynamic interactions between the system and its environment, and these interactions are

manifested most acutely at the boundaries.

Hence, an in-depth study of boundaries is

central to discussions of openness.

Second, openness has its limits. Total openness equates to an absence of system

boundaries, precluding complexity. A fully closed system, meanwhile, obstructs the

exchange of information and energy, similarly preventing complexity. Who moderates this

balance? The answer lies in the boundaries, which regulate the flow of information and

energy. They serve not only to separate the system from its environment but also to connect

them, overseeing two-way interactions. This explains the significant emphasis placed on

the concept of “boundaries” in Japanese thought. Architecture acts as this boundary, with

the degree of openness managed by the architectural form. The architect’s role involves

exploring and determining this degree, adjusting it according to environmental conditions

to facilitate, maintain, or enhance the exchange of information and energy between “inside”

and “outside,” fostering or optimizing an internal structure (order). Like complexity, it

governs the exchange of materials, energy, and information among various mediums,

placing the system in a delicate, volatile, yet remarkably stable state. This perspective

views architecture as a “coordinator,” adjusting not just the relationship between

architecture and the environment but also between individuals and their surroundings, and

among people themselves (Fig. 4.31).

What distinctive characteristics does the “boundary” possess? The complexity of a

system is often understood as stemming from its interactions with the surrounding

environment, highlighting the boundary as a focal point where essential evolutionary

characteristics of the system converge. This boundary is the product of the interplay

between forces of containment and dispersion within the system, notably characterized by

a pronounced “gradation.”

Thus, the “boundary” must necessarily embody an “in-

between” state. This reaffirms the linkage between our comprehension of complexity and

openness from the vantage point of evolutionary order. Consequently, as posited by

Kazunari Sakamoto, architectural openness transcends the mere dimensions of apertures.

It is dictated by environmental exigencies, serving as a mechanism of adjustment rather

than a pursuit of openness for its own sake.

To encapsulate, through the lens of complexity theory, we unravel the intertwined

relationship between complexity and openness: openness is a foundational prerequisite for

complexity. Complex entities are invariably open. The pursuit of complexity is predicated

on openness; the practices and architectural outcomes of Japanese architects similarly

manifest distinct openness. Viewed with a broad historical lens, Japanese architecture

Guangle Yan, Wanchen Wang, “Boundary Thinking,” Journal of Management Sciences in China. Vol.3

No.1 (Mar 2000): p79.

Yan, “Boundary Thinking,” p79.

4.4 Harmonization at the Cognitive Level 169

reveals a progressive trend toward greater openness, encompassing a spectrum of

dimensions from physical to intellectual openness, from public engagement to the

emancipation of the psyche. Openness is identifiable across these various facets, which

suggests that it is a developmental milestone of the Japanese cultural ethos. But does this

progression carry an element of inevitability?

This enquiry propels us toward a subsequent discourse on the higher-order influences

that shape human conduct: thought processes, worldviews, and beliefs.

[Fig. 4.31] From this viewpoint, the dashed lines depicted in the illustration symbolize the architecture.

4.4 Harmonization at the Cognitive Level

There are myriad definitions of complexity, yet the ethos of complex thinking remains

singular. Edgar Morin’s portrayal of complex thinking is pivotal. Complex thinking must

navigate through fog, uncertainty, ambiguity, inexpressibility, and indeterminacy, fortified

with the principles of order and certainty, and drawing on laws, algorithms, and conceptual

precision.

In the realm of Japanese architectural theory, “nature” emerges as a recurrent cliché,

reflecting a philosophy of harmonization with the external environment. Terms associated

with nature are prevalent, underscoring a deep engagement and integration with the natural

world. In comparison with concepts such as dualism, ambiguity, and openness, “nature”

stands out as the overarching theme. This engagement with nature extends to the most

expansive vista—values and cognition. Japanese architects’ frequent invocation of “nature”

stems from their intricate thought processes, where nature is epitomized as the essence of

our world. Hence, the congruence of Japanese architectural philosophy with the principles

of complexity across various dimensions is understandable, given their shared foundational

values. While prior discussions have considered the micro-attributes linking complexity

and Japanese thought, this narrative shifts the focus to a broader line of enquiry, entwining

complexity with Japanese perspectives at the level of worldview and scientific faith.

170 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

Applying complexity theory in design signifies a grasp of scientific tenets rather than

an embodiment of complex thought. This resonates with the macro value alignment in the

Japanese architectural philosophy epitomized by Fujimoto, distinguishing it from the

principles of “emergent architecture.”

4.4.1 What is Complex Thinking?

Complex thinking requires that one acknowledge uncertainty and enter into a dialogue with

it; it represents a worldview.

Is our world deterministic? This question has been pondered for 2500 years, since the

ancient Greek philosophers. From the ancient Greeks to Aristotle, through Ptolemy’s

astronomy, Descartes, Galileo’s mechanics, Copernicus’s heliocentric theory, Newton’s

three laws of motion, Laplace’s demon, thermodynamics, to Maxwell’s electromagnetic

theory, and the scientific revolution of modern quantum mechanics and relativity, scientists

have attempted to provide a satisfactory answer. They have used a whole set of reductionist

scientific methods developed over hundreds of years to prove an orderly, mechanical

universe, searching for a single “rule” that can penetrate the “complex illusion” and

describe a “simple world” like Rule 110. Laplace’s statement in his 1814 “Essai

philosophique sur les probabilités” (Philosophical Essay on Probabilities) is the most

representative of this endeavor:

We may regard the present state of the universe as the effect of its past and the cause

of its future. An intellect which at a certain moment would know all forces that set

nature in motion, and all positions of all items of which nature is composed, if this

intellect were also vast enough to submit these data to analysis, it would embrace in a

single formula the movements of the greatest bodies of the universe and those of the

tiniest atom; for such an intellect nothing would be uncertain and the future just like

the past would be present before its eyes.

Statements like “the world is a giant machine” and “give me a powerful enough computer

and I’ll calculate the past and future” abound. Even life, a typically complex phenomenon,

is seen as mechanical and static. Darwin’s theory of natural selection portrays life as

passive, stable, always rational, and developing in a balanced way, in order to propose the

theory of survival of the fittest.

Morin believes that this kind of thinking stems from the epistemological paradigm

separating subject and object that was founded in the seventeenth century and firmly

established a deterministic worldview in classical science. This is because non-

determinism, contingency, and freedom were completely attributed to the subject, the

spiritual, and the human, while the subject itself was excluded from science.

Gribbin, Deep Simplicity, p30.

Morin,

复杂思想：自觉的科学

, p159.

4.4 Harmonization at the Cognitive Level 171

Discovering the only, simple, and immutable laws that govern our world has been an

ancient and seemingly unchangeable pursuit. This is because science seems to lose its

meaning if the world cannot be understood and therefore controlled.

Since Newtonian mechanics, classical science has outlined a definite picture of the

world. Scientists have been trying to construct a deterministic world and exclude “chance”

and “uncertainty.” It wasn’t until the scientific revolution in physics at the beginning of the

twentieth century, with the development of the two major theories of quantum mechanics

and relativity, that the mechanistic view of determinism was fundamentally shaken, and

the chaotic aspect of the world was revealed.

As Morin writes: “quantum mechanics

destroyed the basic concept of determinism and replaced it with the relative indeterminacy.

It introduced uncertainty and contradiction into the minds of physicists, that is,

disorderliness.”

Morin cites Niels Bohr as a positive example of this, praising his attitude

in facing uncertainty and contradiction in enterprises of scientific knowledge.

However, quantum mechanics and relativity also imply determinism and temporal

symmetry. Einstein often said that time is an illusion. The fundamental equation of

quantum mechanics, the Schrödinger equation, is also deterministic and time-reversible.

As Prigogine writes: “The orthodox formulation of quantum mechanics introduces

probability and irreversibility only when an observer is included.”

Therefore, from a certain perspective, quantum mechanics and relativity are still

negating the direction of time and affirming the deterministic world that has been depicted

by classical science since Newton. However, when “probability” enters into the

formulation of the fundamental laws of physics, Newton’s laws collapse.

Prigogine therefore believes that Baron Jean-Joseph Fourier’s 1811 work on

providing a mathematical description of the propagation of heat in solids marks the birth

of the “science of complexity.”

Prigogine remarks that: “Humanity is at a turning point,

at the beginning of a new rationality. In this new rationality, science is no longer

synonymous with determinism, and probability is no longer synonymous with

ignorance.”

Subsequently, the general systems theory that emerged in the 1920s began to resist

reductionism by taking a holistic perspective. New disciplines such as the dynamics of

unstable systems emerged alongside the popularization of chaos theory and non-

equilibrium physics, including the concepts of dissipative structures and self-organization.

Xiaobing Cai, Wulun Jin, “Holism and Science—Holist Intension in Chinese Cultures,” Studies in

Dialectics of Nature. Vol.26, No.1. (Jan, 2010), p115-118.

Morin,

复杂思想：自觉的科学

, p169.

Prigogine, The End of Certainty, p9.

Prigogine, The End of Certainty, p5.

Ilya Prigogine, Isabelle Stengers, Order Out of Chaos (London: Heinemann, 1984), p104.

Prigogine, The End of Certainty, p5.

172 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

The influence of these developments gradually spread to various scientific fields. Concepts

of fluctuation, contingency, randomness, instability, limited predictability, and other non-

deterministic ideas were being recognized and taken seriously at various levels.

In this period, a whole new lexicon came into usage across different academic

disciplines. In biology, this included terms such as ecological, metabolism, immunity,

morphology; in psychology, Gestalt, self, and personality; in social sciences, integration,

culture, and form. None of these concepts and terms had held scientific meaning fifty years

earlier. They are all qualitative concepts that cannot be described quantitatively, do not

conform to the theorem “the whole is the sum of its parts,” and cannot be linked to

determinism.

Whether complexity is an essential property of the world is still subject to debate.

Before the 1960s, simplicity was considered to be the basic attribute of the world, while

complexity was deemed “unfathomable” and “difficult to handle.” Complexity was

considered to be, at most, a composite product of simplicity, a phenomenon. Complexity

was even considered to be the result of the inability of the subject of knowledge to use the

principle of simplicity to handle problems. Therefore, the statuses of “simplicity” and

“complexity” were asymmetric in both epistemology and ontology. In recent years, there

has still been debate as to whether “complexity” is an attribute of the world, which indicates

that the ontological status of “complexity” has not been recognized.

Regardless of whether or not complexity is recognized as a fundamental property of

the world, no matter where its starting point is, and regardless of which theory it derives

from, the events that occur in various fields indicate that, as Morin claims, a dialogue with

uncertainty and incompleteness has been opened. The laws of nature no longer focus only

on determinism, but also express possibility, contingency, and probability. Symmetry

breaking, the three-body problem, the perfect collision of three spheres, sensitivity to initial

conditions—these are all ancient problems, each involving the death of reductionism, but

they were not taken seriously.

This is a different worldview from simplicity. In this worldview, deterministic things

are all questioned, and familiar things are reexamined by scientists from the perspective of

order. The problem of complexity started to be taken seriously. This is why, Morin claims,

that “the excessive expectation of finding absolute certainty in empirical and logical

verification must be abandoned.”

He writes:

After Newton, established knowledge became the object of science, and scientific

understanding became the pursuit of certainty. But today, the existence of the duality

of order and disorder shows us that knowledge should strive to negotiate with

Cai, “Holism and Science,” p115-118.

Wu, “Objective Complexity in the View of Philosophy of Science,” p44.

Morin,

复杂思想：自觉的科学

, p183.

4.4 Harmonization at the Cognitive Level 173

uncertainty. This also means that the purpose of knowledge is not to discover the

secrets or the dominate equations of the world, but to have a dialogue with the world

[. . .] and to work with uncertainty [. . .] it prompts us to critically examine accepted

knowledge that has been established as certainty. A purely ordered world is not a

rational world, but only a world that has been rationalized. The so-called rationalized

world is a world that is thought to follow the logical patterns of our minds. In this

sense, it is a completely idealistic world.”

However, it is important to note that this is not a complete turn towards uncertainty.

In other words, “determinism” cannot be denied. Determinism and uncertainty need to be

combined, and cannot be separated arbitrarily. As Morin puts it:

a strictly determined universe is a universe with only order, where there is no change,

no innovation, and no creation. On the other hand, a universe with only disorder

cannot form any organization and therefore cannot maintain new things, and is not

suitable for evolution and development. An absolutely determined world and an

absolutely random world are both one-sided and incomplete. The former cannot

evolve, and the latter cannot even generate.

In summary, as one can see, this kind of world is encompassed within the FGO. As

early as 1890, Poincaré demonstrated with the simplified three-body problem that it is

impossible to predict whether or not our solar system is stable. The Earth really could

suddenly fly toward or away from the Sun one day. Laplace’s demon, which described a

deterministic universe, was in principle correct. But under nonlinear motion, the unknown

and sensitive initial values make everything just empty talk.

In this view, some researchers began to realize that the world is one of constant change

rather than stasis. Newton’s world was a static one because “the creation made by the

Creator was a one-time static action. After this, God stood by and let the world clock slowly

unwind.”

The world is constantly changing. Nothing is static. It is similar to life, which

involves an understanding of “order” and “disorder.” These concepts are considered

extensively in Morin’s discussions on complexity. It is a dynamic order, also known as a

dynamic disorder.

This world cannot be predicted perfectly. Weather forecasting is unpredictable. The

trajectory of the movement after three perfect ball collisions cannot be predicted.

The

path of lightning cannot be predicted. The shape of a tree cannot be perfectly predicted. In

Morin,

复杂思想：自觉的科学

, p162.

Morin,

复杂思想：自觉的科学

, p159.

Cramer, Chaos and Order, p210.

According to Newton's laws, if a perfectly elastic ball (A) collides with two other perfectly elastic balls

(B and C), at their point of contact it is impossible to predict the direction of the motion of the three balls

after the collision. If three particles collide in the universe at a certain time and place in this way, the

deterministic picture of the universe no longer exists.

174 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

such a world, not everything is reversible. Indeed, in this world, things are irreversible and

time has a direction. The scope of reductionism is limited; not everything can be controlled.

The orderly and predictable relationship between cause and effect was found to be limited

and was therefore questioned.

What kind of worldview is this? One can find some clues in A. J. Bahm’s “holistic

view.” The central idea of Bahm’s holistic philosophy is “Organicism.” Bam divides the

whole into three categories: aggregate whole; mechanical whole; and organic whole. He

believes that the most obvious characteristics of existing systems, such as the Earth, the

nation, and the individual, is that each is a whole composed of parts:

When we imagine the whole and its parts as being opposed, we tend to overlook an

additional whole that includes both the whole opposed to its parts and the

complementary, polar opposite parts that are opposed to each other and to the whole.

This is an “organic whole,” which is distinct from a “mere whole.”

Existing systems usually involve not only direct and indirect causal relationships between

parts and parts, and between parts and the whole in the sense that the whole is influenced

by its parts, but also the influence of causal relationships between the whole and its parts.

Therefore, understanding organic wholeness involves understanding the variability of the

importance of whole and part relative to the organism.

The concept of an “organic whole” can be further elucidated from a hierarchical

perspective. The principles of hierarchy and “emergence,” a fundamental aspect of

complexity theory, are intertwined, with emergence marking the development of new

hierarchical strata. This conceptual framework is crucial for understanding complex

systems, which defy reduction to mere “parts” or “wholes,” instead focusing on their

overarching architecture. Herbert Alexander Simon, a Nobel laureate in Economics, is

renowned for articulating complexity from this hierarchical viewpoint.

In the graphic for

complexity, hierarchy is depicted through two distinct levels: the micro-level, symbolized

by individual squares, and the ultimate pattern or the macro-level, illustrating the

fundamental simplicity of complexity. In real-world complex systems, the hierarchical

structure tends to be more evident.

Everyday life is replete with examples of emergence, from the natural emergence

observed in the human body and trees to the collective intelligence of ant and bee colonies,

the schooling of fish, the flocking of birds, stock market volatility, climatic shifts,

Wulun Jin, “巴姆的整体论 (Bahm’s Holism),” Studies in Dialectics of Nature. 1993, Vol.9, No.9, p1-21.

Jin, “Bahm’s Holism,” p1-21.

Herbert Alexander Simon posited that hierarchy is a structural characteristic common to the majority of

complex systems observed in nature. He further contended that complexity emerges from simplicity, with

every complex system embodying a hierarchical framework.

4.4 Harmonization at the Cognitive Level 175

population changes, the immune system, and the Internet.

These phenomena represent

tangible instances of emergence, yet abstract layers of hierarchy often remain elusive to

the casual observer.

The holistic views on hierarchy of Bahm and Herbert Alexander Simon reflect a

philosophy of interconnectedness, illustrating a comprehensive perspective on the unity of

all things. In this holistic view, the parts are entirely dependent on the whole, and the whole

is equally dependent on the parts. Without the whole, there are no parts. All wholes are

merely parts of larger wholes, and all parts are actually wholes of smaller parts. The entire

world is a hugely complex system that has self-organized after the Big Bang, with different

levels of organization. Bahm calls this an “organic whole,” which is a more extreme form

of his holistic view.

Fujimoto once wrote: “from a small box on the palm of a hand; to the scale of furniture;

to a house that encloses it; to a city; to the Earth; and to the Universe […] Box in a box in

a box ad infinitum”

This statement vividly illustrates an extreme holistic perspective.

The entire world is seen as an organic whole, and thus as a complex system. Bahm refers

to this holistic view—which is in fact his core idea—as organismic theory or Organicism.

Fujimoto’s attitude to “wholeness” is a kind of organismic perspective in the Bahmian

sense. It is no longer a matter of whether to observe from the perspective of complexity,

but a matter of the degree to which one should do so.

4.4.2 The Ambiguous Whole and the Distinct Parts

Sou Fujimoto, alongside numerous Japanese architects, is recognized for his intricate

approach to conceptual thinking. This analysis ventures into Fujimoto’s delineation of the

architectural “whole” and its “parts.” The exploration commences with Fujimoto’s

conceptual Primitive Future House. The illustration (Fig. 4.32) reveals Fujimoto’s design

intentions for the Primitive Future House, a concept made public in 2001.

NetLogo, the software by Wilensky, features concrete models that encapsulate the concepts discussed.

These models offer an intuitive presentation of the emergent phenomena, capturing the essence of “surprises”

and “unexpected” outcomes.

Organic wholes can also be subdivided into: 1. wholes composed of parts; 2. wholes that have both parts

and a whole, and both together make up the whole. Jin Wulun calls the latter “organic bodies”: “The organic

body consists of a whole and its parts, including both the parts of the whole and the whole of these parts,

which are interdependent.” Jin, Wulun. “巴姆的整体论 (Bahm’s holism),” Studies in Dialectics of Nature.

1993, Vol.9, No.9, p1-21.

El Croquis 151, p206.

Or, it can be said that it is a more extreme form of “Holism.” Just as extreme “Atomism” believes that

there is no whole, extreme Holism believes that there are no "parts.” This extreme holistic view regards the

entire world as a complex organic whole, and the Earth as only a part of the universe. This dissertation does

not intend to delve into the specific types of “wholes” in “Holism.” The point here is only to illustrate that

Fujimoto’s complexity thinking is more thorough than the “Emergentist” perspective.

176 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

[Fig. 4.32] Rows of small letters in the picture read: furniture = structure = stairs = floors = house = street =

garden = terrace = window = outside = inside.

Fujimoto’s model drew attention for its modular construction, which used 350mm

panels. These panels adapt to various roles, serving as tables, chairs, beds, floorings, roofs,

bookcases, gardens, staircases, lighting, and structural components. Fujimoto’s rationale

behind the 350mm module stems from human ergonomic considerations—for instance,

175mm (a halving of 350mm) aligns with an ideal stair height; standard chair heights hover

around 350mm, and desks reach their ergonomic peak at 700mm. This architectural piece

lacks definitive spatial demarcations, prompting users to intuitively navigate and interact

with the space. The essence of the model is one of “unrestricted exploration,” underpinning

the notion of architectural fluidity. The discourse on hierarchy that was introduced in

section 2.1 applies here. Through an architectural lens encompassing particles, atoms,

molecules, materials, furnishings, rooms, buildings, gardens, urban spaces, communities,

cities, nations, and indeed the entire planet (Fig. 4.33), Fujimoto illustrates that architecture

transcends conventional boundaries and can position itself within any stratum of hierarchy.

[Fig. 4.33] Hierarchy diagram.

4.4 Harmonization at the Cognitive Level 177

One encounters Fujimoto’s various analogies: “Tokyo is a city and equally a place

like someone’s home;” “City as house, house as city;” “It is a house and simultaneously a

garden;”

“Then, it will be possible to envision a place that is at the same time a house,

a city and a forest.”

Shifting between the identities of a city and a home, oscillating from furniture to

garden, the concept of architecture as a “whole” undergoes continual transformation, and

so delineating Fujimoto’s concept of the “whole” often poses a challenge.

In the Toilette in Nature project, the area encompassed within the log roll fence is

deemed the “whole.” (Fig. 4.39) For the House Before House project, the architectural

“whole” is seemingly portrayed as a city’s playground. In the House N project, the

architectural framework is likened to a city, and the open-ended House N might as well

represent a room. Fujimoto suggests that in Tokyo, the placement of architecture embodies

considerable ambiguity. Spaces intertwine, blurring the distinction between home activities

and urban exploration. Occasionally, one might find themselves unwittingly transitioning

from public urban spaces into private realms. The clarity of the architectural “whole”

within its hierarchical context remains elusive. The “whole” is characterized by its fluidity

and indistinctness, marking a departure from conventional architectural totality.

Architecture and daily living are broken down and segmented across various dimensions,

from the material to the entirety of the structure, challenging traditional notions of the

“whole.”

Yet, Fujimoto’s distinct “parts” can be recognized. These “parts” span a vast array

from materials to furniture, architectural elements, spaces, rooms, and units. Despite their

fluid nature, we are well-acquainted with their typical hierarchical classification.

These “parts” inherently possess distinct hierarchies. They embody transformative

sequences, such as those from materials, which form furniture and architectural features,

which then in turn create spaces and rooms, Yet, in Fujimoto’s designs, these “parts”

frequently bypass multiple hierarchical levels to merge seamlessly into a “whole.”

Take, for example, projects like the Serpentine Gallery, Final Wooden House, and

Primitive Future House, where the “architecture” is crafted directly from materials (Fig.

4.34). In the Musashino Art University Museum and Library project, Fujimoto moves on

to the hierarchy of “furniture,” a step above mere materials (Fig. 4.36). Here, bookshelves,

which are traditionally seen as mere furniture, take on structural roles, transforming into

stairs and seating, and permeating across both indoor and outdoor spaces. Bookshelves, as

“parts,” become the architectural fabric of the building.

Fujimoto, Primitive Future, p106.

Fujimoto, Primitive Future, p108.

178 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

[Fig. 4.34] Final Wooden House. [Fig. 4.35] House H.

[Fig. 4.36] Left: Musashino Art University Museum and Library. The bookshelf stretches continuously to the

outer wall, rendering the entire structure as something akin to a bookshelf. What is conventionally considered

a piece of furniture transcends numerous hierarchical layers to assume the role of architecture.

[Fig. 4.37] Right: House before house.

If we ascend to the spatial level of hierarchy, it is apparent that architects perceive

space as “parts.” Projects like Atelier House Hokkaido, House H Tokyo, and House OM

distinguish themselves through Fujimoto’s perspective that “the section is an aggregation

of parts” (Fig. 4.35). Here, “parts” are still defined as spaces, which are intricately linked.

In the Seidai Hospital Annex and Group Home in Noboribetsu projects, the layout reveals

a lack of corridors, with the architecture developed through a network of rooms directly

connected to one another, necessitating passage through various rooms to navigate the

space. Extending this hierarchical exploration, Fujimoto intriguingly identifies units as

integral “parts” within his architectural narrative (Fig. 4.37; Fig. 4.38).

4.4 Harmonization at the Cognitive Level 179

[Fig. 4.38] Benetton Building. [Fig. 4.39] Toilate in Nature.

It is evident that Fujimoto’s “parts” navigate intricately through multiple hierarchies.

The “whole” remains profoundly nebulous, often constructed directly from “parts” across

disparate hierarchies. The definition of what constitutes a “part” is deliberately chosen by

the architect, and is tailored to the project’s demands. This methodological perspective

pervades Fujimoto’s early architectural endeavors.

What accounts for the whole’s ambiguity? It can be attributed to a mindset that

embraces complexity. As previously discussed, there is no emphasis on the whole within

an organic whole; its significance is diminished. Viewing the architectural “whole” through

this complex lens leads to questions without definitive boundaries.

Modern science has imposed arbitrary divisions across all fields of study, rooted in a

mechanistic worldview and its approach to the “parts” and “whole” dichotomy. This

paradigm suggests that the world as a whole can be dissected into individual components.

Biologists equate the study of molecules with understanding life in its entirety. Physicists

see the exploration of fundamental particles as a gateway to comprehending the universe.

This analytical dissection allows for the emergence of distinct academic disciplines.

What “part” does the architectural discipline address? The sequence from atoms to

molecules, to cells and organisms, each of which form unique ecological niches and

ecosystems, illustrates layers of emergence within the complex system that is our world.

Physicists, chemists, and biologists each study complex systems defined by observable

components within their respective fields. Given the hierarchical structures apparent in

natural sciences, does architecture possess its inherent levels? Is there an identifiable

complex system within architecture? At which hierarchical level should architectural

180 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

practice be situated? Or, more specifically, with which system of complexity should

architects engage?

The question of the appropriate hierarchical level for architectural intervention

remains unanswered in academic texts, as it is a consideration that arises specifically from

the viewpoint of more thorough complex thinking. Architecture is characterized by the

architect’s role in crafting new, man-made structures. With no predefined entities to

“define,” the field of architecture is propelled by the necessity of making “choices.”

Whether the project involves erecting new structures or renovating existing ones, the

products are creations of human ingenuity, not outcomes of the natural world’s “self-

organization.” These innovations, which did not exist before, must be seamlessly woven

into the fabric of the existing world, a process that hinges on the architect’s selective

judgment. Thus, the array of choices made by architects fundamentally influences their

definition of architecture. Concerning the selection of an intervention level, this can be

interpreted as determining the hierarchical position of architecture as a “whole.”

If the building is regarded as the essence of architecture, then the building’s

comprehensive nature is naturally emphasized. It logically follows that architecture can

equally represent furniture, a garden, or encapsulate the notion of “city as house, house as

city.”

A respectful and modest approach to nature is deeply ingrained in traditional Japanese

ideology. The essence of “wholeness” in this architecture is characterized by its elusive

nature. This wholeness is a broad and ambiguous concept that encompasses an extensive

array of elements. Historically, the stature of Japanese architectural forms—from religious

edifices and symbols of authority to common residential structures—in relation to nature,

has been very much understated. Dominance or intimidation has seldom been the guiding

principle. Instead, architecture is envisioned as part of a larger environmental whole.

The methodology for contemplating the whole and defining its hierarchical

positioning significantly influences the architectural ethos. Rather than positioning itself

as an independent force against nature, Japanese architecture adopts a hierarchical

perspective aimed at achieving symbiosis with the natural world. Within this context,

architectural forms are often considered as secondary to the overarching primacy of nature.

Architecture, in this view, is akin to a crafted element of nature—created by human hands

from natural materials, it strives for integration into the cyclical processes of the natural

environment. This holistic integration of furniture, gardens, lifestyles, and architectural

forms creates an indissoluble whole, with each element representing a microcosm. This

continual learning from and alignment with natural processes aims to bring human

existence closer to a natural state, integrating life itself into the hierarchical fabric. This

philosophical stance fosters an adaptive built environment, one that evolves, matures, and

eventually returns to nature, eschewing the quest for eternal permanence. This approach

perhaps sheds light on Fujimoto’s reference to architecture as embodying a “weak” essence.

4.4 Harmonization at the Cognitive Level 181

Japanese gardens and tea rooms serve as quintessential examples. The construction of

tea rooms is a deliberate architectural choice, reflecting aesthetic values rather than

economic constraints. The presence of exquisite tea utensils underscores this choice.

Within tea room architecture, the emphasis on “Wabi” encapsulates the celebration of

imperfection, asymmetry, and the beauty inherent in incomplete forms. This aesthetic is

predicated on a philosophy that values the beauty of the understated and the incomplete,

offering a more profound affirmation than overtly positive narratives.

The ceremonial

aspects of tea preparation, the precise movements involved in serving tea, and the conduct

and posture of both host and guest adhere to stringent criteria. The evolution of tea room

dimensions toward minimalism, from four and a half tatamis to the austere “one tatami mat”

space, aligns with Sen no Rikyū’s ideal vision of a tea room.

The ceremony of tea,

human behavior, precious tea utensils, extend beyond the acts of making and enjoying tea,

encompassing calligraphy, poetry, ceramics, and a deep respect for the ceremonial space

and the discipline it requires. These elements collectively define the “whole.” The tea room

itself, then, is merely a component within a larger, intricately designed thatched structure.

This ethos is mirrored in garden architecture, where any singular construction is but a

minor fragment of an artisanally curated microcosm, and the residential structure is not the

centerpiece. Yet, within such a universe, as Hiroshi Ota articulates, “Finding solace in the

tranquil and harmonious ambiance of a tea room provides invaluable comfort and spiritual

solace to those amidst life’s turmoil.”

[Fig. 4.40] Left: New York New Museum of Contemporary Art. The entire facade is covered with a perforated

panel.

[Fig. 4.41] Right: Nakamachi Terrace. Community Center and Library.

Hirotaro Ota, Nihonkenchikushi Josetsu, trans. Binjie Lu, Mupin Bao (Shanghai: Tongji University Press.

2016), p149.

Ota, Nihonkenchikushi Josetsu, p150.

Ota, Nihonkenchikushi Josetsu, p154.

182 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

[Fig. 4.42] Architecture without façade. House and Restaurant (2013). Concrete is poured directly into a

series of holes on the site to form the building. The entire structure is located underground.

[Fig. 4.43] Left: House SA. Despite its unassuming exterior, this structure represents a significant work, and

was completed by Kazunari Sakamoto in 1999.

[Fig. 4.44] Right: The notion of the whole’s dissolution appears to be a paramount objective for Japanese

architects. Depicted here is a book by Kengo Kuma that articulates a core argument against wholeness.

[Fig. 4.45] Is it a desk or architecture? House in Kita-Kamakura (2009) by SANAA.

4.4 Harmonization at the Cognitive Level 183

Thus, whether in the context of tea rooms, Sukiya architecture (originally derived

from tea rooms), or gardens, the focal point transcends the physicality of architecture,

aiming instead to appreciate the higher-level “whole” that elevates beyond the mere

structure. Expressions like the “absence of a unified wholeness,” the “element of

temporariness,” and “Anti-object” have become hallmarks of modern Japanese

architectural discourse. Since the 1980s, Japanese architects have offered a holistic

examination of the concept of wholeness. Notably absent are perspectives tailored for

photography, or a façade crafted for external validation, a deliberate indifference to form,

and efforts aimed at obscuring the whole. These elements mirror Japanese architects’

viewpoints on the essence of the “whole,” echoing the ambiguity that is characteristic of

Fujimoto’s creations.

This active engagement with hierarchical choices persists among Japanese architects,

reflecting their enduring traditional ideologies. Fujimoto’s distinction comes from his

theoretical orientation, leading to more straightforward manifestations of these principles.

Such decisions are driven by a nuanced comprehension of the world, allowing for dynamic

shifts in architectural focus according to the architects’ insights in the contemporary

landscape.

[Fig. 4.46] Left: House in a Plum Grove by SANAA (2001-2003). The realized structure bears a striking

similarity to its cardboard model counterpart: its walls are exceedingly thin, with architectural details

meticulously obscured.

[Fig. 4.47] Right: Table Project. Junya Ishigami: “a table is a lot like architecture. The four legs are like

columns and the top almost looks like a roof when seen from underneath. A table can thus be described as

an architectural archetype.” El Croquis 182, p168.

Thus, the idea of the “whole” of architecture holds no significance. In 1997, Sou

Fujimoto’s design, Network by Walk, emerged victorious in the “Living in the Multimedia

Era” competition (Fig. 4.48). Fujimoto’s proposal takes the concept of a fragmented whole

to its zenith. What are traditionally understood as residential spaces are deconstructed into

distinct cells. These cells, which Fujimoto terms “fragments” of housing, are scattered

across the urban expanse. The connections between these spaces are radically stretched,

with the act of “walking” serving to bind these disparate “fragments.”

184 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

It becomes futile to pinpoint any one cell as the epitome of the architectural “whole,”

as the essence of the architecture has diffused throughout the city. Likewise, it is overly

simplistic to equate the entire city with this architectural project, as it is but one component

among many that shape the city’s character.

[Fig. 4.48] Network by Walk (1997).

This forward-thinking model is similarly manifested in Kazuo Shinohara’s House in

Uehara (1976), where the structure’s formidable and ostensibly unrefined form exceeds

the necessities of a small house. Instead, it suggests a support system for the broader “city,”

positioning the building as a communal “room” within the urban collective.

Fujimoto explains:

All architecture is, in a sense, one-room. One space deforms, undulates and pulsates

to create multitude of places. One can even envision urbanity as a large one-room

engulfing a city and its architecture. Here with one-room, interiority and exteriority

are not disparate elements but it is simply an alias provisionally given to the condition

wherein interiority and exteriority stay connected while transforming.

Yoshinobu Ashihara provides a similar description in The Hidden Order. An elevated

structure and a tatami floor make the whole Japanese house a “bedroom.” The whole city

is “a mammoth cluster of ‘bedrooms’ interspersed with ‘family rooms’(parks), ‘parlors’

(office buildings), ‘entryways’ (airports, harbors), and the like.” People who live in the

metropolis in Japan take an hour or two to commute to jobs and schools. Very few hours

are spent in their homes, and when they are, it is in sleeping. Even if they want to meet

Fujimoto, El Croquis 151, p201.

4.4 Harmonization at the Cognitive Level 185

friends or relatives, it will only be in public places, rather than the home, as “the

entertainment and restaurant business in Japan serves needs well.”

Fujimoto’s insights resonate with practical observations. By the 1980s, the fabric of

life in Japan had already begun to reflect such dynamics. The traditional nine-to-five

lifestyle had expanded the domains of learning, dining, sleeping, working, and leisure well

beyond the household, into the many corners of the city. This development stems from

recognizing human actions and societal shifts as integral “parts” of a broader “whole,” with

these components constantly adapting within the societal landscape.

These perspectives allude to an appreciation for living within an organic setting,

where the traditional emphasis on a singular “whole” becomes irrelevant. What, then,

becomes paramount? It is the cycle, the flow, the encompassing whole, the state of being—

in essence, the notion of melding with nature. Through the lens of the FGO, Fujimoto’s

ambitions become more discernible. Having been influenced by complexity theory, his

methodology reveals distinct nuances, yet shares a common objective with other Japanese

architects: to integrate architecture into the natural cycle.

Currently, computer simulation stands as a standard research strategy and a

fundamental methodology for analyzing complex systems. In the realm of modern research

techniques concerning complex systems, the employment of computer simulations to

construct models and monitor the progression of systems is acknowledged as a common

and effective method. This approach fundamentally concentrates on the components to

investigate the interconnections among them. This method is alternatively referred to as

reverse engineering.

First, it is necessary to determine the “whole” of the study object and then to decide

the “part” to be returned to the base of the hierarchy of the determined “whole.” Then,

using computer simulation as a method, patterns can be observed to unfold in time and

space on a “trial and error” basis.

In simple terms, an initial apprehension and judgment is made of the “complex” object

to be studied. Then, the level of the “whole” in which the complex phenomenon appears is

determined, so as to decide the level to which the “part” will return. Finally, using a holistic

perspective, the part is adjusted while the pattern of the whole is observed, until familiar

results are obtained.

Taking “complexity” in the FGO as an example, how does its pattern come about?

Imagine how it could be obtained without knowing the generation rule of the figure.

Obviously, it can only be drawn stroke by stroke—a top-down method. Although it is the

simplest complexity, it is still very difficult. This is not to mention the higher-dimensional

complexity of real life.

Ashihara, The Hidden Order, p45.

186 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

Therefore, if one wishes to obtain the pattern of “complexity,” one must first have a

cognitive understanding and appraisal of the object of study’s complexity and treat it as

complex, using complex methods.

Next, it is necessary to determine the level of the “whole.” In the graphic for

complexity, the level of the “whole” is very simple and intuitive because it only has two

levels. The “whole” is the pattern presented by the figure itself.

After determining the level of complexity, the question that needs to be considered is:

how is such a “whole” pattern produced? If you are not familiar with the cell rules, the only

way is to return to the level of the grid (part) to explore the cause, guess the possible rules,

and at the same time, use a computer (Wolfram used paper and pen in 1981) to observe the

overall pattern under this rule.

Although this logic may seem very simple, it represents the main methodology of

complex systems at present. It is important to grasp both the whole and the part. This is

also the focus of complexity science’s methodology, which differs from that of reductionist

science.

The logic is straightforward throughout the elementary cellular automata, with only

two levels. The overall pattern it presents is the emergent macro-level, which triggers the

patterns one level lower, known as “parts.” In many other types of research, the position of

the “whole” is not necessarily easy to determine.

The position of the “part” is also important. For example, in the study of fish schooling

behavior, the “whole” is the phenomenon of schooling, not the entire marine ecosystem or

the individual “fish.” On the other hand, is it necessary to explore the molecular “parts” of

schooling behavior? The answer is obviously no, just as current research on subatomic

particles cannot answer the phenomenon of consciousness. The disparate “parts” and

“whole” are very difficult to link together.

The main reason for this is the “unpredictability,” “inseparability,” “irreversibility,”

“surprise,” and “instability” brought about by the complex features that appear at various

levels of complex systems. Another main reason is the limitations of current research

methods for complex systems, which often rely on the researcher’s “guesswork.”

Therefore, when dealing with the study of a complex system with multiple emergent

levels, according to existing literature, only two levels are usually involved: one is the level

at which a certain emergent phenomenon appears as a “whole,” and the other is the next

level that causes its appearance as a “part.” Complexity pervades the entire system, and

without limitation, complexity cannot be discussed. Overall, the first step is to determine

the level of complexity (macro-level) that emerges, and then to determine the parts (micro-

level) that need to be traced back. The next step is to try to expand the “parts” in time and

space, and look for key interactive behaviors that can lead to the “whole.”

4.4 Harmonization at the Cognitive Level 187

[Fig. 4.49] The methodological principles for researching complex systems.

The approach to complex systems in contemporary research mirrors navigating with

Google Maps on a journey, employing zooming techniques to bridge hierarchies across

different scales, thus verifying the pathway’s accuracy.

Fujimoto observes:

In these projects, the essence lies in how the connections between individual parts

sculpt the architectural space, with the overall coherence reliant on a sense of

ambiguity. Through the segmentation, dispersion, and reconstitution of key

architectural factors (form, decoration, meaning), it paves the way for the emergence

of spaces that are both more intricate and diverse. Furthermore, amidst the nexus of

parts, despite an underlying structure, the aggregate view presents an image of

disorder, complexity, and ambiguity, cultivating environments with an urban capacity

for inclusiveness.

With this understanding, it is possible to draw a definitive conclusion. Fujimoto’s aim is

clear: to pivot back to the individual components, probing the critical “interrelations

between parts” that catalyze “complexity.”

4.4.3 Nature: Japanese Emergence

When navigating through an irreversible, uncontrollable, unpredictable, and indeterminate

organic whole, the guiding principles for behaviors predominantly fall into two categories:

1) The pursuit of ongoing control; 2) The transition from control to influence. To develop

Fujimoto,

建筑诞生的时刻

, p37.

188 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

this point further, we might consider an insight from biology, as outlined by Ricard Solé

and Brian Goodwin:

We can clearly exercise whatever control remains possible in complex systems. But

there are other options, such as participating rather than controlling, that is,

recognizing that we can influence complex systems and proceeding cautiously with

such influence because of the fundamental unpredictability of our actions and their

consequences. We can no longer be naïve observers who live outside the phenomena

we manipulate. The properties of organisms, their development and health, the

dynamic activities of brains and communities, the characteristic order of ecosystems,

the patterns of evolutionary change, are processes in which we are directly involved.

For better or worse, we participate in them, and of course, we would wish to

participate wisely rather than irresponsibly.

This narrative resonates deeply, echoing the quintessential cliché of Fujimoto (and Japan

at large)—nature. Skimming through publications on Japanese architecture, one

consistently encounters the motif of “nature.” Engaging with nature suggests a philosophy

of emulation, respect, integration, and self-governance, as a vast array of Japanese

architectural concepts are woven together. Nature emerges as perhaps the most

commanding among these themes, uniformly advocating for “influence rather than direct

control.” For instance, to revisit the concept of “weak architecture,” Fujimoto often

emphasizes its symbiosis with the natural world: “In harmonizing with nature, aligning

with its undulations without dictating its own schema, we approach ‘weak architecture’.”

He further notes, “The design evolves from individual components, culminating in an

architectural whole that mirrors the complexity of natural evolution, seamlessly melding

into the forest.”

This engaged attitude is central to Fujimoto’s definition of weak

architecture.

Japanese architects frequently emphasize “fusion with nature,” “harmonization with

the environment,” or natural coding. Typical strategies involve using local materials;

opting for natural substances like wood and stone; embracing “natural” shapes (often

irregular or streamlined); and integrating plant life into architectural designs. These tactics

are evidently influenced by some ineffable, time-honored wisdom. Fujimoto’s approach to

autonomy is even more directly aligned with the principles of complexity theory.

Kengo Kuma, who, like Fujimoto, has embraced “autonomy” within his architectural

discourse, employs the concept of “weakness” to delineate his design philosophy. The

striking similarities in their approaches across various facets raise questions about the

serendipity of such alignment. Kuma’s narrative on “nature” frames it as a phenomenon of

Solé, Signs of life, p28.

Fujimoto,

建筑诞生的时刻

, p22.

Fujimoto, “Architecture of parts,” p10.

4.4 Harmonization at the Cognitive Level 189

“connectivity”—he suggests: “Nature is perceived as such when an element and its

environment engage in a symbiotic connection.”

Touching on the concept of place, Kengo Kuma, in Ten Houses, depicts it as “an

expanse under the sway of a traditional system (code).”

This perspective, as analyzed by

Fatang Wang, implies an architectural trend toward embracing external direction over self-

determination. This stance is reflective of Sou Fujimoto’s explanation of “weak

architecture,” which advocates for adherence to “natural laws” rather than promulgating

its own statutes. Fatang Wang offers a synopsis that dovetails with the discussion of nature,

asserting:

Kengo Kuma’s interpretation of “nature” essentially alludes to the faculties of self-

sustenance and autogenesis, translating into spatial consonance and temporal

continuity. Thereby, the inception of architecture is characterized by its ability to

resonate and persist within its milieu, fostering a lasting, harmonious bond.

Architectural genesis, hence, should be guided by the endemic natural essence and

ordinances of its environment, eschewing its intrinsic regulations.

Clearly, architects who similarly embrace the notion of “weakness” yet offer distinct

interpretations universally agree on the principle of “merging with nature.” This sentiment

is deeply ingrained within the Japanese architectural community.

Returning our attention to the concept of emergence, which appears to be elusive in

Japan, we might ask if this notion is genuinely absent from Fujimoto’s and Japan’s

architectural dialogue. A pivotal insight from the field of complexity is that behind

complex phenomena lie simple rules that can generate complexity, and this is encapsulated

in the principle “Simple rules lead to complex phenomena.” This reveals that chaos is

manageable. Should this perspective be the endpoint, embracing complexity becomes a

methodological approach aimed at understanding causality.

In such a context, a house is viewed as an outcome, which then exhibits a complex

façade. The complexity manifested becomes static, immobilized. Consequently, terms like

complexity, chaos, fractals, and nonlinearity might be confused, as visually, they present

similarities that are indiscernible to the observer. At this juncture, emergence is confined

to the design phase, realized through computational means, and disconnected from the

environmental context. Yet, this perspective does not reflect complex thinking; it

represents a “knowledge” of complexity.

In Fujimoto’s philosophy, the role of buildings is minimized to a mere “part” of an

intricate puzzle: they act as one among many influences. The definition of this “part” is

Kengo Kuma, Natural Architecture, trans. Jing Chen (Jinan: Shandong People’s Publishing House. 2010),

10.

Kengo Kuma, Kengo Kuma's View of Ten Types of Japanese Residences, trans. Zhu E (Shanghai:

Shanghai People's Publishing House. 2008), 21.

Fatang Wang, “Study on Architectural Thought of Kengo Kuma,” The Architect, 2013(6):55-63.

190 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

contingent upon the desired “whole” it aims to complement. The raison d’être of this “part”

is to synergize with other elements, fostering a greater unified and harmonious entity.

What defines nature? Nature embodies the operational principles of the entirety; it is

the framework of the game. Acknowledging complexity as a fundamental characteristic of

the world implies that complexity underpins the essence of the rules to all games. Hence,

complexity becomes an intrinsic feature of the “anticipated whole.” This realization fosters

thought, diverging from mere “knowledge.” The complexity mindset arises from

understanding, and encompasses a philosophy, a worldview, and a belief in science. It is

about recognizing the presence of complexity and uncertainty while exploring alternative

avenues for the exertion of control. Consequently, Fujimoto’s architectural forms

(alongside those of numerous other Japanese architects) do not necessitate complex façades.

Numerous other elements come into play: humans, the environment, behaviors, rituals,

ceremonies, etiquette, etc. These “parts” are on an equal footing with the physical

structures of architecture, akin to Japan’s tea rooms and gardens (Fig. 4.62).

Complexity thrives on dynamics rather than stasis, emphasizing processes over

outcomes, and evolution over mere existence. At its core, complexity is defined by its

dynamic properties: complex systems are inherently dynamic entities. Without change over

time, there is no evolutionary trajectory for the system, and thus, no manifestation of

complexity. While buildings remain immobile, embodying static characteristics, the

essence of complexity calls for “activity.” Humans have the ability to move, like the wind

and the environment that envelops us. It is evident that architecture wields influence. The

endeavor to imbue architecture with “life” has always been a compelling enterprise. With

its roots in the Metabolism movement, Japan has harbored this aspiration. The fusion of

these dynamic elements has the potential to truly animate architecture. Collectively, they

foster a meaningful architectural narrative where genuine complexity can unfold.

This marks the most profound variance between Fujimoto’s conception of complexity

and the complexity inherent in emergent architecture. Fujimoto indeed engages with the

concept of emergence. However, within Fujimoto’s framework, the point of emergence is

strategically postponed. Thus, our narrative loops back to where it began—Fujimoto’s

engagement with “parts.”

4.5 Summary 191

[Fig. 4.50] The occurrence site of “emergence” has experienced a delay.

This dissertation opened by recounting instances of segmentation and integration

within Japanese history. To conclude, it has delved into the 1980s and 1990s, Fujimoto’s

formative years in architectural education. This period was pivotal, marked by the dual

influences of postmodernist ideologies and the principles of complexity science on

architecture. Parallel to this intellectual evolution was a distinctly Japanese approach,

characterized by shifts in behavior, perception, societal evolution, and a transformative

approach to scientific reasoning. This era served as an ideational melting pot. If one

considers Japanese architectural ideology in its entirety, it navigated through this

timeframe in a state of chaos. Architects from this era asserted unique visions and

embarked on varied trajectories, each operating in isolation without overarching

coordination. Remarkably, by the turn of the millennium, a collective convergence around

the notion of “parts” materialized spontaneously, heralding shared traits.

Is this convergence not a quintessential representation of “emergence”? In the 80s-

90s, while discussions on emergent architecture were centered around the concept of

emergence, Japanese architects transcended the realm of mere discourse—they performed

it. This emergence unfolded on a collective scale, surpassing individual endeavors and

epitomizing the emergence of a collective subconscious—a unification of thought.

4.5 Summary

Guided by the FGO, this chapter first solidified various principal notions of order, laying

a concrete base for further exploration. Secondly, an interpretation of complexity was

presented, weaving together an expansive spectrum of Japanese architectural ideologies.

192 4 The Nexus Between “Japaneseness” and “Complexity” under the FGO

Thirdly, an analysis from a wide-ranging intellectual vantage point articulated the synergy

between the ethos of complexity thinking and the principles underlying Japanese

architectural theory. Unlike the mere acquisition of “the knowledge of complexity,” it is a

profound engagement with the thinking of complexity that offers a deeper resonance.

5 Epilogue

5.1 Conclusion

5.1.1 Sou Fujimoto’s “Complexity”

The five graphics adeptly establish a connection between Sou Fujimoto and a distinctive

type of complexity using clear graphic logic. This particular complexity diverges from that

found in common parlance, aligning instead with a structured, systematic form of

complexity that carries an objective significance. Currently, this complexity is

predominantly leveraged metaphorically to elucidate complex phenomena and remains

unquantifiable.

This brand of complexity finds its kinship with the emergent features of current digital

and parametric architecture. Both share a foundational perspective, examining the interplay

and transformation between order and disorder, recognizing that complexity arises from

simplicity. Yet, Fujimoto’s perspective on complexity delves into its dynamic, procedural,

and evolutionary facets, as opposed to static, state-based, or existential attributes.

In Fujimoto’s view, complexity denotes a particular state of complex systems. His

aspiration is that architectural intervention can steer the built environment toward this state.

This interpretation of complexity embraces the notion of uncontrollability and universal

interconnectedness, resonating more profoundly with the core essence of complexity—it

embodies a fuller and more comprehensive approach to complex thinking.

Hence, this insight ensures that Fujimoto’s architectural designs do not merely exhibit

complexity in their aesthetics but function as simplistic entities that serve to influence

others. In essence, this nuanced understanding of complexity provides a cohesive

framework for many of Fujimoto’s discussions and forms the cornerstone of his intellectual

ethos.

5.1.2 The Bond Between Japaneseness and Complexity

Sou Fujimoto’s profound engagement with “complexity” is deeply interwoven with

traditional Japanese intellectual paradigms. Complexity science seeks an alternate mode of

influence, premised on interrelations and a philosophy of concession, not as a compromise

with reality or a confrontational demand for a “revolution,” but as an integrative approach.

This perspective is naturally aligned with the venerable Japanese ethos regarding nature,

an insight that gains further clarity through Archie J. Bahm’s nuanced delineation of

cognitive approaches.

Bahm discerns three philosophical stances toward understanding the interplay

between wholes and parts: rational, intuitive, and apprehensive thinking. Rational thinking

194 5 Epilogue

pieces together the whole from its fragments. Intuitive thinking intuitively connects with

the whole, bypassing analytical dissection of its components. Apprehensive thinking,

however, perceives the whole and its parts in their experiential totality, presenting an

entwined existence where “parts” and “whole” coalesce, mirroring the intrinsic nature of

complexity.

[Fig.5.1] Intuition, apprehension, and ratiocination.

Architecture demands an engagement with its environment, reflecting the complexity

paradigm that underscores a universal interconnectedness and requisite synergy among all

elements. Regardless of our affinity for natural landscapes or forests, our human condition

precludes direct habitation within these realms, necessitating the creation of architecture.

Often, environments are inherently imperfect and require enhancement for human

habitation. In this regard, the environment is dependent on architecture to rectify its

imperfections, a concept deeply resonant with Japanese architectural ideology at a macro

scale. At a micro scale, the plethora of clichés in Japanese architectural theory—regarding

nature, ambiguity, the blending of inside and outside, the concept of openness, and so

forth—all interweave with the theme of complexity. To be more specific, they are tied to

the evolutionary interplay of order and chaos, a dynamic currently best described by

“complexity.”

At both the detailed and overarching levels, complexity is intricately linked with a

wide array of topics within Japanese architectural discourse. The lofty, seemingly fanciful

objectives found in Japanese architecture mirror the attributes of complex systems. This

dissertation advocates viewing complexity as a holistic lens through which to analyze

Japanese architecture, suggesting that the intriguing objectives within Japanese

architectural endeavors could potentially be realized through complexity.

Secondly, a historical perspective reveals a gradual shift in architects’ attitudes away

from the traditional “Japanese” ethos. Yet, this shift is not an abandonment of Japan itself

but rather a move away from a widely accepted Japaneseness. Complexity, while not

inherently Japanese, since it is not a phenomenon arising solely in Japan, resonates

significantly with Japanese characteristics, prompting Fujimoto to adopt complexity in his

5.1 Conclusion 195

conceptual framework. The essence of Japaneseness might be reinterpreted or concealed

within complexity, offering an alternative route to understanding Japanese identity.

Thirdly, employing “complexity” resonates with the Japanese methodological

tradition of “cutting off.” This approach lends insight into Fujimoto’s methodology,

finding roots in a 1990’s architectural narrative that critically questioned the essence of

architecture.

This introspective tradition prompted many Japanese architects to explore the essence

of their craft, questioning the very nature of architecture, with “cutting off” offering a

possible explanation for Fujimoto’s inclination towards “weakness.” Although this

approach was perhaps initially pioneered by Toyo Ito, Arata Isozaki contends that Kazuyo

Sejima’s applications are notably more profound. In projects like the Saishunkan Seiyaku

Women’s Dormitory and the Gifu Kitagata Apartment Building, Sejima’s avant-garde

concepts—large communal areas against minimalistic private spaces, public placement of

personal fixtures, and an overarching theme of dematerialization—challenged every

architectural norm: structural framing, load distribution, and spatial continuity. The very

essence of architectural, societal, and ideological foundations was questioned, suggesting

a bold departure from all known standards, as if starting anew on an alien terrain. Such

radical innovations were initially met with skepticism, yet they paved the way for a

reimagined Japanese architectural ethos. Since then, practices such as locating bathrooms

over staircases, positioning toilets and bathtubs directly in view of entrance doors without

any concealment, and placing washbasins in public hallways became thinkable in Japanese

architecture. Thus, the “in-between” treatment of House N does not seem so radical—it

represents an abstracted contemplation of the relationship between architecture and

environment.

The defining juncture that propelled Fujimoto into a unique trajectory was his

architectural education during the 1980s and 1990s, an era that appeared directionless. In

this timeframe, Japanese architects’ ideologies mirrored a dissipative structure, entrenched

in a chaotic conceptual era without definitive “central control.” Architectural philosophies

existed as autonomous “parts,” each navigating its own way. Yet, around the year 2000,

disparate ideas amalgamated in an ineffable manner, crystallizing into vague

“commonalities.”

Born in 1971, Sou Fujimoto was entrenched in this turmoil, molded by its dynamics.

He was profoundly shaped by the period’s “force of order,” which facilitated the melding

and emergence of varied ideas. This “force of order” is believed to stem from two main

sources: the intrinsic “Japaneseness” and the broader shift in human cognition marked by

complexity thinking, spanning developments in both the natural sciences and

postmodernist thought. Nevertheless, “Japaneseness” is paramount, with “other forces”

serving to refine this principal energy. Complexity thinking resonated exquisitely with

traditional Japanese philosophy, at both micro and macro levels.

196 5 Epilogue

Japan, valuing traditional kimonos while pioneering avant-garde technology, has

remained distinct, cherishing and safeguarding its culture. This very characteristic has

shielded it from descending into chaos or drifting toward equilibrium under “the second

law” but has instead propelled it backward, out of chaos, to the precipice—where

complexity dwells.

5.2 Contribution

5.2.1 The FGO

First, the FGO provides a reference point for discussing order in architecture, anchoring

essential concepts related to this theme. Secondly, it facilitates an understanding of

“complexity.” By elucidating Fujimoto’s interpretation of “complexity,” the FGO emerges

as notably concise and effective, establishing a platform for examining complexity within

Japanese architectural discourse. The discussions in this dissertation pivot around these

five graphics, which serve as a fundamental basis devoid of textual descriptions, metaphors,

or literary embellishments. These figures can be perceived as natural phenomena, offering

a reference point for understanding order in a manner “free from human artifacts.”

5.2.2 Interpretation of the Correlation Between Japanese Architectural Ideas and

Complexity

The second contribution of this dissertation is its use of the FGO approach to discuss

Fujimoto, as well as some Japanese architectural philosophies and their complex

relationships. While each topic might seem clichéd on its own, the dissertation integrates

them all under the “complexity” framework. It elucidates the essence, origins, and

expressions of Fujimoto’s complexity thinking and explains how it resonates with Japanese

architectural ideology. The dissertation argues that viewing architecture through the lens

of complexity offers a valuable holistic perspective, enabling the synthesis and, to some

degree, the materialization of many Japanese architects’ goals.

5.3 Outlook

The study of complexity, which began nearly a century ago, still finds itself at a very early

stage, with vast unexplored territories. The so-called revolution

initiated a conversation

with uncertainty but has concluded prematurely, leaving “complexity” in a precarious

position: it struggles with unification and lacks fresh scientific terminologies for

Conceptual transformations occur amidst scientific revolutions. Thomas Kuhn asserts that, after a scientific

revolution, the revision of dictionaries becomes imperative due to the shifts in concepts. The fundamental

concepts differ markedly before and after such revolutions. There exists an incommensurability between the

new and old paradigms, where the transition between two incommensurable theories resembles a Gestalt

switch, characterized by its untranslatability. Therefore, adjustments in dictionaries are necessary. In The

Structure of Scientific Revolutions, Thomas Kuhn elaborates that paradigm shifts indeed alter scientists’

perception of their research world. Following a revolution, they encounter a world anew: “What was

perceived as a duck in the pre-revolutionary scientific world transmutes into a rabbit post-revolution.”

5.3 Outlook 197

description, necessitating the continued use of a concept that is universally acknowledged

yet not fully understood.

The significance of concepts within any academic field cannot be overstated. Theories

and their application methodologies are constructed on fundamental concepts and

principles. These defined concepts, terms, and principles serve to clarify the focus of the

theory, the issues it addresses, and the patterns of change it observes, thereby constituting

the essential tools of the methodology. To gain a profound understanding of a discipline, it

is crucial to comprehend its basic concepts, which involves knowing their definitions and

applying them within the context of the field, thereby achieving an understanding of the

stipulative academic descriptions.

In the field of architecture, this leads to the confusion between complexity and related

notions of order, which often become easily muddled. Nevertheless, it seems improbable

that this conundrum will be resolved. Deliberating on dimensions such as large, small, tall,

short, heavy, light, cold, and hot suggests that these, much like “complexity,” hinge on

relational assessments, are established by human stipulations and are context-dependent.

Consequently, a cohesive definition of “complexity,” nonexistent in the past, lacking in the

present, and perhaps elusive in the future, leaves us pondering.

In a domain where even rudimentary understanding remains opaque, how is

architecture to chart its course? A universally acknowledged complexity concept spanning

all disciplines might be unattainable, yet within individual fields, it is viable. Although

complexity carries an interdisciplinary essence, delineated by rules applicable to diverse

systems, its exploration is predominantly discipline-centric. Most fields articulate their

definitions of complexity, anchoring their research in designated “complex systems.”

Architecture, conversely, lacks this clarity. Discrepancies emerge in defining what

architectural complexity or a complex system entail, often leading to entrenched thinking.

Debates quickly move to specific definitions, mimic certain features of complexity, or

adopt novel insights. Nonetheless, it is essential to question the significance of directly

adopting and mimicking concepts like fractals, emergence, and self-similarity from science

into architecture.

Complexity is enchantingly multifaceted, touching upon an extensive range of

subjects— human behaviors, perceptions, awareness—and addressing questions about the

environment, sustainability, and the reduction in energy consumption. Is it possible for

architecture to be an integral part of the natural cycle? In what form might it manifest (and

how would this diverge from future cities portrayed in the media)? What logic underlies

this? Is it a viable solution for sustainability, energy-saving, and environmental

conservation? Might future architecture reflect Kengo Kuma’s notion of “weak

architecture,” which is resilient to disasters? Is self-organizing architecture feasible? What

is the vision for future urban environments? Complexity seems poised to address all these

queries.

198 5 Epilogue

In architecture, the emphasis should not lie in creating a unified complexity concept

that purports to explain and encompass the entirety of the discipline. The aim should be

less about rapidly adopting interdisciplinary findings for design or engaging in premature

quantification and more about discerning architecture’s distinct research entities and

complex systems. Hasty quantification, without clear research entities, may yield

inaccuracies or neglect intriguing insights.

Opening the floor for more nuanced and detailed conversations on complexity, and

encouraging stakeholders to engage in dialogue “at the same table and on the same page,”

can provide a robust base for this avenue of research, fostering the accumulation of

knowledge. By exploring broader “contexts” of complexity, this nuanced thought process

can help us to reevaluate our “familiar,” “habitual,” or “assumed” constructs and shed light

on areas untouched by reductionist approaches.

Articulating architecture’s conception of complexity is vital. While defining complexity at

large may not be within architecture’s purview, elucidating what detailed complexity

entails within the discipline remains an essential line of enquiry.

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