Urban dynamics, fractals and generalized entropy

Entropy 2013, 15, 2679-2697; doi:10.3390/e15072679 entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Urban Dynamics, Fractals and Generalized Entropy Sara Encarnação 1,2,*, Marcos Gaudiano 3, Francisco C. Santos 1,4, José A. Tenedório 2 and Jorge M. Pacheco 1,5 1 ATP group - Applications of Theoretical Physics, Centro de Matemática e Aplicações Fundamentais, Instituto para a Investigação Interdisciplinar, P-1649-003 Lisboa Codex, Portugal; E-Mails: [email protected] (F.C.S.); pach[email protected] (J.M.P) 2 e-Geo Centro de Estudos de Geografia e Planeamento Regional, Faculdade de Ciências Sociais e Humanas, Universidade Nova de Lisboa, Avenida de Berna 26-C, 1069-061 Lisboa, Portugal; E-Mail: [email protected] 3 Departamento Electrónica, FCEFyN, Universidad Nacional de Córdoba, & CIEM-CONICET Ciudad Universitaria C.P. 5000, Córdoba, Argentina; E-Mail: [email protected] 4 Departamento de Engenharia Informática & INESC-ID, Instituto Superior Técnico, Universidade Técnica de Lisboa, IST-Tagusparque, 2744-016 Porto Salvo, Portugal 5 Departamento de Matemática e Aplicações & Centro de Biologia Molecular e Ambiental, Universidade do Minho, 4710-057 Braga, Portugal * Author to whom correspondence should be addressed; E-Mail: sara.e[email protected]; Tel.: +351-21-790-8300; Fax: +351-21-790-8308. Received: 2 May 2013; in revised form: 5 July 2013 / Accepted: 8 July 2013 / Published: 11 July 2013 Abstract: We explore the relation between the local fractal dimension and the development of the built-up area of the Northern Margin of the Metropolitan Area of Lisbon (NMAL), for the period between 1960 and 2004. To this end we make use of a Generalized Local Spatial Entropy (GLSE) function based on which urban areas can be classified into five different types. Our analysis of NMAL shows how some of the growth dynamics encountered can be linked to the plethora of social, economic and political changes that have taken place in NMAL (and Portugal), during the last 40 years, allowing for the establishment of urban planning measures to either inhibit or promote sprawl in urban areas. Keywords: fractal dimension; generalized entropy; Lisbon metropolitan area; urban growth; sprawl; region types OPEN ACCESS Entropy 2013, 15 2680 1. Introduction “How do cities form over time?” This key question posited by Herold et al. [1] remains unanswered in urban growth theory. The theoretical framework of urban growth as developed in [1] and based on empirical observation, states that urban growth follows a two phase process of spatial growth: diffusion followed by coalescence and eventually, in the presence of continuous growth, saturation. Urban growth can occur at different scales: as one area reaches saturation it may become the seed of another area, and the cycle may thus repeat itself at a larger scale. The direction of growth is influenced by local factors such as topography, transportation infrastructures and planning efforts [1], and thus urban form can evolve from and into a multitude of patterns that range from highly dispersed to highly compact [1–7]. Sprawl is a general term that has been linked to a kind of spatial growth that occurs in regions which are neither dispersed nor compact. Although this concept has been widely discussed over the last decades, there is still no generally accepted definition [2–7]. For example, the same term is associated with patterns, processes, causes and consequences [3]. On the other hand, there is a general consensus that sprawl is “characterized by unplanned and uneven pattern of growth driven by a multitude of processes and leading to inefficient resource utilization” [2]. Nevertheless, the existence of planning agencies, regulations and policies, does not necessarily imply more efficient resource utilization in urban areas, irrespective of whether they are located in more compact or dispersed territories. It will in fact depend on the space-time context of urban areas, something that varies among country regions and more so among different countries. Cultural, social, political, economic and physical constraints influence different time paths and contexts which may have a different impact on the resulting urban areas, even when planning regulations share some common features (whether these take the form of European legislation that must be transposed, in some sectors, to the national level, or some shared guidelines or strategies as it is the case of the countries in the European Union). Therefore, in this study we explore the wide range of spatial structural patterns that arise in urban areas (from very dispersed to very compact) and, employing a previously developed model [8] [based on local fractal dimension and on a Generalized Local Spatial Entropy (GLSE) function on 1 km2 cells], establish a relation between these patterns and the set of social, economic and political changes that have taken place in NMAL - Northern Margin of the Metropolitan Area of Lisbon (and Portugal), during the last 40 years. Fractal analysis allows us to gain insight on the morphology and spatial organization of urban areas on different scales [4]. A significant amount of work has been developed to link fractal dimension (D) to the morphology of cities or parts of cities [4–5,8–12,14] and also to establish comparisons between different cities or metropolitan areas [11,12,14]. In two dimensions, D ranges from 0 to 2. Generally, lower fractal dimensions typically represent dispersed built-up areas, whereas fractal dimensions close to two are associated with compact built-up areas [8,13,14]. Each built-up environment may be composed of different spatial patterns that reflect the multiple factors involved in its development and growth (topographic, cultural, aesthetic, economic, planning traditions and regulations, etc.) as well as in its context in time. Hence, one expects to find a plethora of fractal dimensions instead of a single one. By translating the multiple fractal dimensions into five, time invariant types of patterns, we are able to characterize, in principle, any given area and, to the extent that we have longitudinal information on this area, we are also able to characterize the main changes Entropy 2013, 15 2681 and transformations that have taken place. Here, we apply this methodology to NMAL and characterize its development over the last forty years. Although a five year data interval would be ideal for the present analysis the available data is limited to three snapshots in time (1960, 1990 and 2004). 2. Fractal Dimension of Built-up Areas and GLSE Previous fractal analysis of built-up areas for the NMAL (North margin of the Metropolitan Area of Lisbon), for the years 1960, 1990 and 2004, have allowed us to develop a model to classify different development stages of urbanization [8]. To overcome the limitations of a global fractal dimension analysis, we calculated the local fractal dimension (D) of square cells of 1 km2 using the standard box-counting method. Here we explore the relation between the local fractal dimension (classified through the GLSE function) and the development of the built-up area of the Northern Margin of the Metropolitan Area of Lisbon (NMAL), for the period between 1960 and 2004. For clarity of reasoning we first summarize in the following sub-sections some methodological procedures already depicted in [8]. 2.1. Data Acquisition Built-up areas from 1960 and 1990 were extracted from the former Portuguese Geographical and Cadastral Institute maps (1:50,000 scale) and from the military maps of the Army Geographical Institute (1:25,000 scale), respectively. Data from 2004 was obtained from photo-interpretation of orthophotomaps (1:25,000 scale). After cartographic generalization the three datasets were made uniform. Each dataset was converted to an array of pixels of 10  10 m. For pixels representing built-up areas we attributed a value of 1 and to non-built a value of 0. The fractal analysis was then performed over a set of cells of 100×100 pixels (1km2) (see [8] for more details). 2.2. Choice of Cell Size for NMAL For the fractal analysis we chose a cell size of 100 pixels (1 km  1 km). This number was chosen after testing for several NMAL matrices of (squared) cells of size of length L the resulting number of fractal dimensions. To this end, the fractal dimension interval D  [0,2] was divided into (2/∆D +1) bins of width ∆D = 0.01. Subsequently, we applied a fractal analysis for each matrix and counted how many bins of fractal dimension were represented. From the set of L sizes that would maximize the number of fractal dimensions and also the number of iterations allowed for the box-counting method, we chose L = 100 (see [8] for more details). 2.3. Fractal Dimension of Built-Up Areas The fractal dimension of each cell was computed using a conventional box counting algorithm. In each iteration k, the minimum set of Nk squares (boxes) of side εk = 2k (pixels, 1 pixel = 10 m) that cover the built-up area inside of the cell was computed. After m = 5 iterations k  [0,…,m], the fractal dimension D will emerge as the slope of a linear regression of the duplets {Nk,εk}, given that cDN kk   loglog , where c is constant (see [1] for a discussion of the quality of the fractal analysis). Given that the area occupied by the Nk boxes reads 2 kkk NA   it is possible to obtain the recurrence relation 2 12  D kk AA . Taking the limit m into account, we obtain 2 0)2(  Dm m AA . This Entropy 2013, 15 2682 can be used to write down the formula for the upper bound of the built-up area as a function of 22 )2()(:  Dm nDUD —where n is the side of each square cell, i.e., n = 100 pixels (or 1 km). The lower bound (L(D)) will be proportional to the upper bound U(D), such that L(D) = αU(D). Since L(0) = 1, we have that 2 )/2( n m   and mD DL 2)( . 2.4. Computation of a Generalized Local Spatial Entropy Function (GLSE) From the expression of k Nlog above, the total number of boxes covering a built-up area A at the kth stage of the box-counting algorithm reads D kk AN  / (assuming that c grows linearly with logA). Let us call ),( DAthe number of possible configurations within each cell characterized by a total built-up area A and fractal dimension D. In [8] it is shown that:                  1; 4 3 , 2 1 , 4 1 ; 4 3 , 2 1 , 4 1 , 4 ),( 34 11 kkkkkkk m kk kNNNWWWWF N N DA (1) Where   k D kNW 12 2  and F is a generalized hypergeometric function. For numerical convenience, we take the logarithm of the total number of configurations at dimension D, given by:     )( )( ),(log)( DU DLA DADSS (2) This implies that the quantity S gives an estimate of the number of possible (at any time) configurations for a given fractal dimension (see [8] for additional details). The logarithm of the number of possible ways of building up area compatible with a pre-defined fractal dimension D, that we designate S(D), together with its dimensional rate of change S’(D), are both bound, continuous and differentiable functions constrained by L(D) and U(D). S(D) can be understood as a generalized local spatial entropy function (GLSE), measuring the number of possible configurations compatible with a given fractal dimension [8]. 2.5. Urban Growth through Fractal Dimension and a Generalized Entropy Function From the above it is given that higher values of S(D) indicate a large number of ways a given cell can be occupied by built-up area, concomitant with a fractal dimension D (Figure 1). Based on the behavior of S(D) and its rate of change S’(D), five different types of cells were identified in the fractal dimensional interval (0–2) allowing an automatic classification of built-up areas. These five region types were determined by the topological properties of S(D) and its derivative S’(D): Type 1 (with D ≤ 1.0) is characterized by small and isolated built-up areas; Type 2 (1 < D ≤ 1.26) includes dispersed built-up areas that can already show some structural patters (e.g., along roads); to Type 3 (1.26 < D ≤ 1.54) we called areas of metastatic growth, which include more fragmented areas that emerge not necessarily near the main built centers. The maximum of S’(D) marks the transition to Type 4 (1.54 < D ≤ 1.78) which is characterized by rapid growth and metastatic consolidation. Type 5 (1.78 < D ≤ 2.0) is defined by a negative S’(D) and corresponds to consolidated compact areas (Figure 1). S’(D) increases rapidly in Type 3 and S(D) keeps high values in Type 4, meaning that these areas are prone to rapid transformation and fragmentation of the landscape if no constraints are present (they can be physical and/or socio-economic, as well as determined by planning regulations). Entropy 2013, 15 2683 Figure 1. Types of built-up areas. (Red line: S(D); Black line: S’(D); D: Fractal dimension. Each region type is illustrated in the insets (after [8]). The cartography of these five types of cells in NMAL reveals that more compact areas expanded from Lisbon city outwards (see [8] for a map representation of these results), in a monocentric form, shaped by the presence of main road and railway infrastructures. This expansion is reflected in the loss of representativeness of Type 1 (59% of NAML total number of cells in 1960, 21% in 1990 and 18% by 2004). Type 2 raised its share from 21% to 28%, between 1960 and 1990, but by 2004 it already accounted for only 18%. Types 3, 4 and 5 increased their share in all three time snapshots. The generalized growth in NMAL (with average annual growth rates of 4.1% and 2.7%, respectively, for both time periods) dictated a strong decrease in region type 1 (Figure 2). Region type 2 grew between 1960 and 1990 but in the second time period already showed negative average annual growth rates, similar to type 1. Region types 3 and 4 show positive growth rates in both time periods, although they are higher between 1960 and 1990. In this period the highest growth is found in region type 4. Region type 5 shows a distinct behavior, since it is the only region type where the average annual growth rate of the second time period is higher than in the first one. Between 1990 and 2004 it is in fact the region type with the highest growth. Figure 2. Region types growth rates (Left) and average annual growth rates (Right), for both time periods. Entropy 2013, 15 2684 From the above it is possible to rationalize the temporal dimension of NMAL, for the time period 1960–2004, in terms of a two stage process: the first stage (1960–1990) was characterized by generalized growth throughout the territory, where both dispersed/fragmented regions (Types 2 and 3) and compact ones (Types 4 and 5) had high positive growth rates. The negative growth rates of region type 1 reflect the metropolitan development that was taking place, as areas of more rural nature were being occupied with new built-up. In the second stage (1990–2004), NMAL continued to show growth in built-up area but at a much slower pace and it was mainly driven into more compact areas, especially type 5. These dynamics may suggest the possible existence of two coevolving processes in NMAL urban expansion, namely: fragmentation/dispersion and consolidation/compactification. By fragmentation we mean the process through which new built-up areas emerge not necessarily contiguous to pre-existing built areas and have the potential to attract and induce new developments. These can be isolated new areas (e.g. leapfrog growth) or grow in a fragmented way from pre-existing ones, for example as a linear branch that stretches from an existing nucleus, very often found in sprawled areas. Consolidation refers to the process of infill of a given area and can occur by contiguous growth or by growth and aggregation of near, not adjacent built-up areas, thus increasing the degree of compactness of the area under study. Both processes refer not to the shape of built-up areas per se but to the territory to which they belong, in the present case, to NMAL. In NMAL and qualitatively, the two processes were equally significant in the first stage, whereas during the second stage consolidation/compactification dominated. 3. Types of Growth in NMAL The above two growth stages can be identified by the way patches of built-up area change. Thus and for NMAL we can understand them in terms of three core growth-types: (1) new areas that emerge isolated in unoccupied sites; (2) existing areas that grew contiguously, and (3) existing areas that grew and aggregated with one or more neighboring areas (Figure 3). Figure 3. Examples of growth types in NMAL. Entropy 2013, 15 2685 The examples in Figure 3 suggest sprawl as a process, as defended in [15,16], i.e., some of the linear branches of the main nucleus (see box 3 of Figure 3), which between 1960 and 1990 could be considered sprawled areas, later became (1990–2004) compact and contiguous areas of that same nucleus. More examples of this type of transition can be found in NMAL, which clarifies the critic to references [15,16] made in [3] stating that “there is little in the literature to indicate when sprawl metamorphoses into nonsprawl”. Overall, and in the first time period (1960–1990), the fragmentation process is visible in the 11,102 new patches that have emerged in NMAL, accounting for 80.6% of the total number of patches in 1990, but only for 16.3% of the total built-up area of the same year (see Table 1). The consolidation process on the other hand is confirmed by: (a) 286.2% growth in built-up area in existing patches (growth-type 2). (b) The decrease in the number of patches (−78.3%) by growth-type 3 (growth and aggregation), but with a 167.5% increase in built-up area. The second time period (1990–2004) was mainly dominated by the consolidation process, whether by growth-type 2 (growth) or growth-type 3 (growth and aggregation) as seen by: (a) 56.3% growth in built-up area in existing patches (growth-type 2). (b) The decrease in the number of patches (−78.8%) in growth-type 3 but with an increase in built-up area by 44.6%. (c) The number of new patches that have emerged (accounting for only 11% of total patches in 2004), that show a much weaker fragmentation process. These dynamics reflect a metropolitan model that, in the course of time, shifted from monocentric to polycentric due to a set of socio, political and economic changes (the end of the dictatorship in 1974, the inclusion into the European Union in 1986, banking privatization, generalized higher income, access to credit, higher foreign investment, etc.) [17,18], and changes in the mobility patterns, with the decrease in the share of public transport in daily travels as opposed to the increase in individual transport [19]. However, and despite the transfer of people, industry and commercial activities to the suburbs [17] these continued to grow in terms of built-up area in a way that surpassed the real necessities. Between 1960 and 2006, the NMAL witnessed an increase by 60.3% in population, a value quite far from the 247.1% and 202.8% increase in buildings and lodgings, respectively [20]. The different growth-types identified in NMAL are also reflected in the proportion of the total number of patches and built-up area of each region type (see Table 2). As expected, the number of patches is higher in less compact regions types (1, 2 and 3) and the built-up area is higher in region types 4 and 5. Due to the fragmentation that characterized the first time period, the highest percentage of patches in NMAL changed from type 1, in 1960, to type 3 in 1990 and 2004. However, the proportion of type 3 built-up area registered a continuous decrease in all three moments (in the same way as types 1 and 2), which indicates the transition into the second growth stage where consolidation by compactification dominates, as shown by the behavior of types 4 and 5. Entropy 2013, 15 2686 Table 1. Types of growth in NMAL *. 1960–1990 N. of patches % % of change Built-up (m2—millions) % % of change 1960 1990 1960 1990 1960 1990 1960 1990 No change 459 459 9.9 3.3 0.0 0.5 0.5 1.1 0.3 0.0 New patches (1) − 11,102 − 80.6 − − 26.7 − 16.3 − Growth (2) 1666 1666 36.1 12.1 0.0 4.1 15.7 8.2 9.6 286.2 (4.6) Growth & Aggregation (3) 2497 542 54.0 3.9 −78.3 45.2 120.8 90.7 73.8 167.5 (−5.0) (3.3) Total 4622 13,769 100 100 197.9 49.8 163.8 100 100 229.1 (3.7) (4.1) 1990–2004 N.  of patches % % of change Built-up (m2—millions) % % of change 1990 2004 1990 2004 1990 2004 1990 2004 No change 9432 9432 68.5 73.5 0.0 16.0 16.0 9.8 6.8 0.0 New patches (1) − 1406 − 11.0 − − 6.0 − 2.5 − Growth (2) 1367 1367 9.9 10.7 0.0 14.0 21.9 8.6 9.2 56.3 (3.2) Growth & Aggregation (3) 2970 629 21.6 4.9 −78.8 133.7 193.4 81.7 81.5 44.6 (−10.5) (2.7) Total 13,769 12,834 100 100 −6.8 163.8 237.4 100 100 44.9 (−0.5) (2.7) * The values in ( ) show the average annual growth rate. Table 2. Number of patches and built-up area, by types (%). Types % N.º patches % of Built-up area 1960 1990 2004 1960 1990 2004 1 32.7 10.7 7.9 4.2 1.2 0.6 2 32.3 29.4 18.0 11.1 7.0 2.9 3 25.9 38.4 41.9 25.7 20.5 15.7 4 7.3 19.2 28.9 24.8 37.7 33.0 5 1.8 2.4 6.4 34.2 33.6 47.8 Total 100 100 100 100 100 100 The Planning System...Neither Just in Case, Nor Just in Time The self-organization component identified in NMAL [8] was not unfamiliar to the central administration and several plans and laws were designed to rectify and control these dynamics, after decades with few approved plans. In fact, until 1960 the only Regional Plan that existed in NMAL was the Urbanization Plan of Costa do Sol (approved in 1948), but it only covered the coastal strip of Lisbon, Oeiras and Cascais municipalities (the southern part of the area under study). After 1960, several planning landmarks could be enumerated: Entropy 2013, 15 2687 (a) The first regional plan for the entire Metropolitan Area of Lisbon was the Plano Director de Desenvolvimento Urbanístico da Região de Lisboa - PDRL (Regional Master Plan). Its scope was defined by a new diploma in 1959, but it was never approved. (b) The non-approval of the PDRL weakened the idea of a regional strategy for urban growth [21] in that the administration limited itself to the evaluation and approval of allotment projects. Without the necessary planning instruments, suburbanization grew “without any supervision and guidance, boosted by improving accessibility and increasing rates of motorization, thus sharpening their effects within” [21]. (c) Parallel to the non-approval of the PDRL, a new law was published in 1965 which enabled the participation of the private sector in the urban allotment processes. By enabling allotment processes in not only urban areas but also in rural areas it triggered the sprawl of built-up areas throughout Lisbon peripheries. Without a regional strategic plan that could orient their co-development, these areas grew based mainly on the strategies of housing market agents that sought profit maximization in the process of land conversion. (d) In 1976, Law No. 794/76 (Lei dos Solos), still in effect today, aimed at avoiding urban speculation and to solve the housing shortage problem. Although ambitious in some measures, as for example the delineation of areas aimed to control future land use changes near urban centers, it was never fully enforced. (e) In 1982, the Municipal Master Plan (Plano Director Municipal—PDM) was enacted, which would encompass and regulate, through zoning regulations, the entire territory of a municipality (previously only urban areas would have been the object of any kind of an urbanization plan). (f) However, before 1990 few municipalities in Portugal had their Master Plans approved. But the scenario changed when in that same year, Law No. 69/90 made them mandatory. Simultaneously, a municipality could not apply to European funds without an approved Master Plan. Following the general national trend, several Master Plans were approved for NMAL between 1993 and 1999. By 2000, the Metropolitan Area of Lisbon was finally covered by municipal plans although with little or no interrelationship among them, not even between neighboring municipalities. (g) In 1992, a new Regional Plan was developed but again not approved, as a result of political decisions. It was only in 2002 that a Regional Plan for the Metropolitan Area of Lisbon (PROTAML) was approved. In its strategic vision, the plan included several scales within MAL and between MAL and the national context [22]. The above landmarks of the Portuguese planning system show that the several planning instruments actually just established existing dynamics and few or even none had the capacity to change those same dynamics into more suitable paths (as for example by mitigating the growth of a disconnected urban metropolis). Urban growth thus seems to have been more conducted by processes than by plans. In [23] Alfasi and Portugali argued that the traditional just-in-case planning approach should be replaced by just-in-time planning. The first is structured from a hierarchical top-down perspective and aims to pre-determine the future needs of a given territory. The second tries to adapt to the self-organization nature of cities. Within this approach “a city does not have any future complete picture in the form of a long-term plan that it should accomplish” [23]. Planning rules and instruments should be flexible Entropy 2013, 15 2694 Figure 10. Informal settlements in NMAL, outside Lisbon city, by 1971 (after [24]). The difference for pre-determined non-sequential transitions will probably lie in the time scale of both kinds of non-sequential transitions. For lack of intermediate time periods it is not possible to ascertain this hypothesis at present. 5. Discussion and Conclusions We explored the relation between local fractal dimension and the development of the built-up areas of NMAL, for the period between 1960 and 2004. Based on the GLSE function it was possible to break-up NMAL into the five types of regions that GLSE defines. The spatio-temporal analysis performed here shows the presence of two co-evolving growth-processes: fragmentation/dispersion and consolidation/compactification. These processes can be identified resorting to the following core growth types of built-up area changes over time: growth-type 1) new areas that emerge isolated; growth-type 2) existing areas that grow contiguously, and growth-type 3) existing areas that grew and aggregated with one or more neighboring areas. Based on these three core growth-types it was possible to identify cases where sprawl areas have changed into more compact and contiguous ones, thus recognizing sprawl as a process in the evolution of territories. In NMAL, we found that the fragmentation and consolidation processes co-evolved during the first time period (1960–1990), whereas in the second time period (1990–2004) the consolidation process dominated, as a result of the overall compactification of NMAL. Given the lack of an efficient planning system in Portugal, the data available does not enable us to ascertain whether planning is able to control the sizeable fragmentation process observed in NMAL. Clearly, further assessment is needed, possibly in connection with other urban areas where planning is known to be well-established. The analysis performed on the evolution of the five region types revealed different types of transitions among region types: (i) sequential (forward) transitions, (ii) reverse transitions and iii) non-sequential (forward) transitions. Sequential transitions should be linked to more self-organized processes with smooth growth. Reverse transitions occur when the increase in built-up area contributes to a more disperse pattern and should thus be rapidly identified in areas where sprawl must be controlled. They can also contribute to the intensification of a fragmentation process if not supported by strategic planning actions. Entropy 2013, 15 2695 In theory, non-sequential (forward) transitions should be identified with top-down planned interventions (as major real estate investment projects) which can be used by planning agencies as a means to rapidly enforce a consolidation process. However, we have also shown how non-sequential transitions may result from self-organized processes as in the emergence of informal settlements. The spatial distribution of each of the aforementioned types of transitions suggests a probable link between their form and function in the context of the metropolitan area: for example, non-sequential transitions usually emerge near a pre-existing main nucleus (e.g., Lisbon city and main suburbs), whereas sequential transitions (especially those from more dispersed types) tend to spread throughout the territory. Region type 3 played a pivotal role in both fragmentation and consolidation processes, and thus likely connects both processes. The number of possible configurations given by GLSE and its rate of change are higher for this type than for any of the other types. Hence, planning agencies should take special attention on the location and evolution of cells of and into this type. More specifically, planning agencies should consider two main options, depending on their medium/long term strategy for the development of the territories under their regulation: If the intention is to promote sprawl, then they should promote the emergence of new Type 3 areas but control growth of existing Type 3 areas into Types 4 and 5. If the intention is to promote compact areas, then they should control the emergence of new Type 3 areas but promote growth of existing Type 3 areas into Types 4 and 5. Compact or fragmented spatial systems should thus be achieved by the interplay between pre-existing and new Type 3 areas and their spatial context regarding more compact areas, such as Types 4 and 5. Although GLSE can help to quickly identify areas that should be intervened it cannot distinguish or characterize (in terms of internal quality and functioning) two cells of the same type. Consequently, even if it is possible to use this model to assess for example whether more compact areas should be promoted and where—at the metropolitan or municipality scales—it will not be possible to ascertain their quality regarding urban design, functions and behavior—at the cell scale. Acknowledgments This research was supported by grants PTDC/FIS/101248/2008, PTDC/MAT/122897/2010 and multi-annual funding of CMAF-UL, CBMA-UM, e-GEO/FCSH/UNL and INESC-ID (under the project PEst-OE/EEI/LA0021/2011) provided by FCT Portugal through PIDDAC Program funds. Conflict of Interest The authors declare no conflict of interest. References 1. Herold, M.; Hemphill, J.; Dietzel, C.; Clarke, K.C. Remote sensing derived mapping to support urban growth theory. 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