Comparing the Morphology of Urban

7/30/2019 Comparing the Morphology of Urban

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in : European Cities Insights on outskirts, Report COST Action 10 Urban Civil Engineering,Vol. 2, Structures, edited by A. Borsdorf and P. Zembri, Brussels, 2004, 79-105

Comparing the morphology of urbanpatterns in Europe a fractal approach

Pierre Frankhauser 1ThMA, UMR CNRS 6049, Universit de Franche-Comt , Besanon, France;

[email protected]

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AbstractThe sprawling urban patterns typical for the outskirts of many European metropolitanareas seem to be amorphous and it is difficult to find references for describing them.However, for managing sprawl it seems important to have quantitative descriptors,

which allow distinguishing different types of urban patterns and which are less

ambiguous than traditional density measures. A better knowledge of the morphology ofthese patterns should also point to the underlying context of urbanisation at their root.More concretely: to what extent are planned patterns different from less planned ones?Do planned or unplanned patterns show comparable morphological features?

The present contribution shows how going back fractal geometry may help to findanswers to these questions. A more intuitive introduction to fractal geometry and itsapplication to urban patterns is followed by a definition of the measuring concept used,

which helps analysing their morphology. The presentation of a large number ofexamples helps to understand the information transcribed by these measures and todevelop another type of approach to sprawling and less sprawling patterns. Moreover it

will indeed be possible to establish links to the planning policy at the root of these

patterns.

The final topic tackles the question, to what extent knowledge about the form of thesepatterns may be used for managing urban sprawl in future under the aspect of a moresustainable development.

KeywordsOutskirts of European Cities; urban morphology; fractal measures; urban planning.

1 Introduction

Despite many attempts to limit urban sprawl, this phenomenon remains a challenge for urbanplanning. It seems that the desire to move out of very dense urban areas persists andcorresponds to a real social demand. Hence policies trying to increase density in the outskirts orto restrict sprawl are usually contested and local decision-makers may even be willing to give into market pressure.

Sprawling urban patterns usually show a highly irregular form, which resemble ink splashesrather than regular geometric objects like circles or squares. The traditional measures used in

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urban planning, like densities, are not really suitable for describing such forms. They representthe mean occupationof space rather than morphological aspects. For a control of sprawl and a

reflection on the form of urban patterns it would be convenient to have data that representtheir particular features and allow a comparison of their morphology.

This leads one to reflect more on what these particular features are from a morphological pointof view. One of the main reasons why these patterns look amorphous is the fact that they area patchwork of structural elements, in a great variety of scales from that of buildings to thescale of metropolitan areas. Thus even in the highly simplified cartographic representation of ametropolitan area in figure 1, it is possible to discover details of very different size: whenfollowing the borderline of an arbitrarily chosen settlement cluster, there appear small bays,

which alternate with larger ones in an irregular rhythm. This feature is not peculiar to theparticular size of a town, it can be found in small as well as large ones.

Another striking feature of metropolitan areas is the fact that they are made up of many clustersof quite different size, spatially distributed in a rather non-uniform way: along valleys ortransportation networks we often observe ribbons of built-up areas, whereas badly accessiblezones are sparsely populated (cf. figure 1).

big bays

little ba s

Figure 1:The metropolitan area of Stuttgart in a simplified cartographic representation.

This also makes it difficult to define real boundaries of an agglomeration: In an individual

housing zone o the periphery, the distances between houses may become larger and larger andfinally a nearly continuous transition to the next settlement can be observed. The distance of200 m between neighbouring buildings, used in France to delimit agglomerations seemstherefore rather arbitrary. Since ramparts have disappeared, the only physical limits left in urbanareas, in a strict sense, are the walls of the buildings.

Despite their complexity, it is nevertheless possible to discover regularities in these patterns thatseem paradox. If we, for instance, in cartographic representations like that of figure 1, measure


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the boundary length of urban clusters and their surface, we observe that both the border lengthand the surface tend to be proportional. This clearly contradicts the usual geometric assumption

that the surface should be proportional to the square of the perimeter length.

Such observations led researchers to turn to a completely different approach for describing themorphology of such patterns, namely one based on fractal geometry. The rationale for usingthis approach lies in its inherent properties. First, the fact that we use a geometric approachallowsus to construct spatial reference models, which can be compared with real world situations.

They may be used to illustrate different types of spatial pattern organisation, which resemblepeculiar aspects of urban patterns like fragmentation or complex morphology of outlines.Moreover, applying fractal geometry helps to find coherent interpretations of the mentionedphenomena and paradoxes.

Beyond this intuitive, more conceptual approach, it is possible to introduce measures, which

help to describe the complex form of fractal objects by means of a unique value. Thus, if urbanpatterns really show the particular features of fractal objects, we may conclude that despite theirhighly irregular aspect, they follow a well-defined spatial organisation principle, which can becharacterised by quantitative factors. The usual notion of regularity or irregularity thenbecomes meaningless.

By using such measures it becomes possible to distinguish different types of urban patternsaccording to their spatial organisation. The observed values may be linked to the historical orplanning context under which the considered town section was built. Thus, on the scale ofdistricts, certain ranges of values may correspond to particular planning concepts like mining

villages, or quarters conceived in the spirit of Le Corbusier. Such planned structures may thenbe compared to patterns emerging from a less controlled urbanisation process. On the scale of

agglomerations, it is interesting to study to what extent planning restrictions really influenceurban pattern morphology. To this aim we can consider the morphology of outlines or explorethe patchwork of the districts. By going across the scales we can identify thresholds in thespatial organisation. Thus, on the scale of districts, urban planning may have imposed smoothurban outlines, but on the scale of the agglomeration, the pattern may appear as a complexpatchwork of districts for which the values of fractal measures are different.

Basic work on fractal investigations of urban patterns has been done since the 1980s, inparticular by M. Batty and P. Longley (1994) as well as by P. Frankhauser (1994). More recentpublications have deepened the methodological aspects and confirmed the interest of using thisapproach (e.g. Batty M., Kim S. K., 1992, Frankhauser P., 2000, Frankhauser P., Pumain, D.,

2002). Recently, the French Ministry of Planning, Housing and Transport has financed thecomparative analysis of a sample of European cities based upon fractal measuring as part of aresearch program about the emergent town. The goal was twofold: on the one hand, thefractal approach was to be validated in view of a potential application in planning purposes, onthe other hand, investigations should show to what extent urban planning really acts on theurban pattern morphogenesis. About fifteen European metropolitan areas were selected andanalysed (Frankhauser, 2003). Since it was only possible for some of the case studies considered in the present


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COST-project to obtain suitable data, the paper refers mainly to the results obtained as part of this Frenchresearch project.

First, a brief more intuitive introduction to fractal models serving as reference for tacklingurban patterns. Then follows in introduction of the concept of fractal measures and adiscussion of the information they transcribe about urban morphology. This helps to interpretthe results obtained from the investigations of the urban patterns. Finally, preliminaryreflections about how such knowledge could serve planners in their actual work are presented,in particular with regard to controlling sprawl.

2 Methodology of fractal analysis of urban patterns

2.1 Fractal reference models for describing urban patterns

The most striking feature of fractal objects is the fact that they are by definition multi-scale. Thisis the direct result of the procedure used to construct a theoretical fractal. This procedure isbased on repeating the same operation, defined by the generator, on smaller and smaller scales.

Thus, in figure 2, an initial grey square is replaced in a first step by a cross-like figure consistingof five smaller grey squares, the base length of each one just a third of the initial square. In thenext step, this procedure is repeated for each of the smaller squares etc. By this iteration ahierarchical structure is generated consisting of smaller and smaller clusters. At the same time,the border of this geometrical object, called Sierpinski carpet, becomes more and morecomplex, since at each step an increasing number of smaller and smaller tentacles appear. Theoutline shows big and small bays reminiscent of the previously encountered morphology of

urban patterns.

L 1/3 L

Figure 2:Generating a Sierpinski carpet: in each step each square is replaced by N=5 squares with the baselength reduced by the factor r = 1/3

In this example, the geometrical structure remains confined to the area of the initial square overall iterations. However, the same type of geometrical object may also be constructed by addingsquares of a given size according to a generating rule. Thus the structure spreads out as shownin figure 3, where a more and more complex cluster is obtained by adding cross-like branches.


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Figure 3: Generating a fractal by adding elements. Each squares contains a cross, reminiscent of a streetnetwork.

This example can easily be linked to urbanisation. Let us assume that a town has first beenconstructed on a square-like scheme, like certain medieval towns. Then, during a first period,districts have been added along the four gateways going out of town. In a next step, the townhas continued to expand along the main road axes, but other districts have been constructedalong some secondary road axes. Thus a network-dominated pattern emerges. This pattern hasof course remarkable advantages for the residents living along these secondary road axes: thenetwork distances to the city centre are shorter than if they had settled further away on themain road, but they also benefit from free space in the immediate vicinity of their residences.

In some sense, this fractal object resembles urban growth along valleys and transportation axes.However, the Sierpinski carpet of figure 2 consists of just one cluster. As pointed out before, astriking feature of metropolitan areas is the existence of a multitude of settlements the size of

which varies within a large range. Figure 4 (a) shows a Sierpinski carpet generated by similarrules to those of figures 2 and 3, but some squares are not connected to the central cluster.Hence the structure consists of many clusters of different sizes, which are spatially distributedin a very inhomogeneous way. At the same time, the outline of each cluster becomes more andmore complex in the course of iteration. Such a structure combines the morphological featuresof metropolitan settlement patterns discussed above.

From the geometrical point of view, Sierpinski carpets have some very curious properties: whencomputing their edge length and the black surface for each iteration step, it turns out that thesurface vanishes eventually, whereas the edge length tends towards infinity.

The example in figure 4 (b) shows a rather compact structure, the outline of which is a normalsquare. Such a structure resembles more an intra-urban situation for which planners haveimposed very smooth borders. When using a simplified cartographic representation of an urbandistrict, the street network doesnt appear, but inside the district there are a great number ofnon-occupied squares of very different size: a few large free spaces which could be huge parksplus an increasing number of smaller and smaller free spaces like small squares or finallycourtyards. The cumulated border length of all lacunas tends, again to infinity. The last example(c) of figure 4 shows a so-called Fournier dust, which consists of a hierarchically organizednetwork of non-occupied spaces that resembles a street-network on the scale of districts.


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(a) (b) (c)

Figure 4:A Sierpinski carpet consisting of a series of clusters (a), a compact one with a inner hierarchy of free

spaces (b) and a Fournier dust reminiscent of an intra-urban street network (c)

Finally, in figure 5, we show another type of constructed fractal, a teragon. Unlike in theprevious examples, here the inner black surface remains constant and completely homogeneousover iteration and only the outline becomes more and more complex. Due to the iteration, thisoutline consists of a few big bays generated at the first steps and more and more small ones.

Figure 5: Generating a teragon: the surface remains constant, whereas the border becomes more and moredendritic.

Hence it resembles again the outline of urban patterns, at least in simplified representations likethat of figure 1. It can be shown that in the course of iteration, the mean distance to the centreof the structure increases less than the mean distance to the edge decreases. Like the dynamicapproach represented in figure 3, this may give an intuitive reason for urban sprawl: the

reduced accessibility of the city centre is more than compensated for by better access to thegreen hinterland outside the city. Instead of returning to a very strong iteration, the position ofthe squares may vary randomly at each step if we respect the lacunas previously generated.

Then a less regular structures is obtained, resembling more the observed complex structures,i.e. urban patterns.

Both types of fractals, regular ones and more irregular ones, are of interest for describing urbanpatterns. Regular fractals may serve as reference models and then play the same role as a circle


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or a square do in Euclidean geometry. They serve also to illustrate the meaning of fractalmeasures.

For the purposes of describing urban patterns, we will therefore consider the constitutiveelements of a structure, like the squares that make up our fractal objects or the buildings in acity, as occupied sites, which together constitute the mass of the structure.

2.2 Fractal measures

Fractals show obvious particularities that are not in accordance with the Euclidean approach togeometry and which cannot be described by the usual measuring concepts. An example is theteragon for which the outline diversifies while the surface remains constant. Thus measuringedge length will no longer be possible. Density measures become obsolete, too: if you try tocompute the density of the occupied sites in a Sierpinski carpet the result will strongly dependon the surface used as reference and it will never be a stable value.

However it is possible to look at these structures from another point if view. By exploring howthe distribution of the occupied sites or the edge length changes across the scales, it is possible tofind parameters that characterise fractals by a unique constant value, the fractal dimension. Thisparameter is a natural generalisation of the usual notion of the Euclidean dimension. Thus thefractal dimension of a uniform black surface will be equal to two, that of a straight line equal tooneand an isolated point would have dimension zero. However for fractal structures like thoseof figures 2 to 5, the values are usually fractional numbers lyingbetween zero and two.

For constructed fractals like those of figures 2 to 5, the value of the fractal dimension of theoccupied sites is directly linked to the parameters of the generator, in particular to the number

Nof elements and the reduction factor r, e.g.N= 5 squares in figure 2 for which the reductionfactor is r= 1/3. In this example the fractal dimension1 would be Ds= 1.47 (cf. Mandelbrot,1977, Frankhauser, 1993). For example (a) of figure 4 the value Ds= 1.59 is obtained, for (b)Ds= 1.89, for (c) Ds= 1.51 and for the teragon Ds= 2, since the surface remains compact anddoesnt tend to vanish like in Sierpinski carpets.

The fractal dimension has a clear meaning and function. It measures the degree of concentrationofthe occupied sites across scale, or, more precisely the relative decrease in masswith increasingdistance from any site where mass is concentrated. Hence, the uniformlythe mass is distributedin a fractal structure, the closer the dimension will be to two, and vice versa, if the mass were

concentrated in one point, Ds would be zero. Indeed the mass is more uniformly distributed inthe carpet (b) of figure 4 than in the case of (a) or (c) which are more contrasted. Consequentlythe dimension value is higher for pattern (b) than for patterns (a) or (c). In figure 4 (a) thedimension value describes the distribution over the whole of the occupied sites. It is possible tocompute the dimension of only the central cluster which amounts to Ds(clust) = 1.37. The value

1the dimension is the ratio between the logarithm ofNand the logarithm ofr.


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expresses the multi-scale dendritic aspect of this cluster. Of course this dimension is also truefor each one of the peripheral clusters but not for the distribution of the clusters in space.

It is also possible to calculate the fractal dimension of the edge of the fractals. For Sierpinskicarpets the dimension of edges is equal to that of the surface. This may come as a surprise, butexpresses the fact that in the course of iteration edge and surface merge eventually, resemblingthe urban planning concepts shown in figure 7 (a) and (b). We argued earlier that observationhas shown that for metropolitan areas the length of the outline of the clusters is proportional tothe built-up surface; from a fractal point of view this would mean that both the edge and thesurface have the same fractal dimension, like a Sierpinski carpet.

For the teragon the situation is different, the border has the dimension Db= 1.5, but as pointedout, the inner surface has the dimension two. The fractal dimension measures the relativelengthening of a borderwhen comparing it with a straight line (figure 6). Again different features of

the border of a pattern may be distinguished. For the fractal (b) in figure 4, the outline issmooth, its dimension is Db(extern)= 1 whereas for the whole outline including all lacunas thedimension is Db = Dsurf= 1.89. This approach will help to analyse the impact of different kindsof planning policy on the morphology of urban districts.

B

A

Figure 6:Comparing a tortuous line with a straight line segment of length.

Observed structures like urban patterns are of course not constructed according to iteration.However, in practice there are different methods, which allow verifying to what extend anobserved pattern is structured according to fractal logic. These methods imitate the logic ofiteration by measuring the distribution of occupied sites or the length of the outline at amultitude of scales. This provides enough information to test whether a pattern is more or lessfractal and if it is possible to compute its dimension. In order to illustrate the principle of suchmeasuring methods, the correlation analysis, which we applied in recent investigations will bepresented as an example.

In order to realize this type of analysis, each occupied site is surrounded by a circle of a given

radius and the occupied sites are counted within this circle. This helps to compute the mean

numberN()of occupied sites lying within such a radius. Then the radius of the circle is variedand again the same mean number is calculated. This procedure is repeated for a large range ofvalues. It can be shown that for a fractal a power-law is obtained between the number N()and the radius .The exponent Dof this power-law is the fractal dimension whereas the so-called prefactor ameasures possible deviations from the fractal law. This relation reads

N() = aD


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When analysing urban patterns, numeric data are used of course, taken from digitalised

cartographic maps or GIS-data where the built-up-area corresponds to the black pixels. N()

then corresponds to the mean numbers of black pixels.

In order to realize fractal analyses of urban patterns, a computer program was developed whichestimates the fractal dimension and the prefactor from the observed data and makes it possible

to verify to what extent the empirical data N() correspond to a fractal law2. Often this is reallythe case, however, in other instances several ranges of should be distinguished for whichdifferent values D are obtained. The power-law doesnt often hold for very small distancesbelow the scale of blocs of houses, for rather complex urban patterns, or for distances largerthan the size of the analysed town. Usually the scales of districts and of the total agglomeration,

which is composed of a patchwork of districts, are easy to distinguish. It can be seen that boththese scales are of interest for analysing the impact of planning concepts on urban patternmorphogenesis.

2.3 The fractal approach to urban patterns

Urban planning imposes regulations on the construction of houses in new districts and tends tolimit urban sprawl by defining smooth outlines to the town boundary. Moreover propertydevelopers often act on this scale by constructing parts of a district on rather regular grids. Onthe more aggregated level of agglomerations, the municipalities try to control urban sprawl bymeans of master plans that define zones for development.

In practice, however, great differences exist between planning policies. In Great Britain for

instance, the concept of green belts avoids urban sprawl in the vicinity of towns, but sprawloften exists beyond the green belt. Various northern countries try to manage urban sprawl bypromoting axial development along public transportation networks and preserving green areasbetween these axes. Other models that try to integrate the new lifestyle into planning policy

would be those concepts of new towns or urban villages, which act on the scale of theagglomeration as well as on that of the districts. There are also planning concepts that try to tiein leisure areas and residential areas across scales as shown in figure 7 (a) and 7 (b).The generalquestion arises then as to what extent such policies and concepts really influence the structureof urban patterns and if their spatial organisation is really different from areas that havedeveloped in a more organic and less controlled way.

Hence the morphology of urban patterns is mainly determined by phenomena referring to two

scales, that of districts and that of whole the agglomeration. Both these scales have beenconsidered in the investigations.

2The computer program fractalyse was developed at the THEMA institute (Besanon). The current,

completely revised, version was realized in cooperation with the institute IMAGE ET VILLE(Strasbourg) by Gilles Vuidel.


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(a) (c)(b)

Figure 7: Different planning concepts, which show fractal features: the plan of Hilberseimer (a) for thereconstruction of Chicago, the proposal of the architect Schoefl for a fractal town outline (b), and the finger

plan of Copenhagen (c)

Approaching these topics the investigations focused on two aspects: first the spatial distributionof the built-up area was analysed, then the form of urban boundaries was considered. Aspointed out, fractal analysis allows measuring whether urban patterns are more homogeneousor more contrasted. It can be expected that densely urbanized city centres show homogenouspatterns, but mining villages or certain residential areas conceived according to a ratherrepetitive plan also show dimension values close to two. More contrasted patterns can resultfrom planning concepts but also be the result of less controlled development. On the scale ofagglomerations, axial development along valleys or transportation axes leads to more highly

contrasted patterns resembling more closely the Sierpinski carpets of figure 2 or 3 (b). Lowerfractal dimensions should be observed here than for compact urban patterns.

The morphology of town outlines is a rather interesting indicator of urban sprawl. We can forinstance test whether the goal of a planning policy to smoothen an outline really works.Moreover, even if planning concepts work on the scale of the districts, what about themorphology of boundaries on the scale of agglomerations? Again we can look at the impact ofmaster plans.

However, as pointed out above, studying urban boundaries requires reflection on how to definethem. Since the present contribution focuses on the form of urban patterns, a morphological

method was introduced for extracting boundaries from detailed cartographic representations ofthe patterns. The buildings were dilated incrementally, so that black clusters appeared whenneighbouring buildings were contiguous. Usually after a few increments such clusters appear

when small courtyards and most of the streets are filled up (figure 8 (b)). The clusters obtainedusually correspond to the size of districts or even main parts of an agglomeration. In case ofdoubt, a sequence of dilation increments was compared. It should be emphasized that filling upfree spaces of less than ca 15 meters distance doesnt really affect the results of fractal analysis;as pointed out, the fractal law doesnt hold for these very small distances and this range was in


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any case eliminated when calculating fractal parameters. The last step is the extraction of theedges of the black clusters.

(a (b

(d)(c)

Figure 8:Extracting the outlines of a town by dilation of the built-up area. Figure (c) shows all the outlines,figure (d) shows the outline of the main cluster.

Different types of outlines are of interest. When looking at the scale of a whole agglomerationor an outskirt, the morphology of the outline of the main cluster will be studied. The fractalreference model will then be the teragon (figure 5). But even having filled up streets andcourtyards there usually remain empty inner islands, which correspond to public squares,large places, parks, or even important pieces of infrastructure. The existence of these emptyinner islands of different sizes can be compared with the hierarchy of lacunas in the Sierpinskicarpet of figure 4 (b). Their fractal behaviour shows that these intra-urban free spaces are notall of the same size, but contrasted according to different functions. Thus it is interesting to

look at the form of the outline of the main aggregate which corresponds to what is usuallyconsidered the boundary of the town (figure 8 (d)), as well as at the morphology of the totaloutline including intra-urban borders and all the edges of other clusters in the area underconsideration (cf. figure 8 (c)).


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3 Measuring the morphology of urban patterns

3.1 The sample of towns and some general results

Now follows a summary of the results, obtained for about fifteen European metropolitan areasfor which cartographic data on the scale of buildings were available. References toinvestigations of some other metropolitan areas, for which aggregate data like those of figure 1

were accessible, complete these results. The chosen agglomerations are mainly located inFrance, Germany, Belgium, Switzerland and Italy3. Even if the data quality was not strictly thesame in all cases, it was possible to compare the results obtained for the differentagglomerations. We found that urban planning and more generally the historical context in

which a town has evolved does indeed influence the pattern morphology. This holds for themicro-scale of districts as well as for the scale of metropolitan areas. However, there is no

fundamental opposition between the different countries: more or less regular patterns exist inall countries studied and local planning decisions or architectural concepts turn out to be amore crucial key-factor. Topographic constraints like mountains may influence urbanmorphogenesis on the scale of the agglomeration, but eventually urban growth alongtransportation axes may generate the same type of patterns as if an agglomeration is situated atthe intersection of several valleys.

As pointed out the fractal surface dimension measure to what extend space is occupieduniformly by the build-up area, thus, in order to simplify the notation, the fractal surfacedimension is in the following expressed as UI (uniformity index). Following the same logic thefractal border dimension is called DI (dendricity index)when referring to the main cluster, andFI (fragmentation index) when applied to the whole of the inner and outer boundaries of allclusters (cf. figure 8).

First the aggregated level of metropolitan areas will be considered, for which the general formof the different settlements was analysed. Three examples, Berlin, Stuttgart and London, wereselected in order to show what type of information might be obtained. The agglomeration ofBerlin yielded a value UI= 1.75, which expresses the rather contrasted pattern, dominated byaxial

growth. The dimension of the boundary of all settlements together is of the same magnitude andconfirms the dendritic aspect of the pattern. The outline of the central cluster, the centre ofBerlin, obtained after one dilation step has a dendricity index ofDI = 1.58, which is rather highfor such a pattern. In contrast, the surface of the London metropolitan area has a UI-value of1.86. The same value is obtained for all the boundaries (FI) as well as for the surface of thecentral cluster, which obviously dominates the pattern morphologically. Thus the built-up areais distributed rather homogenously in one important central cluster, surrounded by a number ofsmall settlements of roughly even size and spatial distribution. The outline of the central

3The investigations within the framework of the contract already mentioned were carried out by D.

Badariotti (Strasbourg and Saarbrcken), I.Thomas and M.-L. De Keersmaeker (Brussels), C. Tannierand B. Reitel (Basel), G. Rabino and M. Caglioni (Milan). The paper refers mainly to the investigationscarried out at ThMA (Besanon) by L. Quivreux and P.Frankhauser.


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aggregate, the city of London, has a dendricity index DI of 1.41, an indication that it isconsiderably smoother than that of Berlin.

The built-up surface of the metropolitan area of Stuttgart (figure 1) has a uniformity ofUI= 1.75, which is rather low and stands for a highly contrasted pattern. The large presence ofsmall and medium-sized towns in the hinterland contributes to a rather high value for the

whole of the outlines (FI= 1.88). The smallness of the central cluster, the town of Stuttgartitself, makes it hard to estimate the boundary of the central cluster, but this case will beconsidered again later on when dealing with detailed data. These examples show that the stronggreen belt policy in London has contributed to the emergence of a rather compact from of thecentral cluster. In general, the built-up surface is more homogenously distributed in themetropolitan area of London than in that of Berlin. In the case of Berlin and Stuttgart, theplanning objective was different: there, local authorities opted for an axial development alongsuburban railway lines and intended a high interpenetration of leisure areas and built-up zones.

Thus a quite different development scheme comes about and shows up in the low valuesreferring to a multi-scale spatial organisation of the pattern.

Earlier investigations dealt with the evolution of some metropolitan areas by comparing theirpatterns for different dates. They showed that the patterns have become more and morehomogeneous over time. This expresses the fact that motorisation allows not only to takeresidence in a greater distance from the city centre, but also further away from maintransportation axes, since the street network irrigates space in a more and more uniform way(Frankhauser, 1998). These results, obtained for Berlin, Munich and the Ruhr region, wererecently confirmed for some smaller towns in France and for Basel by studying detailedcartographic data for different dates (Frankhauser, 2003).

Now we will discuss the results obtained for the agglomerations for which detailed data forwhole the metropolitan area were available. On the one hand, a more aggregated level isconsidered by referring to results where large sections of the agglomerations had been analysedas a whole. On the other hand, the discussion focuses on results obtained on the more detailedlevel of districts. The examples presented relate mainly to the agglomerations of Lille, Lyon,Stuttgart, and Montbliard. This information will be complemented by focussing on someaspects of agglomerations which show particular features like Saarbrcken, Strasbourg andBasel, all located near national borders, the new town of Cergy-Pontoise, some peripheral zonesof Brussels and Helsinki, and an Italian case, Bergamo.

First some information should be given about the particularities of these urban areas. The areaof Lille is a polycentric agglomeration constituted of three towns, Lille, Roubaix and Tourcoing,

but extending beyond the French-Belgian border. The urbanisation was dominated over a longtime by heavy industry and large industrial areas remain, particularly in the South of the highlyurbanised area, which has incorporated a certain number of villages in the course of time.Hence the pattern is a rather disparate patchwork of zones of different morphology; transientareas fill space between the hard core of the three towns and the rural hinterland. Morerecently, the new town Villeneuve dAsq has been built close to Lille. This town has beenconceived according to the general guidelines of these typically French projects, which areinspired by the concept of English new towns.


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Lyon is an agglomeration of more than a million inhabitants with a long history. At the

beginning of industrialisation, Lyon was one of the main centres of the textile industry, whichdeclined later on. But after having converted the industrial areas, Lyon enjoyed an economicrenewal. Due to the topography, the hinterland is highly contrasted. Three areas can beidentified: the western periphery lies in a mountain region and is dominated by individualhousing of high standard, whereas in the south and the east, social housing and industrialactivities are more present. Recently, the east of Lyon saw some rather important developmentbut efforts has been made to preserve some natural areas from a savage urbanisation. In thenorth of the agglomeration there is a large swampy zone unsuitable for development.

The Stuttgart region is a metropolitan area, which was hardly influenced by the presence of carindustry and electric goods industry. Hence the industrialisation is more recent. Many of theindustries, big ones as well as a great number of middle-sized and small ones, are localized in

smaller towns of the hinterland; some of them could be characterised as edge-cities. For anumber of years efforts have been made to coordinate planning policy on the scale of themetropolitan area. To this aim, a special authority has been installed and regional master planshave been developed. These plans have certainly helped to channel urbanisation by definingaxes and encouraging development along valleys and transportation axes and by limiting theestablishment of commercial areas and malls. Much work has been done to draw up landconservation plans that link green areas on different scales. However the various towns remainin competition with each other and try to realize their own development policies, ofteninfluenced by economic actors.

Montbliard is a conurbation made up of several small cities of about 30,000 inhabitants. Theurbanisation was highly influenced by the development of the Peugeot factory, which was

established in the 1950s. Historically, smaller factories existed before in the different towns, butthe rapid development of the car industry necessitated the rapid construction of socialdwellings. Most of these dwellings were constructed within a restricted perimeter around themain factory and conceived, as most social housing in France at this period, according to theprinciples of the Le Corbusier School. Individual housing areas were often constructed in the

vicinity of these zones. On the scale of the agglomeration, the urbanisation didnt follow aparticular strategy but responded to a concrete urgent demand and to economic pressure.Nevertheless the early establishment of an urban district facilitated control of the urbanisationprocess. Nowadays local planning policy is trying to reassess the spatial structure of the area byspecific measures and various master plans. A very subtle analysis of the remaining naturalreserves in the immediate neighbourhood of built-up areas has made it possible to preservethese areas as ecological reserves or and to accord them leisure functions.

Saarbrcken is also an agglomeration hardly marked by industrial activities. However, as inLille, the rather ancient industrialisation was for a long time linked to the presence of the ironand steel industry. Since Saarbrcken lies close to the French-German border, some Frenchtowns belong to the conurbation. Strasbourg and Basel are agglomerations located near nationalborders, too, but they are more monocentric: for Strasbourg, the German town of Kehl is oflittle importance and in the case of Basel, some peripheral towns lie in Germany and France.

The last three cases will be considered only marginally. Cergy-Pontoise is a special case, as, for a


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long time, the French legislation gave the planning authorities of new towns great powers ofcontrol. Thus this new town is constructed according to well-conceived plans, even if the

architectural concepts were not the same for the different districts.

Finally, in the case of Brussels some outskirts in the Walloon Brabant will be taken intoaccount. The main interest of this case lies in the well-known fact that sprawl was lesscontrolled in Belgium than in other European countries. In a similar way some parts ofBergamo were considered, which belongs to an Italian region where urban sprawl is ratherimportant, due to the relative proximity to the Milan agglomeration on the one hand and thelandscape amenities on the other. Both agglomerations are situated on the border of the Alps.For the agglomeration of Helsinki, some outskirts were analysed, too. The regional planningpolicy of Helsinki follows similar tendencies to that of Copenhagen and favours an axialdevelopment while preserving leisure zones close to the agglomerations.

3.2 The results for the built-up area (uniformity analysis)

As mentioned before, the fractal power law is generally rather well suited for describing urbanpatterns. Only for very irregular patterns or when passing from the scale of wards to that of

whole the agglomeration deviations from the fractal law are observed. In the present overviewonly the strictly reliable results are taken into account. First the micro-level of urban districts

will be discussed. Usually a particular fractal method of analysis, the radial analysis, was used foridentifying ruptures in the pattern (cf. Frankhauser, 1993, Batty, Longley, 1994).

Figure 9shows such a selection. After having chosen the position of a site (counting centre) asquare surrounding this centre is progressively enlarged and the built-up mass counted insidethe square. A special representation of the obtained relation between the mass and the size ofthe square allows us to identify the ruptures. This procedure allows us to select districts, whichshow a specific morphologic behaviour that is later expressed in the fractal dimension. Foroutskirts it was often possible to select the whole settlement.

0

0,5

1

1,5

2

2,5

3

0 200 400 600 800 1000 1200

outer ruptureinner ruptureSTUTTGARTcounting

center

Figure 9:Identifying different ruptures by means of a radial analysis. On the left the so-called curve of scalingbehaviour that helps to identify these ruptures on the measuring curve.


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For all city centres of the big towns analysed, the patterns are rather uniform; the values of theiruniformity index UI lie in the range between 1.8 and 1.95. This is linked to the intensity of the

land use, due to the high land prices. Districts situated in the immediate neighbourhood of thecity centres often show similar values.

In urban areas where there are fairly big towns on the periphery of the main city, these townshave often rather lowUIvalues. In the Stuttgart case, the UIvalues of the peripheral towns fallinto a range of 1.61 to 1.73, except in the case of Fellbach, where urbanisation has been lesscontrolled. For conurbations the situation is different since all the cities have more or less thesame size and comparable functions; this holds e.g. for Montbliard where all towns have ageneral value of ca. 1.8.

The values obtained for outskirts or particular types of districts on the periphery of great citiesvary within a rather large range. The differences may easily be linked to the specific context in

which they were constructed. Purely individual housing estates often show a degree ofuniformity comparable to city centres. This shows that the information transcribed by fractal analysis hasnothing to do with density.

Such patterns were observed in the east of Lyon (1.82 to 1.99!) but also in some districts in thewest of Lyon.Comparable values exist for some peripheral districts and outskirts of Stuttgartbut also for some outskirts of Helsinki.Such situations are often the result of regulations thatimpose a constant rate of land-use all over a large zone, and where no public or private service areaslike commercial areas, schools etc. or leisure areas are established. Hence these zones are ratheruniformin their spatial structure.

Less planned and constrained outskirts are often more contrasted and irregular. This is true for

some outskirts in the south of Brussels, but also for Lille and for areas with less controlledprogressive urbanisation in the Stuttgart region. Here we find rather lowUI valuesfrom 1.50 to1.74. Some results obtained for the Bergamo region confirm these observations.

Patterns that contain industrial areas are usually contrasted. This is true for the southern part ofthe Lille region, but also for areas in the south of Lyon or in the region of Strasbourg.

Contrasted patterns also occur when planners intend to integrate public space with differentfunctions and thus different sizes in a town section. Here the situation is completely different fromthat of homogenous individual housing estates. Different types of architectural concepts pursue suchobjectives. Districts constructed according to the scheme of Le Corbusier have rather lowUI

values (1.54 to 1.77). Such districts were identified at Montbliard, Stuttgart, Lyon and

Strasbourg. Very comparable situations occur for the new towns. In the different districts ofCergy-Pontoise, highly contrasted planned patterns were observed (1.60 to 1.73) and also in

Villeneuve-dAsq near Lille.

Some results, obtained for agglomerations near national borders, may complete theseobservations. In all cases no fundamental differences were observed even if there are nuancesin some cases. In the Strasbourg region, residential outskirts show comparable values for bothsides of the Rhine river. In the case of Saarbrcken, rather lowUIvalues are found for German


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and French districts in general. Here one should take into account the fact that industrialisationhas influenced urbanisation greatly, like in some parts of Lille. For the outskirts of Basel, the

differences were more important: the French parts in particular are rather uniform, whereas theGerman and the Swiss estates have UIvalues of about 1.77 indicating a higher contrast.

3.3 The results for the town outlines (dendricity and fragmentation analysis)

As pointed out previously, the local planning policy often tends to act on town outlines. Thissection focuses on the morphology of these outlines. The city centres are not of interest hereand only the peripheral zones of agglomerations and outskirts will be considered. Whencomparing the periphery of agglomerations, considerable differences can be observed. The

fragmentation indexFI for the western part of the Lille agglomeration for instance is 1.87. Thethree persisting big clusters have dendricity indexesDIof about 1.39. The comparison of these

values with that of the Stuttgart region turns out to be interesting, since in the case of Stuttgartthe planning policy tends to control sprawl strongly on the micro-scale of the districts. Indeedthe FI-value for the main cluster of Stuttgart amounts to 1.80, and the DI-value of the mainaggregate is 1.27. The values are lower, the outlines on the scale of the districts are smoothedout, but the Stuttgart agglomeration also features other cases: as mentioned above, the localauthorities in town of Fellbach did not impose such strong controls on urban sprawl: The DI-

value of the main cluster obtained after dilation is 1.45, whereas the FI-value is 1.7. Hence theborder is very dendritic, and the fragmentation index shows that the intra-urban pattern ishighly contrasted.

On a more detailed scale it is interesting to consider the outline of districts situated on theperiphery of towns as well as that of outskirts. For the same reasons as discussed before, someexamples of the Stuttgart region shall be presented. Settlements dominated by individualhousing areas show rather low edge dimensions for the main cluster (about DI= 1.26), buthigh values for fragmentation index(1.80). This can be explained by the fact that these outskirts

were constructed according to a logic of housing estates where planning defined a rectilinearborder and imposed rather rigid constraints about plot size. Thus intra-urban non-built-upspace is distributed rather homogenously.

For the Lyon and the Lille agglomerations, the results are rather different. On the eastern andsouthern periphery of Lille, the DI values lie within a broad range (1.33 to 1.55) and the FI

values indicate a rather homogeneous pattern, but other districts show a higher innerfragmentation. All these districts seem to be the result of a progressive, less controlled growthprocess and some of them show a high mix of residential and industrial areas including publicbuildings like schools. Thus the patterns remind us more of a teragon (DI= 1.50), in particular

when their intra-urban pattern tends to a homogenous mass distribution. In this context twoexamples analysed in the Bergamo region of recently developed mainly residential towns are ofinterest, too: they show highly dendritic borders (1.43 to 1.46). Obviously no restrictions havebeen imposed to smoothen the urban outline.

These results show again that earlier built town sections, particularly if they are the result of a progressive andless controlled urbanisation process, where industrial activities played an important role, are more fragmented. A


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comparable situation arises for recent residential zones resulting from a more spontaneous growthprocess. The differences obtained for the peripheral towns in the Stuttgart region confirm this

result. On the other hand, the stronger planning policy in the Stuttgart region tends in generalto limit sprawling on the scale of the districts.

Finally, the question of a possible influence of the national context on the morphology ofoutlines will be considered again. The comparison of the outlines of different parts of theSaarbrcken region, which was carried out for a couple of French and German districts, did notyield particular differences. In the case of Basel, the main clusters of the Swiss outskirts have DI

values resembling to the values obtained for the Stuttgart region (1.27), the German Lrrachhas a higher value (1.37). For the French part the dendricity is higher (1.47), this couldcorrespond to a slightly looser control.

Finally, the particular case of strongly planned districts like those of Cergy-Pontoise is

discussed. The values observed fall into the same range as those observed for the outskirts ofStuttgart (about 1.29), matching a tendency to smoothen outer edges. The total outlinehowever, has a rather low value (1.7) that corresponds to the very hierarchical spatialorganisation of the intra-urban space. This situation resembles the morphology of theSierpinski carpet of figure 4 (b), which is very contrasted inside but has a smooth outer edge. Itmay be surprising that in contrast to Cergy-Pontoise, the new town of Villeneuve dAsq on theperiphery of Lille has a rather dendritic, tattered outline (DI = 1.38). But this new towngenerally pursues a less strict planning concept than Cergy.

4 Conclusions for urban planning

Obviously fractal measures may serve to characterize by unequivocal values the spatial

organisation of urban patterns, usually perceived as amorphous. They can be used especiallyto measure to what extent the built-up area is distributed in a more uniform or in a morecontrasted way within an urban pattern. For town outlines, first results show how they could beextracted in a coherent way without using more or less arbitrarily chosen criteria. The fractalinvestigations of town outlines have shown that it is possible to describe quantitatively howsmooth or how dendritic they are.

Applying the fractal approach to different kinds of urban patterns at various scales helps to linktheir morphology to the historical context in which they emerged and to establish relationsbetween the measured values and certain planning concepts, indicating concrete intentions ofurbanism. It should be emphasized that the same type of spatial organisation may correspondto strongly planned town sections but may also be found for less planned patterns. The analysis

of the few time sequences of metropolitan areas analysed showed that they tend to becomemore and more homogenous over time and illustrates the fact that motorisation facilitates anurbanisation ever further away from main transportation axes. Thus the sprawl reduces the spatialcontrast between rural and urban areas.

Hence it is possible to give value ranges for different types of pattern:


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Types of districts Characteristics UniformityindexUI4

Dendricityindex DI

City centres Homogenous, patterns withlittle contrast

1.8 to 1.95 -

Residential estates without ofpublic space, smoothed outline

Homogenous, patterns withlittle contrast

1.8 to 1.99 1.26 to 1.30

New towns, Corbusian plans,with different sized public space

Rather contrasted plannedpatterns

1.6 to 1.77 -

Irregular and contrasted,dendritic outline border

Less controlled progressivegrowth

1.64 to 1.85 1.3 to 1.55

Table 1:Comparison of the fractal indices for different types of urban patterns

Obviously these measures are suitable for characterizing the form of urban patterns for planning purposes andallow defining more subtle the orientations of urban development.

Beyond this aspect, what can we learn about planning and urbanisation from theseobservations? Considering only the spatial distribution of the built-up area provides noinformation about how free space between buildings is really used. However it could be arguedthat the uniform distributions typical for city centres as well as for certain individual housingareas can never offer a diversified range of amenities. If homogenously built-up residential areas offeran individual garden for each house, they provide no public spacefor events, which necessitatefree areas on a different scale. Homogeneous sprawl patterns like in the urban plan of Los

Angeles potentially generate traffic flows since the local range on offer is not diversifiedenough. But not only sprawling patterns are susceptible to generating traffic flows, this holds

for compact cities too, since residents will try to reach open space for leisure activities. In fact itis even from a purely climatologic point of view no longer possible to imagine hugepopulation concentrations like those of important metropolis confined in a circular denselypopulated area (cf. figure 10).

But fractal urban pattern organisation goes beyondthe simple preservation of green radial sectorsreaching into the built-up area, as the architects Eberstadt-Mhring-Petersen proposed forBerlin in 1910 (figure 11 (a)). In a fractal structure, the penetration of built-up and empty zones

would be multi-scale as shown in figure 11 (b). Such a spatial organisation offers the chance ofhaving zones of high concentration near urban amenities (shopping, services), e.g. in the

vicinity of public transportation networks, and more diluted zones. So it becomes possible tomaintain a social mix by means of a higher local variety of densely and less densely populated

zones and, on the other hand, to preserve huge empty zones in the neighbourhood ofurbanized areas, which may be imagined as natural reserves, agricultural zones or simply leisureareas offering rural amenities.

4UI = fractal surface dimension, DI= fractal edge dimension of main cluster.


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Figure 10:The built-up area of Berlin and the same surface as a circular disk.

There are various planning concepts and real world situations which are close to such a logic,like the concept of urban villages which tries to introduce operational sub-centres withpertinent service amenities in order to reduce traffic flows to the main centre (Fouchier, 1995).

The lowUI valuesobtained for Cergy-Pontoise correspond to the objective of diversifying therange of public space on offer. Such low values were also observed for districts constructedaccording to concepts from the School of Le Corbusier with comparable planning intentions5.

A similar situation occurs in the case of the green area concept of Stuttgart (figure 11 (c)), butin fact also in the real world pattern of Copenhagen (figure 7 (c)), since the fingers are nothomogeneously filled up with built-up space and it holds also for Berlin (figure 10). The varietyprovided by contrasted planning concepts may also help to reduce social segregation, sincedifferent types of housing can be combined. Referring to the obtained results it can be concluded that UIvalues around 1.75 correspond to a situation where public space could be integrated in a plan on the scale of adistrict.

But existing sprawl situations, which are sufficiently contrasted, would also allow an assessmentof the observed sprawl in such a sense. This is for instance true of Lille. In some cases, like atMontbliard or Lyon, master plans were drawn up in an attempt to define a posteriori leisureareas in the vicinity of such existing districts.

5It should be emphasized that the social problems occurring in these town sections are related to the

effect of crowding, due to the heights of buildings as well to their uniform architectural realization.These effects cannot of course be analysed in our context where we restricted the analysis to theoccupation of the surface, without taking into account the height of buildings. However three-dimensional analysis is possible when one includes data about the height of buildings or the populationdistribution on a detailed scale.


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green sector

lateral branch of green area

Figure 11:(a) The scheme for the future development of Berlin of Eberstadt-Mhring-Petersen(b) The penetration of free space into the built-up area in a fractal structure. The green sectors (Grnkeile)are multi-scale. The peripheral nodes could correspond to sub-centres.(c) From a structural point of view, the Stuttgart region shows similar characteristics: the development axes, thecentral places and the leisure areas (dotted).

The observations about dendritic outlines encourage also some conceptual reflections. On thescale of districts, a policy in favour of limiting sprawl locally by smoothing the outlinescorresponds to DIvalues of about 1.25 to 1.35. This begs the question if patterns that followthe spatial organisation principle of the fractals of figure (1) or 3 (b) are not better adapted topreserve environmental qualities than homogenous patterns or even the compact fractal of

figure 4 (b). The alternative model to smoothing outlines proposed by the architect Schoefl maybe of interest here: such an arrangement lets more house-owners benefit of the situation on theedge of the settlement which seems to be rather appreciated. It is obvious that in reality it

would be more feasible to combine both schemes. Here odd situations like the Bergamo casecould be of interest if the sprawl remains limited by accepting a lengthening of the edges at themicro-scale of districts. This could help to avoid sprawl on a larger scale, which tends to generatehomogeneous land occupation and thus weakens the quality of the landscape. Accepting a local controlledsprawl could be beneficial in terms of avoiding sprawl on a larger scale and encourage sustainability. Such asituation would correspond to DI values of 1.3 to 1.5.

When interpreting the results it becomes obvious that a fractal approach to urban patternshelps us to improve our knowledge about their spatial organisation, regardless if they were

more or less planned. Obviously multi-scale pattern organisation seems to be an interesting wayto manage the consequences of the new lifestyle, which tends to claim good access to differentkinds of both urban and rural amenities, and at the same time helps to reduce the risks of adiffuse sprawl which tends to weaken the environmental quality and to generate more and moretraffic flows.


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A more detailed analysis, differentiating the types of land-use (housing, services, street networketc.) could help to deepen the knowledge about mix and proximity between different types of

activities in an urban context.

5 Acknowledgments

We are very indebted to the French Ministry of Planning, Transport, Housing, Tourism and Seafor having supported the previously presented research activities as part of the program villemergente. We want to thank all participants of the above project as well as all the localauthorities that provided the data. Moreover we are grateful to Gilles Vuidel for havingdeveloped the pertinent computer program fractalyse.

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Comparing the Morphology of Urban

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