PROGRESS IN PLANNING Progress in Planning 67 (2007) 205���294 Review The spatial syntax of urban segregation Laura Vaughan Bartlett School of Graduate Studies, UCL, 1-19 Torrington Place, Gower Street, London WC1E 6BT, UK CHAPTER 1 The city as one thing By Bill Hillier and Laura Vaughan Abstract This section summarises the latest theories in the field of space syntax. It opens with a discussion of the relationship between the form of urban grids and the process of how cities are formed by human activity this is done by a comprehensive review of space syntax theory from its starting point in the 1970s. It then presents research into how cities balance the micro-economic factors which shape the spatial structure of cities with the cultural factors that shape the underlying form of residential areas. It goes on to discuss the relationship between activity and space and how this relationship is formed by the way different activities make different demands on movement and co-presence. It ends with a discussion regarding the manner in which patterns of spatial integration influence the location of different classes and social groups in the city and contribute to the pathology of housing estates. It concludes that spatial form needs to be understood as a contributing factor in forming the patterns of integration and segregation in cities. 1.1. Is the city one thing or two? On the face of it, the city is two things: a large collection of buildings linked by space, and a complex system of human activity linked by interaction. We can call ARTICLE IN PRESS www.elsevier.com/locate/pplann 0305-9006/$ -see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.progress.2007.03.001 Tel.: +442076791981 fax: +442079161887. E-mail address: l.vaughan@ucl.ac.uk.

these the physical city and the social city. Urban practice and theory must connect one to the other. But the reflective disciplines which support and nourish both ��� roughly the morphological disciplines on one side and the social sciences on the other ��� in their nature take an asymmetric view, foregrounding one city and backgrounding the other, in effect seeing the ���other��� city through the foregrounded one, and so at best as a shadowy set of patterns and forces. It is no surprise then that, at the start of the 21st century, we have many partial theories about the city, but no theory of the city as both of the things that it seems to be. But is the city in any case two things or one? It will be one to the degree that the physical and social cities act conjointly to produce significant outcomes. There are good reasons why in principle we might expect it to be one thing. The social city is either side of the physical city: it brings it into existence, and then acts within the constraints it imposes. It seems unlikely that either is a wholly contingent process. But both relations raise uncomfortable issues of determinism: how can a physical process in the material world relate to a social process in a non-trivial yet systematic way? This places philosophical as well as methodological obstacles in the path of reflection and research. In practice, we also find that at any one time, intervention in the city is governed by a consensus of beliefs and practices about the city as one thing: that small-scale inward looking residential developments promote community, for example, or that mixed use reduces crime, or that lower densities lessen the danger of social malaise. But these beliefs shift over time, often dramatically, and it is hard to think of a case where a one thing proposition has acquired the status of a tested ��� or even testable ��� scientific proposition. The beliefs and practices allow us to act as though the city were known to be one thing, because this provides a rationale for our interventions, but all our formations and paradigms make the tacit assumption that the cities can safely be treated as two. Paradoxically, the real challenge to our two city paradigms comes not from the well-formed, well-functioning city, but from its ��� real or apparent ��� pathology. Where cities seem to go wrong, often as a result of belief-based interventions which come in time to appear mistaken, the problem of one city confronts us with immediacy and urgency by demanding to know if there is any sense in which the physical and spatial form of our interventions has contributed to their apparent failure. The challenge was posed in the second half of the 20th century by the preci- pitate decline of many ambitious social housing schemes, and the widespread public belief that the physical and spatial form of these experiments was somehow involved. Today it is posed in a more general form as the problem of social segregation in the city, its nature, its causes and its consequences. We can easily formulate ideas about segregation purely in terms of social and economic factors without invoking space. But segregation is a spatial term and the way in which patterns of segregation and exclusion cluster in the city leads us back to the one city question: does urban segregation have a significant physical meaning over and above its social meaning? Can segregation be, or become, a one city phenomenon? ARTICLE IN PRESS L. Vaughan / Progress in Planning 67 (2007) 205���294 206

1.2. The idea of space syntax Space syntax was conceived in the 1970s as an attempt to address this kind of one city question. Its genesis was in the remarkable architectural changes which began to appear in cities like London in the 1960s, and the increasing sense which they engendered of a contradiction between ��� as seemed at the time ��� their striking architecture and the discomfiting and un-urban nature of their spaces. Space syntax began from the observation that space is the common ground of the physical and social cities. The physical city is a complex pattern of space, while all social activity and interaction happens in space. In itself, of course, this leads to an impasse. All social activity leaves spatial traces in the form of recursive patterns, but how can these relate to a physical and spatial context whose essential patterns were in all likelihood laid down long ago, under the influence of quite different social circumstances? On reflection, the radically different rate of change of the physical and social cities seems in itself to forbid anything but a contingent relation between the two. But space syntax added to the existing panoply of spatial concepts a new one that potentially reshapes research questions: spatial configuration. The hope was that by learning to describe and analyse different kinds of spatial configuration, or pattern, in the city ��� for example the differences between the new social housing and traditional urban areas, which seemed prima facie to be critically different ��� it would be possible to detect any influence there might be of social factors in the construction of these spatial patterns and also to explore any consequences there might be in terms of how social life could and did take place. By learning to control the spatial variable at the level of the complex patterns of space that make up the city, we might begin to gain insight into both the social antecedents and consequences of spatial form, and so detect signs of the social city either side of the physical city. In syntax terms, spatial configuration means relations between spaces which take into account other relations, and so in effect relations between all the various spaces of a system. Space syntax, in effect, takes certain common measures of relationality in graphs, and first theorises them in terms of their potential to embody or transmit social ideas, and then turns them into measures and representations of spatial structure by linking them to geometric representations of the system of spaces under examination (Hillier and Hanson, 1984). These measures are essentially formal interpretations of the notion of spatial integration and segregation, and it was the formalisation of these terms which first seemed to identify structures which linked the social and the spatial. Providing a measurable scale from segregation to integration, enabled statistical comparison of different spatial forms across cultures, and hence provision of a platform from which social origins and consequences might be investigated. This was an unfamiliar idea. It was, in effect, being suggested that space has its own formal logic prior to acquiring a social logic, and indeed that it was this logic of space that was exploited in order to render space social. This is the core argument of ���The Social Logic of Space���. The autonomous potential of space to form patterns was, in effect, seen as the means through which it is able to give expression to social ARTICLE IN PRESS L. Vaughan / Progress in Planning 67 (2007) 205���294 207

meanings. This challenged paradigms on both sides of the two city divide. But it also suggested that there could be a one city approach to urban research which was both quantitative and informed by the search for social and cultural influences and meanings. From these beginnings, space syntax has evolved into a set of tools linked to a set of theories, the two together giving rise to a set of interpretative models for different socio-spatial phenomena. Interpretative models are schemes of analysis which work for particular phenomena. For example, we have an urban movement model, a land use model, a crime model, even a social segregation model, and most important of all a general urban model in which the integration���segregation dimension is shown to be a primary spatial dimension on which cities are organised. These models are quite unlike the more familiar engineering models, since they seek to be explanatory in themselves of the phenomena they address. They show that by clarifying space in a particular way the social origins and consequences of the spatial patterns can be brought into clear view. It is because they seek to be explanatory in themselves that syntax models have proved to be so applicable in design. In what follows we first explain the foundations of space syntax, and go on to give an overview of the range of techniques that are now available, and what questions can be addressed with them. We then outline the general theory of the city to which this has given rise, which shows why the issue of integration���segregation is close to the heart of what cities are when considered as one thing. We then outline a series of characteristic research problems that have been addressed with space syntax, and the kinds of models we have developed to try to solve them. We follow this with sketches of a few of the hundreds of projects on which space syntax has been applied in recent years, and introduce the other parts of this special issue. 1.3. Foundations Space syntax is built on two formal ideas which try to reflect both the objectivity of space and our intuitive engagement with it. The first is that we should think of space not as the background to human activity, as we think of it as the background to objects, but as an intrinsic aspect of everything human beings do (Fig. 1). Moving through space, interacting with other people in space, or even just seeing ambient space from a point in it, all have a natural and necessary spatial geometry: movement is essentially linear, interaction requires a convex space in which all points can see all others, and from any point in space we see a variably shaped, often spiky, visual field we call an isovist (Benedikt, 1979). Each of these geometric ideas describes some aspect of how we use or experience space, and this makes it useful to try to see how buildings and cities are organised in terms of these geometric ideas. For example, it seems to matter that space in cities is for the most part linear ��� streets, boulevards, avenues, alleys and so on are all linear concepts ��� with occasional convex elements we call squares or public open spaces, each the centre of a variable isovist. In fact, urban space has all three properties, and by being clear about this geometry we can begin to see why urban space is the way it is. ARTICLE IN PRESS L. Vaughan / Progress in Planning 67 (2007) 205���294 208

The second idea is that human space is not just about the properties of individual spaces, but about the inter-relations between the many spaces that make up the spatial layout of a building or a city. This is what we formally call the configuration of space, meaning the simultaneously existing relations amongst the parts which make up the whole. It is notable that language has terms for spatial configurations, but insofar as these are precise, they describe at most relations between three entities. English prepositions such as between, beyond or inside all fall into this category. For more complex patterns of space, the undoubted competence that people have in understanding them seems to be, like the structure of language, at the unconscious level of ideas we think with rather than of, since we do not have precise terms for more complex patterns of space. The reason configuration matters is that it is able to express the property of space that, more than any other, is the means by which space both acquires social meaning and has social consequences: that a spatial configuration not only looks but is different when seen from different points of view in the layout. We can make this visually clear by taking the layout in Fig. 2, and drawing justified graphs (in which each circle is a room and each linking line a door, and the graph is aligned upwards in layers from each space in turn) from spaces 5 (left) and 10 (right) to show what the pattern of space looks like from each. The two graphs look quite different, in that one is shallow and the other deep, but are of course the same graph looked at from different points of view. But although different, each graph gives a true picture of what the layout looks like from that space, and so expresses a real property of the layout. The shape of the justified graph, or j-graph, then leads us to our measure of integration���segregation. The shape of each graph shows the degree to which we must pass through other spaces to go from a particular space to all others. This will be high or low according to whether we have a shallow graph, as on the left, or a deep graph, as on the right. To the degree that the graph from a space is shallow we say it is integrated, and to the degree that it is deep, segregated. So we can index each space in the layout in terms of the degree to which it integrates the complex, and the ARTICLE IN PRESS people move in lines interact in convex spaces see changing visual fields as they move around built environments Fig. 1. Space is not a background to activity, but an intrinsic aspect of it. L. Vaughan / Progress in Planning 67 (2007) 205���294 209

average for the whole will be the degree of integration or segregation of the whole complex.1 Space syntax is about applying configurational measures to the patterns of different geometric elements that are created by buildings and cities. Whether we choose lines, convex spaces, isovists, or even points as the elements for our analysis depends on what aspect of functionality we are investigating: that is, what aspect of human spatiality we are investigating. ARTICLE IN PRESS 7 4 8 10 9 6 3 2 7 4 1 2 8 5 3 6 9 10 5 Fig. 2. A spatial layout both looks and is different when seen from different spaces within it. 1 There are a number of measures of the graph which can be used to describe configurational properties of the grid. Hillier et al. (1993, p. 35) describe these in detail: stating that empirically, by far the most important measure is called ���integration radius n��� or ���global integration��� which measures the mean depth from each line in turn to every other space in the system, relativised with respect to how deep they could possibly be with that number of spaces, than standardised as shown in Hillier and Hanson (1984). The most integrated spaces are those from which all others are shallowest on average and the most segregated are those from which they are deepest. ���Integration radius 3��� (commonly described as ���local integration���), measures the mean depth of spaces up to 3 steps away from each space in turn. Other radii are calculated in a similar fashion (radius 7���7 steps away and so on) in order to take account of different areal scales. L. Vaughan / Progress in Planning 67 (2007) 205���294 210

1.4. Making buildings speak By looking at space in this way, we can begin to see both how social and cultural patterns are imprinted in spatial layouts, and how spatial layouts affect functioning. For example, at the simplest level, we can show how cultural differences are expressed through the layout of rooms in domestic space. If we take the French farm house in Fig. 3, we find the salle commune (the space of everyday living and reception of informal visitors) is the most integrated internal space and the grande salle (for formal reception) one of the most segregated, along with the bureau of the male owner. We can show such patterns visually by using colours to index numerical values, always using darker greyscale for the most integrated through to light greyscale for least. ���Colouring-up��� is a vital aspect of space syntax research, since it allows us to search for patterns visually, and therefore intuitively, as well as using simple mathematics. We also find that the salle commune lies on all rings of circulation, so that if you remove it, the layout becomes virtually a single sequence of spaces. This is not always the case in French houses with ���salles communes���. Sometime a transition space ��� say a hallway or corridor ��� is the most integrated space, and where this is so, the salle commune loses is dominant spatial role. Our studies suggest that this may be to do with gender roles, since the integrated salle commune is a space dominated by female activity (Hillier et al., 1987). This is one example of the ways in which spatial configuration is shaped by culture. In general, to the degree that integration values for different activities in the house are in the same or a different order, we can see evidence of cultural commonalities or differences across a sample. What we are seeing is the constructive effect of society and culture on spatial patterning, by giving function a configurational meaning in ARTICLE IN PRESS total depth from grande salle: 31 total depth from outside: 18 total depth from salle commune: 21 grande salle vesti- bule bureau salle salle commune couloir vesti- bule laverie laiterie debarras Fig. 3. The layout of a house looks more, or less, integrated from different points of view. L. Vaughan / Progress in Planning 67 (2007) 205���294 211

the layout, in addition to expression through equipment, furnishing and decorative style. We can also use space syntax to investigate the effect of spatial layout on functioning. In Fig. 4, we show on the left traces of 100 people entering the Tate Britain gallery in London and moving about for 10min. On the right is a more complex version of the analysis we saw with the house, a visual integration analysis of all the visual fields from every point in the Tate plan. Technically, it draws the visual field from the centre of each square of an arbitrarily fine tessellation filling the plan, overlaps these so that an overlap counts as a connection, and calculates how many visual fields you need to use to get to see the whole gallery from any point within it. Again, the darkest locations are the most visually integrated, through to lightest for the least. It is easy to see that the movement and space patterns resemble each other as patterns quite closely. We can check this statistically. By correlating the visual integration values with observed movement, it turns out that about 68% of the differences in movement rates in rooms can be accounted for by the visual field structure, implying that people are using the space structure of the Gallery, rather than, say, the attractive powers of particular exhibits, to guide them around the gallery (Hillier et al., 1996). This then is how space syntax works. By analysing space rigorously, and observing human activity carefully, we can show that space and social activity relate in two ways. A spatial layout can reflect and embody a social pattern, as in the case of the French house, where space was laid out and categorised to give reality to a culturally given pattern of activity, and so reinforce and reproduce it. Space can also shape a potentially social pattern, as in the case of the movement study, since by shaping movement, space also creates a pattern of natural co-presence in space. Another way of saying this is that space can be used both in a conservative mode to structure and reproduce existing social relations and statuses, usually by using space ARTICLE IN PRESS Fig. 4. First 10minute movement traces (left) and visual integration analysis (right) of Tate Britain. L. Vaughan / Progress in Planning 67 (2007) 205���294 212

to segregate, and in a generative mode to create the potential for new relations by using space to create co-presence through integration. As we will see, the conservative mode leaves things much as they are, while the generative mode, by creating a richer field of potential encounter, can lead to the appearance of new social connections. 1.5. The basic urban relation The distinction between the two modes of generating space on the integration��� segregation dimension is critical to understanding how the social city is either side of the physical city that is, how the space of the city comes to embody social ideas in its layout, and how the layout has consequences for the ways in which collections of building come to life ��� or fail to thrive ��� as living cities. First, we must understand a relation we glimpsed in the Tate example, and which we have come to see as the basic urban relation: that the configuration of the urban street network, which is the largest spatial pattern in the city, is in and of itself a key determinant of movement flows and hence co-presence in space. This may not sound very significant, but it has huge consequences for both the form and functioning of cities. We call it the theory of natural movement (Hillier et al., 1993). To some this will be an unexpected idea and smack of long discredited determinism. We will argue that it is nothing of the kind, and that, on the contrary, it is ��� with a little reflection ��� intuitively clear, mathematically necessary and empirically demonstrable. It is also the key to understanding cities as socially meaningful patterns of relative integration and segregation. First, let us look at the idea intuitively. Consider the notional grid in Fig. 5a with a main street, cross street, side streets and backstreets. Imagine that the streets are lined with houses, and people move between the houses by the more or less direct routes: It is clear that more people will pass through the main street than the side streets or back streets, and more people will pass through the central sections of the main street than the peripheral ones. The main street is easier to get to than other streets ��� it is more accessible. The cross street also seems to have good potentials for both to and through movement, but we would guess it to be less than the main street. What is clear is that we intuitively expect the position of each street in the overall grid to affect emergent to ��� and through ��� movement flows in streets and their different parts. It is not a matter of psychology, but the way the grid is put together. Now to ��� and through ��� movement are the two principal components of human movement. For every trip, we select a destination to go to, and a series of spaces to pass through on the way. Both obviously matter to how cities work. For example, over time we are likely to go to more near than far destinations, so if some locations are in some sense ���nearer��� to all locations within a certain radius than others, as in Fig. 5a, this will give these locations greater potential as destinations than others, simply by virtue of having easier accessibility. If we want to open a shop, for example, it would make more sense to put it in an accessible rather than an inaccessible location. Similarly, if routes between all pairs of spaces in a layout pass ARTICLE IN PRESS L. Vaughan / Progress in Planning 67 (2007) 205���294 213

through some spaces more than others, as is clearly the case, it will likewise be sensible to locate the shop in one of those spaces, though it may not always be intuitively obvious which these spaces are. The point is that these potentials are commonsense and even familiar properties of spatial layouts. Both of these potentials can be measured. The measure of accessibility for to- movement of a space is our integration measure. The measure of through-movement potential assesses the degree to which each space lies on simplest or shortest paths between all pairs of spaces in the system. In syntax this is called the choice measure.2 ARTICLE IN PRESS Fig. 5. (a) A notional grid with a horizontal main street, vertical cross street, side streets and back streets. (b) Notional grid: pattern of ���integration��� values ��� or the closeness of each line to all others ��� from dark for highest through to light for least. (c) Notional grid: pattern of ���choice��� values, or the degree to which each line lies on simplest paths from each line to all others, from dark for highest through to light for least. 2 In mathematics, the integration measure is more familiar as closeness, or closeness centrality, but syntactic integration has a little more mathematics to take out the effect on the measure of the number of elements in the system (Hillier and Hanson, 1984, pp. 108���114). The choice measure is known in mathematics as betweenness, or betweenness centrality, though again the syntactic version of the measure is calculated in a slightly different (and to our mind better) way. L. Vaughan / Progress in Planning 67 (2007) 205���294 214

Figs. 5b and c show the integration and choices measures applied to the axial map, and coloured up in shades of grey, from dark for integrated to light for segregated. Syntax also applies both measures at different radii, that is, it calculates integration with respect to the system up to a certain distance away, and choice for trips up to a certain length. This allows us to apply both measures on a continuum from local to global, yielding a powerful matrix of measures to investigate structural features of urban space in terms of its basic movement potentials. But what should we apply these measures to? Urban space is after all continuous and more often than not offers no obvious or natural division into units. The syntax approach to this question was first to take the predominantly linear nature of urban space seriously, and propose a representation of the street network based on the longest and fewest lines that could be drawn through the system (Hillier and Hanson, 1984).3 We then treated the lines as the elements of a graph, with the junctions as links,4 and we could then calculate the measures of integration and choice at variable radii as we wanted. The decision to make the lines into elements, had the effect of internalising the line structure into the graph, and so in effect capturing key features of the geometry of the street network in the graph. These least line axial maps turned out to have some remarkable properties. First they turned out to have a fractal nature (Carvalho and Penn, 2004), in that all urban street networks, from Shiraz to Chicago, at whatever urban scale we consider them, are made up of a very small number of long lines and a very large number of small lines. Second by simply applying the integration and choice measures to the least line map and correlating the spatial values with observed movement rates, we commonly found that somewhere between 60% and 80% of the differences in movement flows along lines could be accounted for in terms of the configuration of the grid itself (see Hillier, 1989 Hillier and Penn, 1996 etc.) There was a second problem. In making our calculations on the basis of the axial map, we are in effect calculating distance as the number of times we have to turn (that is, to move from one line to another). Is this how human beings do it? It is commonly assumed that people, insofar as they make spatial (as opposed to temporal) judgements in selecting routes, will simply minimise distance. But there is increasing evidence that our notions of distance are severely compromised by geometrical and topological factors, and even by the direction in which the estimate is made.5 To solve this problem, and also to make the analysis more precise, a far more powerful and disaggregated version of the line analysis technique has been developed (Hillier and Iida, 2005). Starting from the least line axial map, we divide each line into its segments (between intersections) and represent the segments as the nodes of the graph with the intersections as links. We then assign integration and choice measures using different definitions of distance: shortest path (metric), least ARTICLE IN PRESS 3 In The Social Logic of Space the relation between the linear organisation of space and the local convex properties, where by definition each point is visible from all others, is also dealt with at some length. 4 This reverses the customary practice in traffic engineering, where the junctions are the nodes of the graph and the street sections the links. 5 This work is reviewed in Hillier and Iida (2005). L. Vaughan / Progress in Planning 67 (2007) 205���294 215

angle change (geometric), fewest turns (topological) weightings to relations between each segment and all others, and we apply them at different radii from each segment, also defining radii for shortest, least angle change, and fewest turns paths. This yields a matrix of measures which we can use to explore how people actually move in cities (Fig. 6) (Hillier and Iida, 2005, p. 479). With these techniques, we can make different mathematical analyses of the same urban grid, and then ask which analysis agrees best with the observed pattern of movement. In a recent study of four different urban areas of London, the answer was unambiguous: least angle analysis is the best predictor of movement, followed closely by fewest turns, and with metric shortest path analysis well back in third place. The only plausible interpretation of this result is that people do not navigate with a mental model of metric distances, but with a geometric and angular model of how the alignments of the grid are connected to each other. As cognitive scientists have long suspected, but been unable to show conclusively, we navigate with an architectural model in our heads, not a simple account of metric distances. This has major implications for how we design cities. The bringing to light of the relation between grid structure and movement also opens up the possibility of a new way of modelling cities. Historically, mathematical approaches to modelling cities have been Newtonian. The city is conceptualised as a set of discrete zones represented as points. Exchange between zones is proportional to their combined masses inverse to some definition of distance (Wilson, 2000). We can call this the attractor theory of cities. There are of course familiar problems with such models. They are coarsegrained and neglect micro-structure, and it is not clear ARTICLE IN PRESS a b a b w ( ) w ( ) S S w ( ) w ( ) Fig. 6. From the line model to the segment model. L. Vaughan / Progress in Planning 67 (2007) 205���294 216

how there can be a theory of macro-structure without a theory of micro-structure. Zones are arbitrary constructs and do not exist in any physical sense, which makes it hard to relate reality and model in a morphologically useful way. But if it is the case, as we believe has now been amply shown, that the fundamental determinant of movement is the configuration of the street network itself, a factor given scant attention in attraction models, then it seems that these models are not theoretically optimal either ��� especially if, as we will show, the pattern of attraction is itself powerfully shaped by the grid-induced movement pattern and so should not be treated as primary in a model. 1.6. The structure of the urban grid Let us then use the syntax technique to investigate the structure���function relation in cities, starting with the structure of the urban street network itself. First we can use the analysis to show how cities tend to acquire a certain generic large-scale structure. For example, if we take Apt, a small town in France (Fig. 7a) and analyse its integration pattern using the segment least angle analysis6 (colouring up from dark grey to light grey, Fig. 7b) as before, we find the darker lines form a striking pattern: a kind of deformed wheel: there is a ���hub��� of integrated lines at or near the centre, integrated ���spokes��� which link centre to edge, and sometimes also we find integrated ���rims��� or edge lines. The wheel forms the dominant pattern of public space, where most of the shops are, while the lighter areas in the interstices are predominantly residential, though of course with gradations between the two. So this means that the structure is not purely formal matter. It has to do with what is going on in the social and economic life of the town. As with the house, the analysis has detected a certain social logic in the plan. While not universal, the deformed wheel pattern is found again and again in the large-scale structure of cities. Fig. 8 shows it in the central areas of Atlanta. More remarkably, Fig. 9 shows it in a more complex form with multiple rims in the metropolitan area of Tokyo, a very much larger system. We find it the same underlying pattern in Venice, even without the canals, and in London we find it approximated at two levels: that of the metropolitan area as a whole, and at the level of the local area, as in Fig. 10. This may be why people think of London as a set of urban villages. Its ���villages��� are usually the hubs of local deformed wheels, with the spokes acting as strong linkages to the larger-scale grid, so providing locally the strong centre-to-edge links that the large-scale deformed wheel provides for the city as a whole. Why the deformed wheel? The answer is simple. It is a way of overcoming the natural tendency for centres to become segregated as the city grows around them by linking centres to edges, so accessing strangers to the heart of the system and inhabitants to the edges. So this underlying structure of the city is a spatial phenomenon, but one which is shaped by the city as a social thing. ARTICLE IN PRESS 6 We find the same result with the simple axial map, but the more recent segment angular analysis is used here for consistency with other illustrated cases. L. Vaughan / Progress in Planning 67 (2007) 205���294 217

The integration patterns we are finding, it will be recalled, measure the accessibility of street segments as destinations, and so can be thought of as recording the to- movement structure of the city. If we look at the patterns formed by the choice measure, we are looking at the through-movement patterns, and we find these, while often overlapping with the deformed wheels, are rather different and always take the form of a network. Fig. 11 shows on the left the structure of metropolitan Tokyo and on the right that of London revealed by the measure of choice: The two measures can be used separately or in combination to examine the structures of different cities. Both are measures of integration���segregation, though of ARTICLE IN PRESS Fig. 7. (a) The plan of Apt, a small town in the South of France. (b) The integration map of Apt, a small town in the South of France. L. Vaughan / Progress in Planning 67 (2007) 205���294 218

course in rather different senses. Most important, they can be applied at different urban scales by restricting the radius at which it is applied. For example, at the level of the whole city, choice often identifies the natural boundaries of areas (Peponis et al., 1990), but by restricting the radius, the measure often brings to light a much finer scale structure, reflecting the fact that shorter trips will tend to prioritise more local spaces. Fig. 12 shows part of North West London analysed first (left) for trips of any length (and so for the most part for longer trips) and then (right) for trips up to 1.25 km. The right figure picks out core spaces of several ���urban villages���. 1.7. The dual city But we have generated something of a puzzle. Cities are geometrically very different ��� a city in the Arab world for example will have little in common geometrically with a North American city ��� so how do they come up with similar large-scale patterns? Do cities, in spite of their differences, have certain commonalities in how they are generated? Our studies suggest that cities in general are created by a dual process, and each side of the duality exploits the relation between space and movement in a different way. On the one hand, there is a public space process which is about bringing people together, and which therefore orders space in such a way as to optimise the reach of ARTICLE IN PRESS Fig. 8. The street plan of the central areas of Atlanta showing the deformed wheel. L. Vaughan / Progress in Planning 67 (2007) 205���294 219