Space syntax as a theory as well as a method Bill Hillier Space Syntax Laboratory UniversityCollege London Space syntax is commonly thought of as a set of techniques for analysing architectural and urban space and foreseeing functional outcomes. It is of course both, but it aspires to be more than this: a theoretical model of human space: how it is structured, how it works, how it is understood, and how it is part of the thing we call society. The underlying belief is that you cant have the first without the second: foreseeing functional outcomes at the design stage depends on having a theory that connects the two: a structure-function theory, or form-function theory if you prefer. Part of the theoretical model, as it has so far developed, is a theory of the city as a spatial system. In this paper, I will explain the space syntax theory of the city, and how it reflects aspects of societies spatially But first I will look at the theoretical foundations of space syntax, as these will play an important role in the theory of the city. So forgive me if talk about architecture for a while because in the last analysis, space syntax is an architectural theory of the city. I hope you will see what I mean by this as the argument progresses. Theoretically, space syntax is rooted in a problem that seems a first sight to forbid a structure-function theory for either buildings or cities. It is the simple fact that most of the basic elements that make up buildings and cities rooms in buildings and streets in cities are, give or take size and shape - more or less, the same kind of thing. This suggests that the relation between space and human activity must be pretty well indeterminate: you can do most things in most spaces. The answer that space syntax proposes to this question is the foundation of space syntax: that spatially speaking buildings and cities are configurations. What is missing in our descriptions of spaces in terms of shape and size is a configurational description of the position of each space in relation to all the others. Configuration is defined not simply as connections, but as relations that take into account other relations For example, we can graph what the simple layout above looks like as a pattern from the point of view of two spaces We see that in one case it is relatively shallow, or integrated, in the other, deep, or segregated 52 3 89610471063 91 5742 810 By summing the depth of each space from all the others, we can mathematically place every space on a continuum from integration to segregation. We can then make these values visible by colouring from red for integrated through to blue for segregated. So we see a pattern. We can then investigate, say, a regional housing culture, by comparing the functions of spaces with their integration values. To the extent that different functions are statistically associated with different values, we can say that a spatial meaning has been given to the idea of function. A form-function relation exists because a particular function, or range of functions, has been realised spatially through the positioning of the function in the layout as a whole.So the spatial configuration of the layout can be said to have, within that culture, a social meaning. 52 3 89610471063 91 5742 8sallecommunesallecommunesallecommunesallecommunesallecommunesallecommunepeople move in lines interact in convex spaces see changing visual fields as they move around built environmentspeoplespacesBut once we have the concept of configuration, we encounter another fundamental problem in developing a structure-function theory: people use space in different ways for different kind of activity. For example, we move linearly, interact in convex space, and experience space as isovists with a convex core and more linear spikes. However, each of thesecan form the basis of configurational analysis. For example, on the right above is a visual integration analysis meaning using visual isovists as the basis for integration calculation of the Tate Britain Gallery. On the left are traces of 100 visitors entering the gallering and moving for ten minutes. Although each individual takes a different route, the two patterns are remarkably similar, and in fact statistical analysis shows a 70% correlation between the two patterns. The spatial structure of the building is shaping, not individual routes, but emergent patterns of movement densities and co-presence. It is mixing people up and bringing them together again in terms of the spatial structure of the building. We have found another structure-function relation. But the two structure-function relations wehave found are different in important respects, and in fact illustrate two fundmentally different ways in which space can relate to society, which I call, on the one hand, the conservative or reproductine, and on the other the generative or morphogenetic. A spatial layout can reflect and embody a social pattern, as in the case of the house, where space was laid out and categorised to give reality to a culturally given pattern of activity, and so reinforce and reproduce it. We call this the conservative use of space, since space is being used to reflect and so reproduce a given social pattern by the control of co-presence. But space can also shape a social pattern, as in the case of gallery, since by shaping movement, space also creates a pattern of natural co-presence in space, and new possibilities of social interaction. We can call this the generative use of space, since we are using space to create new patterns of co-presence and potentially new elements in social patterns. Both of these will turn out be vital in understanding the processes through which collections of buildings become living cities. And this in turn reflects distinctive properties of cities as spatialized societies. So what about cities ? Cities are large collections of buildings held together by a network of space: the street network. The network is the largest thing in the city. It is what holds it all together. It has an architecture, that is a certain geometry and a certain topology and a certain scaling. But does it matter?part of TOKYO part of LONDON Lets look more closely. Looking at least line maps syntactic representation of street network as the fewest lines that cover their structure - of organic grids like London and Tokyo, we begin to find some interestinggeometry. First, the eye intuitively picks out line continuities, that is lines joined by nearly straight connections. If we move along one of these we are very likely to find another at the end of the line, and then another. This happens at all scales, but at each scale the lines are locally longer than lines which lack this kind of angular connection. Probabilistically, we can say the longer the line, the more likely it is to end in a nearly straight connection to another line.part of TOKYO part of LONDON Lets look more closely. Looking at least line maps syntactic representation of street network as the fewest lines that cover their structure - of organic grids like London and Tokyo, we begin to find some interestinggeometry. First, the eye intuitively picks out line continuities, that is lines joined by nearly straight connections. If we move along one of these we are very likely to find another at the end of the line, and then another. This happens at all scales, but at each scale the lines are locally longer than lines which lack this kind of angular connection. Probabilistically, we can say the longer the line, the more likely it is to end in a nearly straight connection to another line.part of TOKYO part of LONDON We also see a large number of shorter lines with near right angle connections, forming more local grid like patterns. Again if you find one then there are likely to be several others in the immediate neighbourhood. We can also say the shorter the line, the more likely it is to end in a right angle or near right angle. These are the opposite properties to those we find in highly formal cities, like Brasilia or pre-Columbian Teotihuacan, where the longest lines end at right angles on the most important buildings. Organic grids have the inverse properties.part of TOKYO part of LONDON It goes further. If we make least line maps for a number of real cities we find other consistencies. At all scales, from the local area to the whole city, we find cities are made up of a very small number of long lines and a very large number of short lines, so much so that in terms of the line length distributions in their least line maps cities have been said to have scale-free properties (Hillier 2002, Carvalho & Penn 2004). This means that wherever we are, we are not far from a line much longer than the one we are on. part of TOKYO part of LONDON So geometrically, cities seem to acquire a dual structure, in the form of a global foreground network and a local background network, with the former nested in the latter, and each with its own metric,geometric and topological properties. This poses a puzzle. How and why do such network consistencies emerge from decades or centuries of activity by innumerable uncoordinated agents acting in very different social, economic and cultural situations and working with very different, and highly variable, overall geometries ? We can take steps towards understanding this by showing how space syntax techniques identify configurationalstructure in urban street networks through the UCL DepthMap software (which is freely available). The fundamental element is the street segment between junctions. This is the graph element, and we are interested in its relations to all other segments in the system.

DepthMap allows 3 definitions of the distance between each segment and each of its neighbours: metric, that is the distance in metres between the centre of a segment and the centre of a neighbouring segment; topological, assigning a value of 1 if there is a change of direction between a segment and a neighbouring segment, and 0 if not; and geometric -assigning the degree of the angular change of direction between a segment and a neighbour, so straight connected are 0-valued and a line is a sequence of 0-valued connections, so that the linear structure of cities is captured

It then uses these 3 concepts of distance to calculate two measures: syntactic integration, or mathematical closeness, which measures how close each segment is to all others under each definition of distance; and syntactic choice or mathematical betweenness, which calculates how many distance-minimising paths between every pair of segments each segment lies on under different definitions of distance. So using the metric definition of distance, we find the system of shortest paths for integration and choice, with the topological definition we find the system of fewest turns maps, and with the geometrical definition we find the system of least angle change maps.

So using the etric definition of distance we find the system of shortest path maps forintegration and choice, with the topological definition we find the system of fewest turns maps, and with the geometrical definition we find the system of Each of these measures can then be calculated at any radius from each segment, using any of the three definition of distance to define the radius. So a typical measure would be least angle choice at a radius of 2 kilometres.

Each measure will identify structure in the network which can be made intuitively clear by using colours to represent mathematical values, as usual from red for high throughto blue for low. The most powerful measures are, as we will see, those based on least angle distance, metric radius and a combination of integration and choice we call normalised choice. We can think of this measure as indexing the movement potential of each space, reflecting both through- and to-movement. We can use it, for example - least angle normalised choice at radius n, meaning no radius restriction - to compare the global structures of cities.

LONDON and its region within the M25, with its strong centre and strongradials, but weak lateral connections between the radials BEIJING with its relative weak centre and weak radials, but strong lateral structure between radials TOKYO with its fairly strong centre, strong radials and strong laterals, generating the strong sub-city structure characteristic of Tokyo So the analysis can identify different kinds of structures, global and local, in the network, and makes them visible by colouring segments red for high movement potentials through to blue for low.On the left we see the movement potentials of each of the 285000 segments of London within the M25 for large scale movement. It predicts the real main movement arteries. On the right we see much finer scale structure for local movement potentials up to 750 metres. The red pattern you see is essentially Londons urban villages and the links between them.The configurational approach has led to a key discovery about cities: that in an of itself the architecture of the street network shapes movement flows. Research shows that between 50% and 80% of the movement flows on streets are due to the structure of the network itself, that is to the potential flows identified mathematically. This does not mean that space determines individual movement. It means that if people go under their own volition from everywhere to everywhere else, some spaces get more used than others.The relation between grid structure and movement is an emergent effect, as it was in the Tate. It happens whether we intend it or not. But by examining real movement patterns in cities, we have shown that people move by reading the angular geometry of the network, not actual metric distances. So by analysing the network in terms of its least angle change paths from all street segment to all others, we can approximate movement potentials from the architecture of the network, and of course for new designs inserted into the network. But more importantly, once the influence of the grid on movement is understood it opens then way for a new theoretical understanding of the city as a self-organising system through what we call the city-creating process. On the right are the 168 largest local centres in London. There are 10 times as many smaller ones. They reflect the structure of the network. How does it happen? It works like this. Because the network structure shapes flows, it also shapes land use patterns, in that movement-seeking land uses seek locations that the grid has already made movement-rich, while others, often including residence, migrate to less-movement rich parts of the network. Economic values follow this process. With feedback and multiplier effects once one shop appears, others follow -this is the fundamental city creating process by which cities evolves from collections of buildings to living cities, with busy and quiet zones, often in close juxtaposition, and with differentiation of areas according to the detail of howthey are embedded in the larger scale grid. So the pattern of centres (right above) is shaped by the structure of the urban grid (left above). This leads us to a definition of the spatial form of cities. Cities in general not just organic ones - self-evolve into a foreground network of linked centres at all scales, from a few shops and a caf through to whole sub-cities, set into a background network of largely residential space. The two networks have different geometric and metric properties. The foreground network has longer lines, nearly straight connections and route continuity, the background network shorter lines, right angle connections and more local grid-like structures.Good cities, we suggest, have pervasive centrality in that centrality functions diffuse throughout the network. The pattern is far more complex than envisaged in theories of polycentrality. Pervasive centrality is spatially sustainable because it means that wherever you are you are close to a small centre and not far from a much larger one. This process of self organising into the dual network formwith pervasive centrality is not just found in organic cities.Suzhou, for example, is planned on a grid, but we candetect the same process.At radius-n the whole Suzhou region the North- south alignment is secondary andfades as it goes north At radius 5000 metres, however, the whole alignment becomes on of the strongest in Suzhou. However, the northern end, wheremain cluster is found, is weaker But atradius 3000, the main alignment fades, and the northern end of the line, where the centre is, becomes one of the strongest lines in the whole of Suzhou. It is the combin- ation of local and global strength that creased the centre in that location.What about the wonderfulshoppingstreets in the south east of the old city. At radius-n these do not appear at all. At radius 5000 the local group of street begin to appear. But at 2000 the analysis seems to identify a central seed for all three areas. But at 2000 the analysis seems to identify a central seed for all three areas. BRASILIA choice radius 5000 metres BRASILIA choice radius 1600 metres All of these patterns are bought to light by least angle analysis of the segment network. Does this mean that metric analysis has no role ? On the contrary, metric analysis brings to light not linear structures, but area patchworks, reflecting the functional pattern of centres, with their smaller scale grids, and non-centres with larger scale grids. On the left we see, for Istanbul, the patchwork produced by metric segment analysis metric depth analysis at a radius of 500 metres. On the right we represent this asa scattergram, with metric depth at radius n, that is, for the city sa a whole, on the horizontal axis, and metric depth at radius 500 metres on the vertical. Each of the mountains represents a local area with the peak defininig the centre of thearea, and so potentially the most intensive activity. This periodic structure is found in most cities, showing once again the generation of spatial structure by functional factors.

In general we can say that the foreground network is generated by micro-economic activity, and because this tends to follow invariant principles (you want to maximise the number of people), foreground grids tend to take a generic form, for example the deformed wheel you see in Nicosia above. But the background network is shaped by socio-cultural factors and these will be different and so differentiate the form of the network. So in the case above, we see two very different residential networks, the Turkish in the north-east and the Greekin the south west, but held together by the foreground network. Certain general principles about space in cities follow from this theory of city formation.. The first is that the grid-movement relation we call it the law of natural movement - is fundamental to cities. Most relations between the form of the city and theway it functions pass through this relation in some way. Most significantly of all, it is the grid-movement relation which generates the life of the city. For much of the twentieth century we thought of place as one thing and movement between places as another. Now we see that in the ways cities self-organize to create the endless diversity of places which is their most amazing characteristic, movement is the heart of place. The second is that the fact that syntax models have the ability to bring to light structures at many scales, from the most local to the most global, is vital, because research has amply shown that most urban phenomena are multi-scale. For example, the degree and nature of the movement passing along a street will be shaped by how the street is embedded in both the global as well as the local network. The same applies to local centres. These will occur and grow to the degree that that are embedded in a local metric system (brought about by small blocks) and a more global least angle system - in other words, with how they are linked to both components of the dual grid. Similarly, public squares are affected in their functioning not only by how the space is defined by the surrounding buildings, but also by how it is spatially embedded in the larger scale systemof space. The third is that the relations between form and function in cities are generic, not specific. Cities appear to us as patterns of activity related to patterns of space. This is how the task of design is presented to the designer: how a specific pattern of activity is to be related to a specific pattern of space. But theoretically it is not like that, and this is not how cities become as they are. Space is created not directly by the inter-related demands of specific activity patterns, but indirectly by the different demands that kinds of activity place on the movement and co-presence that is created by space. This is why good city form can adapt easily to new patterns of use. Finally, space in cities works in more that one way. The foreground network is structured to maximise movement, and it is so because it is driven by micro-economic factors which benefit from high levels of movement, while the background network restricts and structures movement, and does so because it is driven by social and cultural factors which find expression in the way residential space is structured. So the dual network in cities reflects functional as well as spatial processes This is an instance of the more general potential of spaceto operate in two ways. Space can be use generatively to create new patterns of movement and so co-presence and potentialrelations in the social system, or it can be used conservatively to express and so reproduce existing social patterns and structures. The former is associated with spatial integration, the latter with spatial segregation. The difference between the foreground and background networks is the difference between more morphogenetic and more conservative space. The former focuses movement tocreate development and change, the latter diffuses it to keep things as they are. This generic structure seems to underlie all cities in some sense, and we must conclude that beneath the individuality and cultural typing of cities, there is a universal generic city which makes the city what it essentially is. All societies must in some sense be morphogenetic in order to cope with changing technological and social circumstances, and all societies must also act in ways thatreproduce their structures hence the dual use of space Cities are spatially massive morphogenetic machines that produce change, set into a conservative background which stabilises their structure. This is the generic city. It was I believe the discovery of the generic city that first made urban societies possible. So we have a testable theory of how urban space is organised and how it works. It brings to light structures of various kinds in the urban grid, and these structures are powerfully related to functional patterns. What can we do with it ? Well first we can use it as a frame for all kinds of urban data by simply adding data to the model segment by segment: movement flows, land uses, densities, demographic information, land and rental values and so on. We then have a tool for asking spatial questions of the city, of the form: is there a spatial dimension to this or that urban problem to social malaise, to migration patterns, crime distributions, to the emergence of centres, to the success or failure of areas all these are areas we have investigated using space syntax.But more importantly, perhaps,it can be used in design Essentially, the procedure is this: - we build a model of the site and its context, usually the whole city these days - we test the model against existing movement flows and land use pattern - we can then use the verified model to test out designs by inserted them into the model and re-running the analysis - and suggest new design ideas from the analysis. Let us look at real examples of where space syntax is being used, or has been used: - to support the development of whole cities - to design urban areas - to redesign public squares - and to create new urban linksExisting New plan Former plan We can show the structural isolation of the historic centre in two more ways First we analyse the whole structure of Jeddah as it has evolved. We see the integration core of Jeddah has moved to the north and east of the old centre, which is now a green patch rather than a focus of red and orange lines. We then expand the analysis to include all current plans for extending the city. And re-run the analysis. We see that the structure of the city has moved even more decisively north and east and the old centre has become blue as well as green. In other word, current plans will exacerbate the structural problems of the city Effects of growth on the centre show former plans are unsustainable Historic Core Historic Core We can show this dramatically by colouring up all the street segments in Jeddahaccording to how muchurban integration each gains by theplanned new developments. Red means high. We see that all the gains are away from the old centre, and none are in the centre itself. The plans would makethe structural problems of the city worse rather than better.Historic Core ExistingOld local plansNew plan The whole structure of the city will be drawn back from the east and north towards to historic centre. At the same time, the patches of unplanned settlement will become more integrated into the urban fabric.NAChn Spatial accessibilityExistingCity-wideSpatial accessibility high low 4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Downtown Dubai Deira Business Bay Dubai Creek Site location NAChn Spatial accessibilityProposed masterplanCity-wide4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Dubai Creek Downtown Dubai Deira Business Bay Spatial accessibility high low Site location NAChn Option testingExperiment 1Spatial accessibilityCity-wideSpatial accessibility high low 4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Dubai Creek Downtown Dubai Deira Business Bay NAChn Option testingExperiment 2Spatial accessibilityCity-wideSpatial accessibility high low 4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Dubai Creek Downtown Dubai Deira Business Bay Option testingExperiment 3Spatial accessibilityCity-wideNAChn 4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Dubai Creek Downtown Dubai Deira Business Bay Option testingExperiment 4Spatial accessibilityCity-wideNAChn 4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Dubai Creek Downtown Dubai Deira Business Bay Option testingExperiment 4bSpatial accessibilityCity-wideNAChn 4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Dubai Creek Downtown Dubai Deira Business Bay Option testingExperiment 5Spatial accessibilityCity-wideNAChn 4km 4km 4km 4km 4km 4km 4km 4km 4km 00000000 0 22222222 2Dubai International Airport Dubai Creek Downtown Dubai Deira Business Bay MeanCity-wide accessibility (NACh_n) MaximumCity-wide accessibility(NACh_n) MultiScale core% Proposed0.891.290.18% Option 11.101.38Option 21.091.38Option 31.091.38Option 41.141.40Option 4b1.141.40Option 51.141.39Option 61.151.41Option 6b 1.424.80% Option 6c 1.425.63% Option testingComparison This is lunchtime 20040060080010001200140016001800non_tourists_12to2wd3 3.5 4 4.5 5 5.5 6 6.5spatial integration (local)non_tourists_12to2wd = -1241.28 + 486.386 * sp. integration; R^2 = .89p = 0.0047Blackfriars BridgeHungerford BridgeLondon BridgeSouthwark BridgeWaterloo BridgeWestminster BridgeLet me end with an advertisement. Space syntax is now being applied to the complete street and road network of whole countries. The first research on this will be presented on Friday afternoon by Miguel Serra. So if you would like to know if least angle analysis can predict movement for thousands of locations at the level of a whole country, dont miss it ! Thank you for your attention.