The Hidden Geometry of Deformed Grids

or, why space syntax works when it looks as though it shouldn't 0 Abstract A common objection to the space syntax analysis of cities is that even in its own terms the technique of using a non-uniform line representation of space and analysing it by measures that are essentially topological, ignores too much geometric and metric detail to be credible. In this paper it is argued that far from ignoring geometric and metric properties the 'line-graph' internalises them into the structure of the graph and in doing so allows the graph analysis to pick up the nonlocal, or extrinsic, properties of spaces that are critical to the movement dynamics through which a city evolves its essential structures. Nonlocal properties are those which are defined by the relation of elements to all others in the system, rather than intrinsic to the element itself. The method also leads to a powerful analysis of urban structures because cities are essentially nonlocal systems. 1 Preliminaries 1.1 The critique of line graphs Space syntax is a family of techniques for representing and analysing spatial layouts of all kinds. A spatial representation is first chosen according to how space is defined for the purposes of the research-rooms, convex spaces, lines, convex isovists, and so on-and then one or more measures of 'configuration' are selected to analyse the patterns formed by that representation. Prior to the researcher setting up the research question, no one representation or measure is privileged over others. Part of the researcher's task is to discover which representation and which measure captures the logic of a particular system, as shown by observation of its functioning. In the study of cities, one representation and one type of measure has proved more consistently fruitful than others: the representation of urban space as a matrix of the 'longest and fewest' lines, the 'axial map', and the analysis of this by translating the line matrix into a graph, and the use of the various versions of the 'topological' (i.e. nonmetric) measure of patterns of line connectivity called 'integration'. (Hillier et al 1982, Steadman 1983, Hillier & Hanson 1984) This 'line graph' approach has proved quite unexpectedly successful. It has generated not only models for predicting urban et al 1998), but also strong theoretical results on urban structure, and even a general theory of the dynamics linking the urban grid, movement, land uses and building densities in 'organic' cities …