CASA Working Paper 75

A New Theory of Space Syntax

Relations between different components of urban structure are often measured in a literal manner, along streets for example, the usual representation being routes between junctions which form the nodes of an equivalent planar graph. A popular variant on this theme - space syntax - treats these routes as streets containing one or more junctions, with the equivalent graph representation being more abstract, based on relations between the streets which themselves are treated as nodes. In this paper, we articulate space syntax as a specific case of relations between any two sets, in this case, streets and their junctions, from which we derive two related representations. The first or primal problem is traditional space syntax based on relations between streets through their junctions; the second or dual problem is the more usual morphological representation of relations between junctions through their streets.

The unifying framework that we propose suggests we shift our focus from the primal problem where accessibility or distance is associated with lines or streets, to the dual problem where accessibility is associated with points or junctions. This traditional representation of accessibility between points rather than between lines is easier to understand and makes more sense visually. Our unifying framework enables us to easily shift from the primal problem to the dual and back, thus providing a much richer interpretation of the syntax. We develop an appropriate algebra which provides a clearer approach to connectivity and distance in the equivalent graph representations, and we then demonstrate these variants for the primal and dual problems in one of the first space syntax street network examples, the French village of Gassin. An immediate consequence of our analysis is that we show how the direct connectivity of streets (or junctions) to one another is highly correlated with the distance measures used. This suggests that a simplified form of syntax can be operationalized through counts of streets and junctions in the original street network.

This working paper is available as a PDF. The file size is 3.51MB.

Authors: Michael Batty

Publication Date: 1/3/2004

Download working paper No. 75.