To move through space: lines of vision and movement

Space syntax studies of pedestrian behaviour in building and urban environments have shown that there is a consistent correspondence between the configuration of space and the patterns of usage found within it. In particular, it has been shown that the topological relationships within a spatial system correlate to observed aggregate pedestrian movement. However, there is no proposed mechanism supporting the theory at the level of the individual. Although links between space syntax and individual movement decisions have been suggested through way-finding studies of building environments, virtual reality experiments, and agent-based models, none have proposed a formal link to the axial line analyses used within space syntax. Here we extend work on agent-based models to build a bridge between the line-based topological analyses of space syntax and visually directed agents, through the analysis of what we call ’through vision’. The decision rules for visually directed agents form a Markov transition matrix. We recap the mathematics of Markov chains in order to show that the steady state movement corresponds to an eigenvector of the transition matrix. As the agent transition matrix is extremely complex, we demonstrate that a good approximation of the eigenvector is achieved through the summation of the lines of vision through any one location within an environment. This set of lines forms a superset of the all-line axial map comprising the edges of the visibility graph, or lines of through movement. We show that the lines may be reduced in number (or bundled together) by an algorithmic process and connected into paths, thus making a direct connection between a moving individual with vision and the space syntactic topological analysis of space.