Graph-based cellular automaton models of urban spatial processes

The impact of spatial organisation on the dynamics of spatial change is a topic of great interest in geography. The impact of spatial form is of particular interest in the context of urban systems where the associated issues are most acutely felt. Various concepts of space and their implications are reviewed. Two existing mathematical concepts—graphs and cellular automata—which have been used as representations of spatial systems, are discussed. Examination of the use of these concepts reveals that in urban models they have usually been applied separately to represent, respectively, structural properties, and the behaviour of dynamic processes. It is suggested that a model which combines aspects of both approaches—the graph-based cellular automaton (graph-CA)—can be introduced. This enables research into relations between the spatial structure and process dynamics of systems. Conceptual tools for this investigation are discussed, drawing on previous work in cellular automata and graph theory. A measure of spatial pattern—spatial information—useful for characterising dynamic behaviour, is developed. The computer implementation of these concepts is described, and experiments conducted using it are reported. A tentative finding is that process dynamics can be usefully distinguished according to the extent to which they are robust or fragile under spatial change. The application of the graph-CA model to a particular urban process gentrification is also described. Theories of gentrification are reviewed, and a model for the phenomenon developed. Rather than develop a detailed empirical model of the process, a single urban setting (in Hoxton in East London) is used to generate a number of different graph-CA models. The similarities and differences in the behaviour of these are reported and implications discussed. Attention is drawn to possible extensions of this work throughout.