Graph-Cellular Automata: A Generalised Discrete Urban and Regional Model

Abstract

A new type of dynamic spatial model is described: graph-cellular automatoa (graph-CA). First, the proximal model of space and geo-algebra are briefly introduced. Then, the graph-CA model is described, with an emphasis on understanding it as a reworking of the proximal model of space and also of geo-algebra. It is shown that graph-CA with particular structural properties defined in terms of the relationships between subsets of cells are a useful generalisation of traditional cellular automaton (CA) which enable meaningful descriptions of model structure to be developed. This enables further development of novel types of model in the same ‘family’ while retaining links to simpler, better understood examples. It is further argued that the derivation of the graph-CA from both the graph and CA formalisms permits the simultaneous use of well-developed ways of describing model structure and process dynamics, and that this could form the basis of a research programme into the elusive relations between the two. The relationship of graph-CA to other discrete models is briefly discussed, and a classification scheme which indicates the particular geographical interest of such models is suggested.