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Since mathematical models came to be applied to problems of architectural and urban form, new concepts based on predicting large-scale structure from local rules have emerged through insights originating in computation and biology. The clearest of these are computer models based on cellular automata (CA) and their recent generalization in evolutionary biology and artificial life. Here we show how such models can be used to simulate urban growth and form, thus linking our exposition to the longer tradition of ideas in studies of built form emanating from the ‘Cambridge School’. We first review developments of CA in general and then in urban systems in particular. We propose a general class of CA models for urban simulation and illustrate two simple applications, the first a simulation of the development of the historical ‘cell’ city of Savannah, Georgia, the second, a generic hypothetical application. We then …