Possible urban automata

New developments in computation based on cellular automata (CA), which are finding widespread application in simulating evolution, are beginning to suggest that science is not simply about the study of actual phenomena but about potential or possible phenomena. This notion is central to design but the prospect of a new science through computation which enables systematic and formal study of 'possible worlds' has clear relevance to the scientific understanding of human systems such as cities. In this paper, we provide a framework for such understanding based on a generic model of the dynamics of urban systems. After formally presenting the framework, we show how it can be used to generate existing model structures which can be seen as samples from a wide, indeed infinite, array of possible forms. In fact, the emphasis here is not just upon possible model structures per se but upon possible urban forms which such structures are able to generate. Accordingly we formulate models in terms of ideas from CA which treat space and time in its most disaggregate or local form. We begin by developing models both of areal and of linear growth processes and then combine these into a more general structure which forms the basis for a comprehensive model of urban structure. We illustrate the varieties of form which such models can generate, concluding by suggesting that such an approach might constitute the basis for more systematic exploration of the space within which possible urban morphologies exist.