One hundred years ago, the father of modern British town planning, Patrick Geddes, produced the first draft of his influential work which he ultimately titled Cities in Evolution. In fact, although he followed the prevalent mood of the times which had begun to generalise Darwinism to the social realm, his work and that of others like him who followed such as Lewis Mumford, phrased their explanations and their plans for urban structure in much more static ways. The idea that cities are composed of very rapid, indeed volatile change, of continual and surprising innovations, has only very recently emerged as a predominant concern, due perhaps to the period of rapid change brought about through the genesis of computers and kindred technologies. One hundred years ago, the rapid urban change of the early industrial revolution had already quietened, and the idea of cities in equilibrium rather than evolution had taken hold.
For the first time, we not only have computational techniques which help us to conceive urban dynamics but there is widespread agreement that cities are systems which are far from equilibrium, that cities develop through the positive accumulation or feedback of many seemingly random events most of which never fire but some of which generate surprising and novel changes, discontinuities and bifurcations. These events take place at the very local or micro scale and the patterns that result at more macro levels are ordered in a way that suggests that the mechanisms of local development coordinate themselves in subtle ways whose form is communicated through different spatial and temporal scales, reflected in geometrical as well as social constraints on what is possible. Moreover the patterns that result are often scale invariant, fractal, suggesting that urban morphology is built from self-similar processes operating at the most local scale (Batty, 1995).
In this paper, we suggest and demonstrate a class of dynamic models of urban development which are built around these notions. The models are operationalised as cellular automata whose processes of development are entirely local in the neighbourhood sense. Development is the product of local transitions, positive feedback in which cells grow or decay according to their existing size, and random innovations which continue to 'bubble' throughout the urban space. This is how we conceptualise the 'potential' for urban development - the demand side of the model. What actually gets developed - the supply side - depends upon a much more limited transformation of the potential for development into actual development, with actual development then interacting with the potential. These models can thus be conceived as the interaction between a rapidly changing, indeed volatile potential surface, and actual development which is much smoother. These are the two faces of urban change which in the past, we would argue, have been confused in articulating urban structure and dynamics (Batty & Howes, 1996).
We operationalise the model using a massively parallel form of CA based on the Logo programming language. We generate a series of simulations which we articulate not through snapshots of urban change but as movies. We can see how cities develop rapidly in terms of demand potential and slowly in terms of the supply of development. We are able to change the simulations on-the-fly so-to-speak and thus generate a very wide range of spatial and temporal patterns. We show how intra- and inter-urban issues are one and the same and how the internal structure of the city is simply a more local morphology than that of a system of cities. From these simulations, we are not only able to demonstrate global order which shows itself as fractal patterns in space, but also show the kind of global order in fractal patterns which change through time. In this way, we open up the study of temporal as well as spatial order. This is manifested in the fact that the power laws describing fractal patterns - rank size for the system of cities that are generated in interurban terms, and urban density representing the internal structure of the city - are a natural consequence of our simulations.
We will illustrate these ideas in three ways - in simple formal terms, then as a pedagogic example of how such CA models can be built up, and finally as a series of QuickTime movies generated from many simulations.
Batty, M. 1995. New Ways of Looking at Cities, Nature, 377, 574.
Batty, M. and Howes, D. 1996. "Visualising Urban Development". In Parker, D., ed., Innovations in GIS 3. London: Taylor and Francis, 177-192.