MODELING URBAN-GROWTH PATTERNS

CITIES grow in a way that might be expected to resemble the growth of two-dimensional aggregates of particles, and this has led to recent at tempts(1-3) to model urban growth using ideas from the statistical phy sics of clusters, In particular, the model of diffusion-limited aggreg ation(4,5) (DLA) has been invoked to rationalize the apparently fracta l nature of urban morphologies(1). The DLA model predicts that there s hould exist only one large fractal cluster, which is almost perfectly screened from incoming 'development units' (representing, for example, people, capital or resources), so that almost all of the cluster grow th takes place at the tips of the cluster's branches. Here we show tha t an alternative model, in which development units are correlated rath er than being added to the cluster at random, is better able to reprod uce the observed morphology of cities and the area distribution of sub -clusters ('towns') in an urban system, and can also describe urban gr owth dynamics, Our physical model, which corresponds to the correlated percolation model(6-8) in the presence of a density gradient(9), is m otivated by the fact that in urban areas development attracts further development. The model offers the possibility of predicting the global properties (such as scaling behaviour) of urban morphologies.