Modelling urban growth patterns

Abstract

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 attempts1a¤-3 to model urban growth using ideas from the statistical physics of clusters. In particular, the model of diffusion-limited aggregation4,5 (DLA) has been invoked to rationalize the apparently fractal nature of urban morphologies1. The DLA model predicts that there should exist only one large fractal cluster, which is almost perfectly screened from incoming a¤˜development unitsa¤™ (representing, for example, people, capital or resources), so that almost all of the cluster growth takes place at the tips of the clustera¤™s branches. Here we show that an alternative model, in which development units are correlated rather than being added to the cluster at random, is better able to reproduce the observed morphology of cities and the area distribution of sub-clusters (a¤˜towns') in an urban system, and can also describe urban growth dynamics. Our physical model, which corresponds to the correlated percolation model6a¤-8 in the presence of a density gradient9, is motivated 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.