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Abstract

The evolution of a stochastic reaction-diffusion model whose dynamics leads to the development of a strongly inhomogeneous, spatiotemporally intermittent density field is analytically and numerically studied. The processes underlying the model can be identified with those that govern urban development. The results for the reaction-diffusion model are thus compared with data obtained from real human demography. Statistical properties of urban distributions—in particular, the universal power law observed in the population frequency of cities—are successfully reproduced by the model.