Urban growth as a reaction-diffusion process

Abstract

Urban areas are rapidly expanding around the world but a quantitative description of how population and urban infrastructures evolve in time and space is still missing. Here we show that complex urban patterns are produced by a minimalist reaction-diffusion model coupled with economic constraints and an adaptive transport network. After an initial phase of diffusion limited growth, the urban population coevolves with a hierarchical transport system, displaying an invasive behaviour typical of biological systems. These results shed light on the emergence of urban morphologies and demonstrate that population-transport feedbacks are key controls of long-term urbanization patterns.

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