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Random walk, cluster growth, and the morphology of urban conglomerations

M. Pica Ciamarra·A. Coniglio
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Abstract

We propose a new model of cluster growth according to which the probability that a new unit is placed in a point at a distance $r$ from the city center is a Gaussian with mean equal to the cluster radius and variance proportional to the mean, modulated by the local density $ρ(r)$. The model is analytically solvable in $d=2$ dimensions, where the density profile varies as a complementary error function. The model reproduces experimental observations relative to the morphology of cities, determined via an original analysis of digital maps with a very high spatial resolution, and helps understanding the emergence of vehicular traffic.

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M. Pica Ciamarra, A. Coniglio. 2005-11-23. Random walk, cluster growth, and the morphology of urban conglomerations. https://arxiv.org/abs/physics/0511200

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