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

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

2005-11-23

arxiv.org/abs/physics/0511200v1

Physics

Physics and Society

Physica A. To appear

Scientific paper

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 $\rho(r)$. 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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