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

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  • Ciamarra, M. Pica
  • Coniglio, A.

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.

Suggested Citation

  • Ciamarra, M. Pica & Coniglio, A., 2006. "Random walk, cluster growth, and the morphology of urban conglomerations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 551-557.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:551-557
    DOI: 10.1016/j.physa.2005.08.049
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    References listed on IDEAS

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    1. Benguigui, L., 1995. "A new aggregation model. Application to town growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(1), pages 13-26.
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