dorsal/arxiv
View SchemaRandom walk, cluster growth, and the morphology of urban conglomerations
| Authors | M. Pica Ciamarra, A. Coniglio |
|---|---|
| Categories | |
| ArXiv ID | physics/0511200 |
| URL | https://arxiv.org/abs/physics/0511200 |
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 $\rho(r)$. 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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"date_modified": "2026-03-02T18:01:03.277000Z",
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"abstract": "We propose a new model of cluster growth according to which the probability\nthat a new unit is placed in a point at a distance $r$ from the city center is\na Gaussian with mean equal to the cluster radius and variance proportional to\nthe mean, modulated by the local density $\\rho(r)$. The model is analytically\nsolvable in $d=2$ dimensions, where the density profile varies as a\ncomplementary error function. The model reproduces experimental observations\nrelative to the morphology of cities, determined via an original analysis of\ndigital maps with a very high spatial resolution, and helps understanding the\nemergence of vehicular traffic.",
"arxiv_id": "physics/0511200",
"authors": [
"M. Pica Ciamarra",
"A. Coniglio"
],
"categories": [
"physics.soc-ph",
"cond-mat.stat-mech"
],
"title": "Random walk, cluster growth, and the morphology of urban conglomerations",
"url": "https://arxiv.org/abs/physics/0511200"
},
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"type": "Model",
"variant": "snapshot-2026-03-01",
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