Modeling Urban Growth Patterns with Correlated Percolation

TL;DR

This paper introduces a correlated percolation model with a gradient to simulate and analyze urban growth patterns, accurately reflecting city morphology, perimeter scaling, and area distribution based on observed data.

Contribution

It presents a novel application of correlated percolation with a gradient to model urban growth, capturing multiple aspects of city morphology and dynamics.

Findings

Model aligns with observed urban data qualitatively and quantitatively.

Captures scaling laws of urban perimeters and area distributions.

Provides insights into interactions driving urban morphology.

Abstract

We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. The resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient.