Modeling Morphology of Cities and Towns

TL;DR

This paper introduces a new model for urban growth that better captures the morphology and distribution of cities, aligning well with real data and considering interactions among urban units.

Contribution

It develops an alternative to the DLA model using correlated percolation with a gradient, providing a more accurate description of urban morphology and distribution.

Findings

The model matches actual urban data qualitatively and quantitatively.

Urban growth morphology is influenced by interactions among constituent units.

The model explains the scaling of urban perimeters effectively.

Abstract

Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban growth, and results in tree-like dendritic structures which have a core or ``central business district'' (CBD). The DLA model predicts that there exists only one large fractal cluster that is almost perfectly screened from incoming ``development units'' (people, capital, resources, etc), so that almost all the cluster growth occurs in the extreme peripheral tips. Here we propose and develop an alternative model to DLA that describes the morphology and the area distribution of systems of cities, as well as the scaling of the urban perimeter of individual cities. Our results agree both qualitatively and quantitatively with actual urban data. The resulting growth morphology can be understood in terms of the effects of interactions among the constituent units forming a urban region, and can be modeled using the correlated percolation model in the presence of a gradient.