Universal roughness and the dynamics of urban expansion

TL;DR

This paper investigates the quantitative laws of urban sprawl by analyzing built-up expansion in 19 cities using surface growth physics, revealing universal roughness and complex scaling behaviors.

Contribution

It introduces a novel application of surface growth physics to urban expansion, uncovering universal roughness and anisotropic growth patterns in cities.

Findings

Universal local roughness exponent of approximately 0.54

Piecewise linear scaling between area and population

Coexistence of universal and variable growth exponents

Abstract

Urban sprawl reshapes cities, yet its quantitative laws remain elusive. Analyzing built-up expansion in 19 cities (1985-2015) with tools from surface growth physics in radial geometry, we reveal anisotropic, branch-like growth and a piecewise linear scaling between area and population. We uncover a robust local roughness exponent $\alpha_{\text{loc}}\approx 0.54$, coexisting with variable $\beta$ and $z$. This unusual coexistence of universal and variable exponents offers a rare empirical testbed for nonequilibrium growth and an empirical basis for modeling urban sprawl.