Universal Roughness and the Dynamics of Urban Expansion

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, branchlike growth and a piecewise linear scaling between area and population. We uncover a robust local roughness exponent α_{loc}≈0.54, coexisting with variable β and z. This unusual coexistence of universal and variable exponents offers a rare empirical test bed for nonequilibrium growth and an empirical basis for modeling urban sprawl.