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, 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.