Scaling properties of urban facilities

Two measurements are employed to quantitatively investigate the scaling properties of the spatial distribution of urban facilities: the K function [whose derivative gives the radial distribution function ρ(t)=K'(t)/2πt] by number counting and the variance-mean relationship by the method of expanding bins. The K function and the variance-mean relationship are both power functions. This means that the spatial distributions of urban facilities are scaling invariant. Further analysis of more data (which includes eight types of facilities in 37 major Chinese cities) shows that the the power laws broadly hold for all combinations of facilities and cities. A double stochastic process (DSP) model is proposed as a mathematical mechanism by which spatial point patterns can be generated that resemble the actual distribution of urban facilities both qualitatively and quantitatively. Simulation of the DSP yields a better agreement with the urban data than the correlated percolation model.