Fractal Dimension Analysis of Urban Morphology Based on Spatial Correlation Functions

Abstract

A number of mathematical models in urban studies are associated with spatial correlation functions. However, the theory and method of spatial correlation modeling have not been developed for urban morphology. Based on power-law urban density models, a density–density correlation function can be constructed for urban modeling. Using scaling analysis and spectral analysis, we can derive a set of fractal parameter equations, which can be employed to explore urban form and growth. The main results and findings are as follows: first, if urban density follows power law, the spatial correlation function and its energy spectral density will follow scaling law; second, the reasonable numerical ranges of fractal parameters can be derived by the ideas from multifractals; third, the spatial correlation modeling can be generalized to spatial autocorrelation and gravity models. As an example, the analytical process is applied to the city of Beijing in China to show how to use this method. A conclusion can be drawn that the scaling analysis, spectral analysis, and spatial correlation analysis can be integrated into a new framework to form the 3S analysis for urban morphology.