Modeling Fractal Structure of Systems of Cities Using Spatial Correlation Function

TL;DR

This paper introduces a fractal-based spatial correlation method to analyze urban systems, demonstrating that Chinese cities exhibit fractal properties with correlation dimensions between 1.3 and 1.6.

Contribution

It presents a novel approach linking spatial correlation functions to fractal dimensions in urban systems, applicable across different sample sizes.

Findings

Chinese urban system has a correlation dimension of 1.3 to 1.6.

Fractality is observed in city networks in geographic and 'time' space.

The method links various fractal dimensions in urban analysis.

Abstract

This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial correlation function of cities. Suppose that the spatial correlation follows the power law. It can be proved that the correlation exponent is the second order generalized dimension. The spatial correlation model is applied to the system of cities in China. The results show that the Chinese urban system can be described by the correlation dimension ranging from 1.3 to 1.6. The fractality of self-organized network of cities in both the conventional geographic space and the "time" space is revealed with the empirical evidence. The spatial correlation analysis is significant in that it is applicable to both large and small sizes of samples and can be used to link different fractal dimensions in urban study, including box dimension and radial dimension.