Defining urban and rural regions by multifractal spectrums of urbanization

TL;DR

This paper introduces a novel method using multifractal geometry to quantitatively characterize and define urban and rural regions based on their spatial patterns and levels of urbanization.

Contribution

It proposes a new multifractal-based approach to define urban and rural areas, employing a space-filling index derived from correlation dimensions.

Findings

Empirical analysis using US and China census data demonstrates the method's applicability.

Multifractal spectra effectively distinguish urban from rural spatial patterns.

The approach offers a normative framework for studying urbanization processes.

Abstract

The spatial pattern of urban-rural regional system is associated with the dynamic process of urbanization. How to characterize the urban-rural terrain using quantitative measurement is a difficult problem remaining to be solved. This paper is devoted to defining urban and rural regions using ideas from fractals. A basic postulate is that human geographical systems are of self-similar patterns associated with recursive processes. Then multifractal geometry can be employed to describe or define the urban and rural terrain with the level of urbanization. A space-filling index of urban-rural region based on the generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanization. The census data of America and China are adopted to show how to make empirical analyses of urban-rural multifractals. This work is not so much a positive analysis as a normative study, but it proposes a new way of investigating urban and rural regional systems using fractal theory.