Defining urban and rural regions by multifractal spectrums of urbanization

摘要

The spatial pattern of urban-rural regional system is associated with thedynamic process of urbanization. How to characterize the urban-rural terrainusing quantitative measurement is a difficult problem remaining to be solved.This paper is devoted to defining urban and rural regions using ideas fromfractals. A basic postulate is that human geographical systems are ofself-similar patterns associated with recursive processes. Then multifractalgeometry can be employed to describe or define the urban and rural terrain withthe level of urbanization. A space-filling index of urban-rural region based onthe generalized correlation dimension is presented to reflect the degree ofgeo-spatial utilization in terms of urbanization. The census data of Americaand China are adopted to show how to make empirical analyses of urban-ruralmultifractals. This work is not so much a positive analysis as a normativestudy, but it proposes a new way of investigating urban and rural regionalsystems using fractal theory.