Defining Urban and Rural Regions by Multifractal Spectrums of Urbanization

The spatial pattern of the 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 correlated 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 a generalized correlation dimension is presented to reflect the degree of geo-spatial utilization in terms of urbanism. The census data of America and China are used to show how to make empirical analyses of urban–rural multifractals. This work is a normative study rather than a positive study, and it proposes a new way of investigating urban and rural regional systems using fractal theory.