关键词: 城镇体系, 空间结构, 多分形, 分维, 河南城市

Abstract: The study is made of the spatial structure of the systems of cities and towns in Central Plains, mainly including North Henan, China, using the theory of multifractals. By means of the box counting method and μ-weight formulae, we calculate the values of the Lipschitz-Hölder exponent α(q), the fractal dimension of the support of singularities f(α), the sequence of mass exponent τ(q), and the dimensions of fractal measures D_q of the urban systems in the studied area. The resultant values show that there is a scaling breakdown in the f(α) curve as well as the spectrum of fractal dimensions D_q when the moment order q≈-1, where q_c=-1 perhaps is a critical value for q, i.e., the multifractals come on well when q∈[0, ∞], as for q≤-1, the multifractal measures are abnormal (dysplasia or hypolasia): the f(α) curve and the D_q function cannot converge, which maybe implies a sort of phase transition from a rural to urban settlement system during the course of regional urbanization. This research demonstrates that the spatial structure of urban systems can be characterized with multifractal geometry, and moreover, wavelet transformation can be used to analyse the multifractal structure of urban systems.

Key words: urban system, spatial structure, multifractal measures, fractal dimension, Henan cities of China