SCIENTIA GEOGRAPHICA SINICA ›› 2003, Vol. 23 ›› Issue (6): 713-720.doi: 10.13249/j.cnki.sgs.2003.06.713

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Multifractal Measures Based on Man-Land Relationships of the Spatial Structure of the Urban System in Henan

LIU Ji-Sheng1, CHEN Yan-Guang2   

  1. 1. Department of Geography, Northeast Normal University, Changchun, Jilin 130024;
    2. Department of Geography, Peking University, Beijing 100871
  • Received:2002-11-25 Revised:2003-04-30 Online:2003-11-20 Published:2003-11-20

Abstract: By means of the theory of multifractals, this paper is devoted to studying the spatial structure of urban systems, taking man-land relationships into consideration. Taking the system of cities and towns in Henan Province, China, as a example, and using the box counting method and μ-weight formulae, we calculate the values of the Lipschitz-Hlder 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 Dq of the urban systems in the studied area. The data processing reveals that the scaling range reflecting log-linearity of complex fractals is narrower than that of simple fractals. This denotes that fractal systems are some kinds of evolving systems, and multifractals usually come from common fractals at least where geographical phenomena are concerned. The computation results show that the spatial structure of the Henan urban system has multifractality to some extent, with a scaling breakdown in the f(α)curve as well as the spectrum of fractal dimensions Dq when the moment order q=-4. That is to say, qc=-3 perhaps is a critical value for q, the multifractals come on well only when q∈[-3,∞], as for q≤-4, the multifractal measures are abnormal: the f(α) curve and the Dq function fail to converge, which maybe implies a sort of phase transition from a rural to urban settlement system during the course of regional urbanization. Moreover, this is another evidence that multifractals generate by evolution from simple fractals. A discovery is made that the fractal dimension of spatial structure of urban systems is less than that of river systems in the same studied region, which maybe means that urban systems as fractals must be included by hydrographical nets, i.e. water systems. We can develop what is called "inclusion principle" about man-land relations that is as important as the "matching principle" about urban systems. Both the matching principle and inclusion principle will be supposed to be the basic principles of fractal urban geography, which will play a significant role in urban plan and geographical space optimization in the future.

CLC Number: 

  • K928.5