地理研究

地理研究 ›› 1998, Vol. 17 ›› Issue (1): 82-89.doi: 10.11821/yj1998010012

• 论文 • 上一篇    下一篇

城镇体系等级结构的分形维数及其测算方法*

刘继生1, 陈彦光2   

  1. 1. 东北师范大学地理系 长春 130024;
    2. 信阳师范学院地理系 信阳 464000
  • 收稿日期:1997-05-05 修回日期:1997-12-22 出版日期:1998-03-15 发布日期:1998-03-15
  • 作者简介:刘继生,男,1955年9月生,副教授,博士。主要从事人文地理学基本理论研究,出版《区位论》等3部著作,发表“东北地区城市体系空间结构的分形研究”、“人地非线性相关作用的探讨”等40余篇论文。
  • 基金资助:
    *国家自然科学基金(49771035);河南省自然科学基金(974071200)

FRACTAL DIMENSIONS OF HIERARCHICAL STRUCTURE OF URBAN SYSTEMS AND THE METHODS OF THEIR DETERMINATION

Liu Jisheng1, Chen Yanguang2   

  1. 1. Department of Geography, Northeast Normal University, Changchun 130024;
    2. Department of Geography, Xinyang Normal College, Xinyang 464000
  • Received:1997-05-05 Revised:1997-12-22 Online:1998-03-15 Published:1998-03-15

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摘要： 文章探讨了城镇体系等级结构的分形研究方法。首先,讨论了区域城镇规模分布的Zipf模型,并通过分形退化分析将其应用范围加以拓广,从而与非分形研究接口;第二,引进了分形结构因子,以此开创了城镇体系等级结构的FSF分析;第三,提出了表征城镇体系等级差异的差异度概念和度量方法。文章给出实例说明了各种方法的应用,并比较了三种方法的异同。

关键词: 城镇体系, 等级结构, 规模分布, 分形, 分维

Abstract: Three parameters were presented in the paper to characterize the hierarchical structure, especially size distribution of cities, of an urban system, including Zipf's dimension, fractal structure factor (FSF), and difference degree.1.Zipf's dimension.Zipf's law is very familiar to urban geographers, it is equivalent to Pareto's distribution and can be expressed mathematically as P(k)=P1K-q, where q is sometimes called Zipf's dimension, which is actually the reciprocal of fractal dimension, namely, q=1/D.2.FSF.The parameter is put forwards by two Chinese geo scientists and has been introduced to the studies of urban geography by the authors of the paper.FSF can be defined as I(r)=I0+DI lnr, where I(r) is information capacity of size distribution of cities corresponding to a certain scale (r, when r=1, I(r)=I0), and DI is what is called FSF.3.Difference degree.The parameter is given by the authors of the paper, it can be defined as follows: C=1-I/Imax, where I=- PilnPi, Imax=lnN, and PiP(k)/ P(k),P(k) is the population of the kth city of an urban system (k=1, 2, …, N).Difference degree C can be linked with fractal dimension D by means of Zipf's formula under some conditions.The geographical meanings of the three parameters were illuminated, the methods of using them were illustrated, in particular, the degenerational forms of Zipf's model were discussed so as to connect fractal studies with non-fractal studies of urban systems, and finally, a preliminary comparison was made between them.

Key words: urban system, hierarchical structure, city size distribution, fractal, fractal dimension

PACS: 

  • K928.5