地理科学进展

地理科学进展 ›› 1999, Vol. 18 ›› Issue (3): 255-262.doi: 10.11820/dlkxjz.1999.03.009

• 论文 • 上一篇    下一篇

Davis二倍数规律与Zipf三参数模型的等价性证明——关于城市规模分布法则的一个理论探讨

陈彦光1, 刘继生2   

  1. 1. 信阳师范学院地理系,信阳464000;
    2. 东北师范大学地理系,长春130024
  • 收稿日期:1998-12-01 修回日期:1999-05-01 出版日期:1999-08-25 发布日期:1999-08-25
  • 作者简介:陈彦光(1965-),男,1987年毕业于华中师范大学地理系,1995年在东北师范大学获硕士学位,现任教于信阳师范学院地理系。从事地理分形和城市地理学研究,重点研究分形城市系统,发表《城市空间体系的Koch模式》等30余篇论文。
  • 基金资助:

    国家自然科学基金;河南省自然科学基础研究项目

A Proof of Davis’ 2\+n law as a Special Equivalent of the Three-parameter Zipf Model

CHEN Yan guang1, LIU Ji sheng2   

  1. 1. Department of Geography, Xinyang Teachers College, Xinyang, Henan 464000, China;
    2. Department of Geography, Northeast Normal University, Changchun 130024, China
  • Received:1998-12-01 Revised:1999-05-01 Online:1999-08-25 Published:1999-08-25

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摘要： 本文从城市规模分布的Davis 二倍数规律（2n 规律：ai= ai+ n·2n,fi= fi+ n·2- n）中推导出具有一般意义的三参数Zipf模型：P（r）= C（r- α）- dz,揭示了2n 规律隐含的分形几何性质， 论证了2n 法则为Zipf维数dz= 1 时的特殊情形， 并将2n 规律推广到具有普遍意义的δn 规律， 给出了Zipf维数及分维与邻级倍数δ的数值关系：dz= 1/D= ln2/lnδ。最后从三个方面对文中的理论成果进行了实证分析。

关键词: 城市规模分布, 城市体系, 分维, 分形

Abstract: The Zipf’s model with three parameters, P(r)=C(r-α) - d z , is deduced from Davis’ 2 n law: a i=a i+n ·2 n, f i=f i+n ·2 -n , by means of a series of mathematical transformation, where d z proves to have some nature of fractal dimension (D) because d z=1/D. The 2 n rule is generalized to δ n rule and δ represents an arbitrary number which is greater than one, namely δ >1. The relationships between δ and the fractal dimensions of city size distributions can be expressed as D=lnδ/ln2 : when δ =2, we have d z =1, so the 2 n rule is only a special case of the three parameter Zipf’s model. The result of the demonstration of Davis’ law as an equivalent of the generalized Zipf’s law is illustrated and verified by some examples including the data in which 2 n rule of urban systems is discovered.

Key words: City size Distribution, Fractal, Fractal dimenson, Urban system

中图分类号: 

  • TU984