地理学报 ›› 1999, Vol. 66 ›› Issue (5): 471-478.doi: 10.11821/xb199905011

• 论文 • 上一篇    

交通网络空间结构的分形维数及其测算方法探讨

刘继生1, 陈彦光2   

  1. 1. 东北师范大学地理系,吉林长春130024;
    2. 信阳师范学院地理系,河南信阳464000
  • 收稿日期:1998-01-10 修回日期:1999-05-11 出版日期:1999-09-15 发布日期:1999-09-15
  • 基金资助:
    国家自然科学基金(49771035);河南省自然科学基金项目(974071200)

A Study on Fractal Dimensions of Spatial Structure of Transport Networks and the Methods of Their Determination

LIU Ji sheng1, CHEN Yan guang 2   

  1. 1. Department of Geography, Northeast Normal University, Changchun 130024;
    2. Department of Geography, Xinyang Teachers College, Xinyang, Henan 464000
  • Received:1998-01-10 Revised:1999-05-11 Online:1999-09-15 Published:1999-09-15
  • Supported by:
    National Natural Science Foundation of China,No.49771035;Natural Science Foundation of Henan Province,No.974071200

摘要: 分形维数是刻画交通网络空间结构的有效参数, 本文系统地论证了反映交通网络分形特征的三种基本分维: 一是长度 半径维数, 由回转半径和相应网络长度的双对数关系定义, 其数值反映交通网络密度从中心城市向腹地的变化特征;二是分枝数目 半径维数, 由回转半径和相应网络分枝数目的双对数关系定义, 其数值反映交通网络的区域 “渗透”能力和复杂程度; 三是空间关联维数, 由码尺长度和空间关联函数(用相应的距离数目表征) 的幂指数关系定义, 其数值反映城市体系空间分布与联系的自相似特征。文章以实例说明了三种维数的测算方法。

关键词: 交通网络, 城市体系, 地理分形

Abstract: Three types of fractal dimensions were presented to characterize the spatial structure of transport networks. The geographical meanings of these dimensions were illuminated and the methods of the determination of them were illustrated. The three fractal dimensions can be expressed as follows. 1 Length radius dimension: it is always defined by the expression L(r)∝rDL where r is radial distance, L(r) is total length of communication lines in the area of π r 2, and D L is the fractal dimension reflecting the change of density of the transport network around a measured center. 2 Dendrite radius dimension: it can be given by the formula N(r)∝rDb and N(r) is defined as N(r)=∑rk=1n(k) (r=1,2, …, k=1,2, …,r) where r is gyration radius, k is ordinal number of each ring belt divided with r,n(k) is the amount of branches of communication lines in the k th ring belt, and Db is the fractal dimension revealing the spatial complexing of transport network. 3 Spatial correlation dimension: it can be expressed in the formula C(r)∝rDS where C(r)=1/N2∑Ni∑Njθ(r-dij ) is spatial correlation function, θ(x) is Heaviside function (when x≥0, θ(x)=1 ; whereas, when x<0, θ(x)=0), r is yardstick, dijis distance between two cities, N is the total amount of cities and towns in a region. When dijrepresents‘cow distance’, Ds can be regarded as fractal dimension mirroring the features of spatial connection and configuration of transport network.

Key words: transport network, urban system,geographical fractals

中图分类号: 

  • U491.13