• 论文 •

### 交通网络空间结构的分形维数及其测算方法探讨

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

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.

• U491.13