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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)∝r D L 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...

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)∝r D L 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)∝r D b 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 D b is the fractal dimension revealing the spatial complexing of transport network. 3 Spatial correlation dimension: it can be expressed in the formulaC(r)∝r D S where C(r)=1N 2∑Ni∑Njθ(r-d ij ) 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, d ij is distance between two cities, N is the total amount of cities and towns in a region. When d ij represents‘cow distance’, D S can be regarded as fractal dimension mirroring the features of spatial connection and configuration of transport network.

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。

A lot of case researches on the fractal features in traffic network of city by scholars at home and abroad have shown that the fractal feature and fractal dimension will become a relatively ideal and useful indicator to remark the form and property of traffic network in a city. This paper takes the traffic network in Shanghai as a case, the fractal dimension of the traffic network in Shanghai and its districts have been measured and calculated so as to research on the spatial changes of the fractal features....

A lot of case researches on the fractal features in traffic network of city by scholars at home and abroad have shown that the fractal feature and fractal dimension will become a relatively ideal and useful indicator to remark the form and property of traffic network in a city. This paper takes the traffic network in Shanghai as a case, the fractal dimension of the traffic network in Shanghai and its districts have been measured and calculated so as to research on the spatial changes of the fractal features. By using the fractal dimension of the network in the city and districts measured and estimated in different periods, the temporal evolution of the fractal features has been investigated. The results have shown that as to the spatial field, the fractal feature of the traffic network in the inner city of Shanghai is more complicated than that in the outer city, and the fractal dimension is gradually decreased from the inner to the outer along the main developing axes of the city. As to the temporal field, the fractal feature and complexity of the traffic network in the recent period is higher than that in the earlier. It is believed that the evolution of fractal dimension can be used to describe and explain the morphological processes of the city explicitly together with other useful urban indicators.

以上海城市交通网络为例 ,通过不同行政区域交通网络的分维值测算 ,研究了分形特征的空间变化 ;利用上海全域及典型行政区交通网络不同时代的分维 ,研究了分形特征的时间演化。结果表明 ,上海城市交通网络的分形特征在空间域上城区内域明显复杂于外域 ,在城市发展主轴方向上表现为由内向外分维测度值的降低 ;而在时间域 ,近期的交通网络分形复杂度明显高于早期 ,反映了城市发展与形态演化的时间过程

 
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