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《Geographical Research》 2004-02
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Relationship between Zipf dimension and fractal dimension of city-size distribution

TAN Ming-hong, FAN Cun-hui (Institute of Geographic Sciences and Natural Resources Research,CAS, Beijing,100101, China)  
China has a long history of urban development and has numerous cities.Macroscopically the congnition of development law of China’s urban system provides an ideal source for enrichment of urban system theoretical research.Furthermore,China,as a developing country on the fast track,is experiencing rapid urban growth.A better understanding of China’s urban system development will be helpful for predicting the city scale(such as,urban land scale,urban population scale)and macro-planning of China’s urban growth. The urban rank-size and the fractal theories are the important bases for studying the urban system.The former can perfectly depict the distribution of urban size,and the latter can be employed to explain the characteristics of distribution of urban size.At the same time,the fractal dimension and the Zipf dimension are the basic parameters of the two theories.But when studying the urban rank-size rule and the fractal,some scholars theoretically believe there is the relationship between Zipf dimension and the fractal dimension of distribution of urban size,that is,their product equals 1.But,we think,if D and q are the results of OLS(Ordinary Least Square)estimation,then their product should be R2(R2,the coefficient of determination).Then,this paper deduces and proves this result. To study the relationship between Zipf dimension and the fractal dimension of distribution of urban size is helpful to understanding the rule of urban rank-size.Moreover,this study is also necessary for grasping urban development in the future characteristics of urban system evolution in the past and predicting in the urban development future because China is experiencing rapid urbanization process.
【Key Words】： city-size distribution Zipf dimension fractal dimension
【Fund】： 中国科学院知识创新工程项目 (KZCX2 3 10 );; 欧盟项目 (ICA4 CT 2 0 0 1 10 0 85)
【CateGory Index】： F299.2
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