| Derivations of fractal models of city hierarchies using entropy-maximization principle |
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| 作者姓名： | CHEN Yanguang LIU Jisheng |
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| 作者单位： | Department of Geography, Peking University, Beijing 100871, China,Department of Geography, Northeast Normal University, Changchun 130024, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (Grant No.40071035) |
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| 摘 要： | A pair of models of fractal recursion on city hierarchy, fm=f1r?1-m?f and Pm=P1r?m-1?p, are derived using entropy-maximizing methods, and the relationship of inverse proportion between the number (fm) of cities at a given level of the urban hierarchy and the average population size (Pm) of the fm cities is established, i.e fm∝1/P. It is demonstrated that the underlying rationale of both the scale law of city rank-size distribution and the Zipf dimension value in standard state (dz=lnrp/lnrf=1) rests with maximization of information entropy of city hierarchies.
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| 关 键 词： | urban system rank-size rule fractal dimension principle of entropy-maximization Beckmann-Davis' |
Derivations of fractal models of city hierarchies using entropy-maximization principle |
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| CHEN Yanguang,LIU Jisheng.Derivations of fractal models of city hierarchies using entropy-maximization principle[J].Progress in Natural Science,2002,12(3):208-211. |
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| Authors: | CHEN Yanguang Liu Jisheng |
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| Institution: | 1. Department of Geography, Peking University, Beijing 100871, China
2. Department of Geography, Northeast Normal University, Changchun 130024, China |
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| Abstract: | A pair of models of fractal recursion on city hierarchy, fm=f1r1-mf and Pm=P1rm-1p, are derived using entropy-maximizing methods, and the relationship of inverse proportion between the number (fm) of cities at a given level of the urban hierarchy and the average population size (Pm) of the fm cities is established, i.e fm∝1/P. It is demonstrated that the underlying rationale of both the scale law of city rank-size distribution and the Zipf dimension value in standard state (dz=lnrp/lnrf=1) rests with maximization of information entropy of city hierarchies. |
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| Keywords: | urban system rank-size rule fractal dimension principle of entropy-maximization Beckmann-Davis' |
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