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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 5243287, 15 pages
Research Article

A Hierarchical Allometric Scaling Analysis of Chinese Cities: 1991–2014

Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China

Correspondence should be addressed to Jian Feng; nc.ude.ukp@naijgnef

Received 1 January 2017; Revised 22 March 2017; Accepted 9 April 2017; Published 22 May 2017

Academic Editor: Charalampos Skokos

Copyright © 2017 Yanguang Chen and Jian Feng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in observational data. In theory, both the allometric growth law and Zipf’s law are related to the hierarchical scaling laws associated with fractal structure. In this paper, the scaling laws of hierarchies with cascade structure are used to study Chinese cities, and the method of analysis is applied to analyzing the change trend of the allometric scaling exponents. The results show that the hierarchical scaling relations of Chinese cities became clearer and clearer from 1991 to 2014 year; the global allometric scaling exponent values fluctuated around 0.85, and the local scaling exponent approached 0.85. The Hurst exponent of the allometric parameter change is greater than 0.5, indicating persistence and a long-term memory of urban evolution. The main conclusions can be reached as follows: the allometric scaling law of cities represents an evolutionary order rather than an invariable rule, which emerges from self-organized process of urbanization, and the ideas from allometry and fractals can be combined to optimize spatial and hierarchical structure of urban systems in future city planning.