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Open AccessArticle

Hierarchical Scaling in Systems of Natural Cities

by Yanguang Chen 1,* and Bin Jiang 2
Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
Faculty of Engineering and Sustainable Development, Division of GIScience, University of Gävle, SE-801 76 Gävle, Sweden
Author to whom correspondence should be addressed.
Entropy 2018, 20(6), 432;
Received: 21 April 2018 / Revised: 30 May 2018 / Accepted: 31 May 2018 / Published: 4 June 2018
(This article belongs to the Special Issue Power Law Behaviour in Complex Systems)
Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many natural and social phenomena such as cities, earthquakes, and rivers. This paper reveals the power law behaviors in systems of natural cities by reconstructing the urban hierarchy with cascade structure. Cities of the U.S.A., Britain, France, and Germany are taken as examples to perform empirical analyses. The hierarchical scaling relations can be well fitted to the data points within the scaling ranges of the number, size and area of the natural cities. The size-number and area-number scaling exponents are close to 1, and the size-area allometric scaling exponent is slightly less than 1. The results show that natural cities follow hierarchical scaling laws very well. The principle of entropy maximization of urban evolution is then employed to explain the hierarchical scaling laws, and differences entropy maximizing processes are used to interpret the scaling exponents. This study is helpful for scientists to understand the power law behavior in the development of cities and systems of cities. View Full-Text
Keywords: allometry; hierarchy; scaling; fractals; entropy; natural cities allometry; hierarchy; scaling; fractals; entropy; natural cities
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Chen, Y.; Jiang, B. Hierarchical Scaling in Systems of Natural Cities. Entropy 2018, 20, 432.

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