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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 4863907, 14 pages
Research Article

Describing Urban Evolution with the Fractal Parameters Based on Area-Perimeter Allometry

1Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
2Department of Urban Planning and Design, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong

Received 15 October 2015; Revised 10 December 2015; Accepted 10 December 2015

Academic Editor: Vicenç Méndez

Copyright © 2016 Yanguang Chen and Jiejing Wang. 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 area-perimeter allometric scaling is an important approach for researching fractal cities, and the basic ideas and models have been researched for a long time. However, the fractal parameters based on this scaling relation have not been efficiently utilized in urban studies. This paper is devoted to developing a description method of urban evolution using the fractal parameter sets based on the area-perimeter measure relation. The novelty of this methodology is as follows: first, the form dimension and boundary dimension are integrated to characterize the urban structure and texture; second, the global and local parameters are combined to characterize an urban system and individual cities; third, an entire analytical process based on the area-perimeter scaling is illustrated. Two discoveries are made in this work: first, a dynamic proportionality factor can be employed to estimate the local boundary dimension; second, the average values of the local fractal parameters are approximately equal to the corresponding global fractal parameters of cities. By illustrating how to carry out the area-perimeter scaling analysis of Chinese cities in Yangtze River Delta in the case of remote sensing images with low resolution, we propose a possible new approach to exploring fractal systems of cities.