Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 728420, 22 pages
Research Article

A Wave-Spectrum Analysis of Urban Population Density: Entropy, Fractal, and Spatial Localization

Yanguang Chen

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

Received 9 December 2007; Revised 15 May 2008; Accepted 16 August 2008

Academic Editor: Michael Batty

Copyright © 2008 Yanguang Chen. 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 method of spectral analysis is employed to research the spatial dynamics of urban population distribution. First of all, the negative exponential model is derived in a new way by using an entropy-maximizing idea. Then an approximate scaling relation between wave number and spectral density is derived by Fourier transform of the negative exponential model. The theoretical results suggest the locality of urban population activities. So the principle of entropy maximization can be utilized to interpret the locality and localization of urban morphology. The wave-spectrum model is applied to the city in the real world, Hangzhou, China, and spectral exponents can give the dimension values of the fractal lines of urban population profiles. The changing trend of the fractal dimension does reflect the localization of urban population growth and diffusion. This research on spatial dynamics of urban evolvement is significant for modeling spatial complexity and simulating spatial complication of city systems by cellular automata.