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Discrete Dynamics in Nature and Society
Volume 2010, Article ID 974917, 20 pages
Research Article

Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis

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

Received 16 October 2009; Revised 14 May 2010; Accepted 10 October 2010

Academic Editor: Michael Batty

Copyright © 2010 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 Fourier transform and spectral analysis are employed to estimate the fractal dimension and explore the fractal parameter relations of urban growth and form using mathematical experiments and empirical analyses. Based on the models of urban density, two kinds of fractal dimensions of urban form can be evaluated with the scaling relations between the wave number and the spectral density. One is the radial dimension of self-similar distribution indicating the macro-urban patterns, and the other, the profile dimension of self-affine tracks indicating the micro-urban evolution. If a city's growth follows the power law, the summation of the two dimension values may be a constant under certain condition. The estimated results of the radial dimension suggest a new fractal dimension, which can be termed “image dimension”. A dual-structure model named particle-ripple model (PRM) is proposed to explain the connections and differences between the macro and micro levels of urban form.