Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis
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 c...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/974917 |
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| author | Yanguang Chen |
| author_facet | Yanguang Chen |
| author_sort | Yanguang Chen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-74f4b609c12a48ec999c2a77cecb62cd |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-74f4b609c12a48ec999c2a77cecb62cd2025-08-20T03:19:14ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/974917974917Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum AnalysisYanguang Chen0Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, ChinaThe 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.http://dx.doi.org/10.1155/2010/974917 |
| spellingShingle | Yanguang Chen Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis Discrete Dynamics in Nature and Society |
| title | Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis |
| title_full | Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis |
| title_fullStr | Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis |
| title_full_unstemmed | Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis |
| title_short | Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis |
| title_sort | exploring the fractal parameters of urban growth and form with wave spectrum analysis |
| url | http://dx.doi.org/10.1155/2010/974917 |
| work_keys_str_mv | AT yanguangchen exploringthefractalparametersofurbangrowthandformwithwavespectrumanalysis |