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Fractal Modeling and Fractal Dimension Description of Urban Morphology

Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
Entropy 2020, 22(9), 961; https://doi.org/10.3390/e22090961
Received: 28 July 2020 / Revised: 26 August 2020 / Accepted: 27 August 2020 / Published: 30 August 2020
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a scale-dependence measure, which indicates the scale-free distribution of urban patterns. Thus, the urban description based on characteristic lengths should be replaced by urban characterization based on scaling. Fractal geometry is one powerful tool for the scaling analysis of cities. Fractal parameters can be defined by entropy and correlation functions. However, the question of how to understand city fractals is still pending. By means of logic deduction and ideas from fractal theory, this paper is devoted to discussing fractals and fractal dimensions of urban landscape. The main points of this work are as follows. Firstly, urban form can be treated as pre-fractals rather than real fractals, and fractal properties of cities are only valid within certain scaling ranges. Secondly, the topological dimension of city fractals based on the urban area is 0; thus, the minimum fractal dimension value of fractal cities is equal to or greater than 0. Thirdly, the fractal dimension of urban form is used to substitute the urban area, and it is better to define city fractals in a two-dimensional embedding space; thus, the maximum fractal dimension value of urban form is 2. A conclusion can be reached that urban form can be explored as fractals within certain ranges of scales and fractal geometry can be applied to the spatial analysis of the scale-free aspects of urban morphology. View Full-Text
Keywords: fractal; fractal dimension; pre-fractal; multifractals; scaling range; entropy; spatial correlation; fractal cities fractal; fractal dimension; pre-fractal; multifractals; scaling range; entropy; spatial correlation; fractal cities
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MDPI and ACS Style

Chen, Y. Fractal Modeling and Fractal Dimension Description of Urban Morphology. Entropy 2020, 22, 961. https://doi.org/10.3390/e22090961

AMA Style

Chen Y. Fractal Modeling and Fractal Dimension Description of Urban Morphology. Entropy. 2020; 22(9):961. https://doi.org/10.3390/e22090961

Chicago/Turabian Style

Chen, Yanguang. 2020. "Fractal Modeling and Fractal Dimension Description of Urban Morphology" Entropy 22, no. 9: 961. https://doi.org/10.3390/e22090961

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