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Box-Counting Dimension of Fractal Urban Form: Stability Issues and Measurement Design

Box-Counting Dimension of Fractal Urban Form: Stability Issues and Measurement Design

Shiguo Jiang, Desheng Liu
Copyright: © 2012 |Volume: 3 |Issue: 3 |Pages: 23
ISSN: 1947-3087|EISSN: 1947-3079|EISBN13: 9781466610910|DOI: 10.4018/jalr.2012070104
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MLA

Jiang, Shiguo, and Desheng Liu. "Box-Counting Dimension of Fractal Urban Form: Stability Issues and Measurement Design." IJALR vol.3, no.3 2012: pp.41-63. http://doi.org/10.4018/jalr.2012070104

APA

Jiang, S. & Liu, D. (2012). Box-Counting Dimension of Fractal Urban Form: Stability Issues and Measurement Design. International Journal of Artificial Life Research (IJALR), 3(3), 41-63. http://doi.org/10.4018/jalr.2012070104

Chicago

Jiang, Shiguo, and Desheng Liu. "Box-Counting Dimension of Fractal Urban Form: Stability Issues and Measurement Design," International Journal of Artificial Life Research (IJALR) 3, no.3: 41-63. http://doi.org/10.4018/jalr.2012070104

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Abstract

The difficulty to obtain a stable estimate of fractal dimension for stochastic fractal (e.g., urban form) is an unsolved issue in fractal analysis. The widely used box-counting method has three main issues: 1) ambiguities in setting up a proper box cover of the object of interest; 2) problems of limited data points for box sizes; 3) difficulty in determining the scaling range. These issues lead to unreliable estimates of fractal dimensions for urban forms, and thus cast doubt on further analysis. This paper presents a detailed discussion of these issues in the case of Beijing City. The authors propose corresponding improved techniques with modified measurement design to address these issues: 1) rectangular grids and boxes setting up a proper box cover of the object; 2) pseudo-geometric sequence of box sizes providing adequate data points to study the properties of the dimension profile; 3) generalized sliding window method helping to determine the scaling range. The authors’ method is tested on a fractal image (the Vicsek prefractal) with known fractal dimension and then applied to real city data. The results show that a reliable estimate of box dimension for urban form can be obtained using their method.

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