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Fractal dimensions derived from spatial allometric scaling of urban form

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  • Chen, Yanguang
  • Wang, Yihan
  • Li, Xijing

Abstract

Allometric scaling of cities is associated with fractals, and can be divided into three categories: longitudinal allometry, transversal allometry, and spatial allometry. There are many studies on the first two types, but few reports on the last one. This paper is devoted to exploring the fractal dimension proceeding from urban spatial allometry. The improved city clustering algorithm is used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the different spatial measurements within the series of boundary curves of a city follow allometric scaling law, which indicates spatial allometry of cities. Three fractal dimensions can be derived from the spatial allometry and the basic property of the new fractal parameters can be revealed by theoretical reasoning and empirical analysis of urban traffic network. The main findings are as follows. First, the fractal dimension values of traffic lines are higher than those of traffic nodes. Second, the fractal dimension values based on variable boundaries are lower than those based on the concentric circles. Conclusions can be reached that the fractal dimensions coming from spatial allometry are a type of correlation dimension rather than capacity dimension, and the relative growth rate of traffic points is greater than that of traffic nodes. This study provides new way of understanding allometry, fractals, scaling, and complex network in urban systems.

Suggested Citation

  • Chen, Yanguang & Wang, Yihan & Li, Xijing, 2019. "Fractal dimensions derived from spatial allometric scaling of urban form," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 122-134.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:122-134
    DOI: 10.1016/j.chaos.2019.05.029
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