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Characterizing Growth and Form of Fractal Cities with Allometric Scaling Exponents

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  • Yanguang Chen

Abstract

Fractal growth is a kind of allometric growth, and the allometric scaling exponents can be employed to describe growing fractal phenomena such as cities. The spatial features of the regular fractals can be characterized by fractal dimension. However, for the real systems with statistical fractality, it is incomplete to measure the structure of scaling invariance only by fractal dimension. Sometimes, we need to know the ratio of different dimensions rather than the fractal dimensions themselves. A fractal-dimension ratio can make an allometric scaling exponent (ASE). As compared with fractal dimension, ASEs have three advantages. First, the values of ASEs are easy to be estimated in practice; second, ASEs can reflect the dynamical characters of system's evolution; third, the analysis of ASEs can be made through prefractal structure with limited scale. Therefore, the ASEs based on fractal dimensions are more functional than fractal dimensions for real fractal systems. In this paper, the definition and calculation method of ASEs are illustrated by starting from mathematical fractals, and, then, China's cities are taken as examples to show how to apply ASEs to depiction of growth and form of fractal cities.

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  • Yanguang Chen, 2010. "Characterizing Growth and Form of Fractal Cities with Allometric Scaling Exponents," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-22, September.
    • Handle: RePEc:hin:jnddns:194715
    DOI: 10.1155/2010/194715
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    Cited by:

    1. Chen, Jihong & Fei, Yijie & Wan, Zheng & Yang, Zaili & Li, Haobo & Choi, Kyoung-Suk & Xie, Xiaoke, 2020. "Allometric relationship and development potential comparison of ports in a regional cluster: A case study of ports in the Pearl River Delta in China," Transport Policy, Elsevier, vol. 85(C), pages 80-90.
    2. Chen, Yanguang, 2013. "A set of formulae on fractal dimension relations and its application to urban form," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 150-158.
    3. Chen, Yanguang, 2014. "An allometric scaling relation based on logistic growth of cities," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 65-77.
    4. Wang, Ping & Gu, Changgui & Yang, Huijie & Wang, Haiying, 2022. "The multi-scale structural complexity of urban morphology in China," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Chen, Yanguang, 2021. "Exploring the level of urbanization based on Zipf’s scaling exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    6. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    7. Chen, Yanguang, 2012. "Zipf’s law, 1/f noise, and fractal hierarchy," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 63-73.
    8. Haosu Zhao & Bart Julien Dewancker & Feng Hua & Junping He & Weijun Gao, 2020. "Restrictions of Historical Tissues on Urban Growth, Self-Sustaining Agglomeration in Walled Cities of Chinese Origin," Sustainability, MDPI, vol. 12(14), pages 1-29, July.

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