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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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    as
    1. He, Ji-Huan & Huang, Zhende, 2006. "A novel model for allometric scaling laws for different organs," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1108-1114.
    2. Kwon, Okyu, 2018. "Scaling laws between population and a public transportation system of urban buses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 209-214.
    3. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    4. Hernán D. Rozenfeld & Diego Rybski & Xavier Gabaix & Hernán A. Makse, 2011. "The Area and Population of Cities: New Insights from a Different Perspective on Cities," American Economic Review, American Economic Association, vol. 101(5), pages 2205-2225, August.
    5. Chen, Yanguang & Lin, Jingyi, 2009. "Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 615-629.
    6. TANNIER, Cécile & THOMAS, Isabelle & VUIDEL, Gilles & FRANKHAUSER, Pierre, 2011. "A fractal approach to identifying urban boundaries," LIDAM Reprints CORE 2297, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Bin Jiang & Junjun Yin, 2014. "Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features," Annals of the American Association of Geographers, Taylor & Francis Journals, vol. 104(3), pages 530-540, May.
    8. Kühnert, Christian & Helbing, Dirk & West, Geoffrey B., 2006. "Scaling laws in urban supply networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 96-103.
    9. repec:cai:popine:popu_p1998_10n1_0240 is not listed on IDEAS
    10. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1997. "A General Model for the Origin of Allometric Scaling Laws in Biology," Working Papers 97-03-019, Santa Fe Institute.
    11. Brian J. Enquist & James H. Brown & Geoffrey B. West, 1998. "Allometric scaling of plant energetics and population density," Nature, Nature, vol. 395(6698), pages 163-165, September.
    12. José Lobo & Luís M A Bettencourt & Deborah Strumsky & Geoffrey B West, 2013. "Urban Scaling and the Production Function for Cities," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-10, March.
    13. Samaniego, Horacio & Moses, Melanie E., 2008. "Cities as Organisms: Allometric Scaling of Urban Road Networks," The Journal of Transport and Land Use, Center for Transportation Studies, University of Minnesota, vol. 1(1), pages 21-39.
    14. Lucien Benguigui & Daniel Czamanski & Maria Marinov & Yuval Portugali, 2000. "When and Where is a City Fractal?," Environment and Planning B, , vol. 27(4), pages 507-519, August.
    15. Chen, Yanguang & Zhou, Yixing, 2008. "Scaling laws and indications of self-organized criticality in urban systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 85-98.
    16. Chen, Yanguang, 2017. "Multi-scaling allometric analysis for urban and regional development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 673-689.
    17. Isabelle Thomas & Pierre Frankhauser & Benoit Frenay & Michel Verleysen, 2010. "Clustering Patterns of Urban Built-up Areas with Curves of Fractal Scaling Behaviour," Environment and Planning B, , vol. 37(5), pages 942-954, October.
    18. M. Batty & R. Carvalho & A. Hudson-Smith & R. Milton & D. Smith & P. Steadman, 2008. "Scaling and allometry in the building geometries of Greater London," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 303-314, June.
    19. 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.
    20. He, Ji-Huan, 2006. "An allometric scaling law between gray matter and white matter of cerebral cortex," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 864-867.
    21. Chen, Yanguang, 2014. "Urban chaos and replacement dynamics in nature and society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 373-384.
    22. Brian J. Enquist & James H. Brown & Geoffrey B. West, 1998. "Allometric Scaling of Plant Energetics and Population Density," Working Papers 98-11-104, Santa Fe Institute.
    23. Chen, Yanguang, 2012. "The mathematical relationship between Zipf’s law and the hierarchical scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3285-3299.
    24. Luís M A Bettencourt & José Lobo & Deborah Strumsky & Geoffrey B West, 2010. "Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-9, November.
    25. Chen, Yanguang, 2009. "Spatial interaction creates period-doubling bifurcation and chaos of urbanization," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1316-1325.
    26. Lucien Benguigui & Efrat Blumenfeld-Lieberthal & Daniel Czamanski, 2006. "The Dynamics of the Tel Aviv Morphology," Environment and Planning B, , vol. 33(2), pages 269-284, April.
    27. Chen, Yanguang, 2014. "An allometric scaling relation based on logistic growth of cities," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 65-77.
    28. Chen, Yanguang & Jiang, Shiguo, 2009. "An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 49-64.
    29. Peter B. Reich & Mark G. Tjoelker & Jose-Luis Machado & Jacek Oleksyn, 2006. "Universal scaling of respiratory metabolism, size and nitrogen in plants," Nature, Nature, vol. 439(7075), pages 457-461, January.
    30. Geoffrey B. West & James H. Brown & Brian J. Enquist, 1999. "The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms," Working Papers 99-07-047, Santa Fe Institute.
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