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Preliminary Evidence for a Theory of the Fractal City

Author

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  • M Batty

    (Centre for Advanced Spatial Analysis, University College London, 1-19 Torrington Place, London WC1E 6BT, England)

  • Y Xie

    (Department of Geography and Geology, Eastern Michigan University, Ypsilanti, MI 48179, USA)

Abstract

In this paper, we argue that the geometry of urban residential development is fractal. Both the degree to which space is filled and the rate at which it is filled follow scaling laws which imply invariance of function, and self-similarity of urban form across scale. These characteristics are captured in population density functions based on inverse power laws whose parameters are fractal dimensions. First we outline the relevant elements of the theory in terms of scaling relations and then we introduce two methods for estimating fractal dimension based on varying the size of cities and the scale at which their form is detected. Exact and statistical estimation techniques are applied to each method respectively generating dimensions which measure the extent and the rate of space filling. These methods are then applied to residential development patterns in six industrial cities in the northeastern United States, with an innovative data source from the TIGER/Line files. The results support the theory of the fractal city outlined in books by Batty and Longley and Frankhauser, but with the clear conclusion that different scale and estimation techniques generate different types of fractal dimension.

Suggested Citation

  • M Batty & Y Xie, 1996. "Preliminary Evidence for a Theory of the Fractal City," Environment and Planning A, , vol. 28(10), pages 1745-1762, October.
    • Handle: RePEc:sae:envira:v:28:y:1996:i:10:p:1745-1762
    DOI: 10.1068/a281745
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    References listed on IDEAS

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    1. T V Mesev & P A Longley & M Batty & Y Xie, 1995. "Morphology from Imagery: Detecting and Measuring the Density of Urban Land Use," Environment and Planning A, , vol. 27(5), pages 759-780, May.
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    Cited by:

    1. Heitor Reis, A., 2008. "Constructal view of the scaling laws of street networks — the dynamics behind geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 617-622.
    2. Carvalho, Rui & Penn, Alan, 2004. "Scaling and universality in the micro-structure of urban space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 539-547.
    3. Zhonghao Zhang & Rui Xiao & Weixuan Yu & Yue Liu & Meng Lin & Meng Wang, 2017. "Characterizing Factors Associated with Built-Up Land Expansion in Urban and Non-Urban Areas from a Morphological Perspective," Sustainability, MDPI, vol. 9(8), pages 1-15, August.
    4. Isabelle Thomas & Pierre Frankhauser & Dominique Badariotti, 2012. "Comparing the fractality of European urban neighbourhoods: do national contexts matter?," Journal of Geographical Systems, Springer, vol. 14(2), pages 189-208, April.
    5. François Sémécurbe & Cécile Tannier & Stéphane G. Roux, 2019. "Applying two fractal methods to characterise the local and global deviations from scale invariance of built patterns throughout mainland France," Journal of Geographical Systems, Springer, vol. 21(2), pages 271-293, June.

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