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Diffusion‐Limited Aggregation And The Fractal Nature Of Urban Growth

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  • A. Stewart Fotheringham
  • Michael Batty
  • Paul A. Longley

Abstract

ABSTRACT This paper introduces the mechanism of diffusion‐limited aggregation (DLA) as a new basis for understanding urban growth, Through DLA, urban form is related to the processes of rural‐to‐urban migration and contiguous growth. However, despite being bused on very simple principles, DLA simulations are shown to have properties found in most urban areas such as negative density gradients and ordered chaotic structures. The paper examines variations in the simulated urban structures produced by different assumptions regarding the rural‐to‐urban migration mechanism. An important finding is that urban density gradients can occur independently of the generally accepted reasons for their presence. We also comment on boundary effects in the measurement of urban density gradients.

Suggested Citation

  • A. Stewart Fotheringham & Michael Batty & Paul A. Longley, 1989. "Diffusion‐Limited Aggregation And The Fractal Nature Of Urban Growth," Papers in Regional Science, Wiley Blackwell, vol. 67(1), pages 55-69, January.
    • Handle: RePEc:bla:presci:v:67:y:1989:i:1:p:55-69
    DOI: 10.1111/j.1435-5597.1989.tb01182.x
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    Cited by:

    1. 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.
    2. 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.
    3. Chen, Yanguang, 2009. "Analogies between urban hierarchies and river networks: Fractals, symmetry, and self-organized criticality," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1766-1778.
    4. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    5. Chen, Yanguang & Feng, Jian, 2012. "Fractal-based exponential distribution of urban density and self-affine fractal forms of cities," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1404-1416.
    6. Michael Batty & Kwang Sik Kim, 1992. "Form Follows Function: Reformulating Urban Population Density Functions," Urban Studies, Urban Studies Journal Limited, vol. 29(7), pages 1043-1069, October.
    7. Jian Feng & Yanguang Chen, 2021. "Modeling Urban Growth and Socio-Spatial Dynamics of Hangzhou, China: 1964–2010," Sustainability, MDPI, vol. 13(2), pages 1-25, January.
    8. Yunfei Li & Diego Rybski & Jürgen P. Kropp, 2021. "Singularity cities," Environment and Planning B, , vol. 48(1), pages 43-59, January.

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