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Generating Urban Forms from Diffusive Growth

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  • M Batty

    (Department of Town Planning, University of Wales at Cardiff, Cardiff CF1 3YN, Wales)

Abstract

In this paper, a formal model of diffusion-limited aggregation is presented which can be used to generate a continuum of urban forms from linear to concentric. A brief derivation of this continuum model is presented in terms of its relationship to potential theory, and a method for its solution is outlined. The forms produced by the model are subject to fractional power laws which relate the occupancy of sites and densities to distances. Fractal dimensions can be derived from these fractional powers, and conventional and fast methods of estimation are introduced. A large-scale simulation provides the baseline for comparison and its average fractal dimension is estimated as 1.701 ± 0.025 from thirty aggregates. The effect of constraining the physical limits of the lattice on which such aggregates are grown is explored and the model is then used to generate a continuum of forms determined by a control parameter which distorts the potential field of the model. A series of forms from the linear with fractal dimension close to 1 to the concentric with a fractal dimension near to 2, are grown. The model is then applied to urban development in the town of Cardiff and various simulations are attempted which point the way to further research.

Suggested Citation

  • M Batty, 1991. "Generating Urban Forms from Diffusive Growth," Environment and Planning A, , vol. 23(4), pages 511-544, April.
    • Handle: RePEc:sae:envira:v:23:y:1991:i:4:p:511-544
    DOI: 10.1068/a230511
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    Cited by:

    1. Jean Cavailhès & Pierre Frankhauser & Dominique Peeters & Isabelle Thomas, 2010. "Residential equilibrium in a multifractal metropolitan area," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 45(3), pages 681-704, December.
    2. Geoffrey Caruso & Gilles Vuidel & Jean Cavailhès & Pierre Frankhauser & Dominique Peeters & Isabelle Thomas, 2011. "Morphological similarities between DBM and a microeconomic model of sprawl," Journal of Geographical Systems, Springer, vol. 13(1), pages 31-48, March.
    3. Claes Andersson & Koen Frenken & Alexander Hellervik, 2006. "A Complex Network Approach to Urban Growth," Environment and Planning A, , vol. 38(10), pages 1941-1964, October.
    4. Sintes, Tomás & Moragues, E. & Traveset, A. & Rita, J., 2007. "Clonal growth dynamics of the invasive Carpobrotus affine acinaciformis in Mediterranean coastal systems: A non-linear model," Ecological Modelling, Elsevier, vol. 206(1), pages 110-118.
    5. Fei Liu & Qing Huang, 2019. "An Approach to Determining the Spatially Contiguous Zone of a Self-Organized Urban Agglomeration," Sustainability, MDPI, vol. 11(12), pages 1-16, June.
    6. Marco Criado & Antonio Martínez-Graña & Fernando Santos-Francés & Sergio Veleda & Caridad Zazo, 2017. "Multi-Criteria Analyses of Urban Planning for City Expansion: A Case Study of Zamora, Spain," Sustainability, MDPI, vol. 9(10), pages 1-18, October.

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