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Urban Growth and Form: Scaling, Fractal Geometry, and Diffusion-Limited Aggregation

Author

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  • M Batty
  • P Longley
  • S Fotheringham

    (National Center for Geographic Information and Analysis, and Department of Geography, State University of New York at Buffalo, Buffalo, NY 14260, USA)

Abstract

In this paper, we propose a model of growth and form in which the processes of growth are intimately linked to the resulting geometry of the system. The model, first developed by Witten and Sander and referred to as the diffusion-limited aggregation or DLA model, generates highly ramified tree-like clusters of particles, or populations, with evident self-similarity about a fixed point. The extent to which such clusters fill space is measured by their fractal dimension which is estimated from scaling relationships linking population and density to distances within the cluster. We suggest that this model provides a suitable baseline for the development of models of urban structure and density which manifest similar scaling properties. A typical DLA simulation is presented and a variety of measures of its structure and dynamics are developed. These same measures are then applied to the urban growth and form of Taunton, a small market town in South West England, and important similarities and differences with the DLA simulation are discussed. We suggest there is much potential in extending analogies between DLA and urban form, and we also suggest future research directions involving variants of DLA and better measures of urban density.

Suggested Citation

  • M Batty & P Longley & S Fotheringham, 1989. "Urban Growth and Form: Scaling, Fractal Geometry, and Diffusion-Limited Aggregation," Environment and Planning A, , vol. 21(11), pages 1447-1472, November.
    • Handle: RePEc:sae:envira:v:21:y:1989:i:11:p:1447-1472
    DOI: 10.1068/a211447
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    1. repec:brs:ecchap:16 is not listed on IDEAS
    2. repec:rri:bkchap:16 is not listed on IDEAS
    3. Grant I. Thrall, 1987. "Land Use and Urban Form," Wholbk, Regional Research Institute, West Virginia University, number 16, July-Sept.
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    Cited by:

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    2. James PL Tan, 2016. "A Generalized Population Dynamics Model of a City and an Algorithm for Engineering Regime Shifts," Papers 1612.08338, arXiv.org.
    3. Lang, Wei & Long, Ying & Chen, Tingting & Li, Xun, 2019. "Reinvestigating China’s urbanization through the lens of allometric scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1429-1439.
    4. Xia, Linlin & Zhang, Yan & Sun, Xiaoxi & Li, Jinjian, 2017. "Analyzing the spatial pattern of carbon metabolism and its response to change of urban form," Ecological Modelling, Elsevier, vol. 355(C), pages 105-115.
    5. Netto, Vinicius M. & Brigatti, Edgardo & Meirelles, João & Ribeiro, Fabiano L. & Pace, Bruno & Cacholas, Caio & Sanches, Patricia Mara, 2018. "Cities, from information to interaction," SocArXiv jgz5d, Center for Open Science.
    6. Paul M. Torrens, 2016. "Exploring behavioral regions in agents’ mental maps," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 57(2), pages 309-334, November.
    7. 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.
    8. Doménech-Carbó, Antonio, 2019. "Rise and fall of historic tram networks: Logistic approximation and discontinuous events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 315-323.
    9. Erjia Ge & Yee Leung, 2013. "Detection of crossover time scales in multifractal detrended fluctuation analysis," Journal of Geographical Systems, Springer, vol. 15(2), pages 115-147, April.

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