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Urban Settlement Transitions

Author

Listed:
  • Claes Andersson

    (EES-6 MS T003, Los Alamos National Laboratory, Los Alamos, NM 87545, USA, and Physical Resource Theory, Göteborg University/Chalmers University of Technology, 41296 Göteborg, Sweden)

  • Steen Rasmussen

    (EES-6 MS T003 and T-CNLS MS B258, Los Alamos National Laboratory, Los Alamos, NM 87545, USA, and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA)

  • Roger White

    (Department of Geography, Memorial University, St. John's, Newfoundland A1B 3X9, Canada, and RIKS, Postbox 463, 6200 AL Maastricht, The Netherlands)

Abstract

Urban growth dynamics attracts the efforts of scientists from many different disciplines with objectives ranging from theoretical understanding to the development of carefully tuned realistic models that can serve as planning and policy tools. Theoretical models are often abstract and of limited applied value while most applied models yield little theoretical understanding. Here we present a mathematically well-defined model based on a modified Markov random field with lattice-wide interactions that produces realistic growth patterns as well as behavior observed in a range of other models based on diffusion-limited aggregation, cellular automata, and similar models. We investigate the framework's ability to generate plausible patterns using minimal assumptions about the interaction parameters since the tuning and specific definition of these are outside of the scope of this paper. Typical universality classes of the simulated dynamics and the phase transitions between them are discussed in the context of real urban dynamics. Using suitability data derived from topography, we produce configurations quantitatively similar to real cities. Also, an intuitive class of interaction rules is found to produce fractal configurations, not unlike vascular systems, that resemble urban sprawl. The dynamics are driven by interactions, depicting human decisions, between all lattice points. This is realized in a computationally efficient way using a mean-field renormalization (area average) approach. The model provides a mathematically transparent framework to which any level of detail necessary for actual urban planning application can be added.

Suggested Citation

  • Claes Andersson & Steen Rasmussen & Roger White, 2002. "Urban Settlement Transitions," Environment and Planning B, , vol. 29(6), pages 841-865, December.
    • Handle: RePEc:sae:envirb:v:29:y:2002:i:6:p:841-865
    DOI: 10.1068/b12813
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    References listed on IDEAS

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    1. R White & G Engelen, 1993. "Cellular Automata and Fractal Urban Form: A Cellular Modelling Approach to the Evolution of Urban Land-Use Patterns," Environment and Planning A, , vol. 25(8), pages 1175-1199, August.
    2. Benguigui, L., 1995. "A new aggregation model. Application to town growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(1), pages 13-26.
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    Cited by:

    1. Yanguang Chen & Yixing Zhou, 2006. "Reinterpreting Central Place Networks Using Ideas from Fractals and Self-Organized Criticality," Environment and Planning B, , vol. 33(3), pages 345-364, June.
    2. 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.
    3. Alberto Vancheri & Paolo Giordano & Denise Andrey & Sergio Albeverio, 2008. "Urban Growth Processes Joining Cellular Automata and Multiagent Systems. Part 1: Theory and Models," Environment and Planning B, , vol. 35(4), pages 723-739, August.
    4. 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.

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