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Self-organized criticality and urban development

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  • Michael Batty
  • Yichun Xie

Abstract

Urban society is undergoing as profound a spatial transformation as that associated with the emergence of the industrial city two centuries ago. To describe and measure this transition, we introduce a new theory based on the concept that large-scale, complex systems composed of many interacting elements, show a surprising degree of resilience to change, holding themselves at critical levels for long periods until conditions emerge which move the system, often abruptly, to a new threshold. This theory is called ‘self-organized criticality’; it is consistent with systems in which global patterns emerge from local action which is the hallmark of self-organization, and it is consistent with developments in system dynamics and their morphology which find expression in fractal geometry and weak chaos theory. We illustrate the theory using a unique space–time series of urban development for Buffalo, Western New York, which contains the locations of over one quarter of a million sites coded by their year of construction and dating back to 1773, some 60 years before the city began to develop. We measure the emergence and growth of the city using urban density functions from which measures of fractal dimension are used to construct growth paths of the way the city has grown to fill its region. These phase portraits suggest the existence of transitions between the frontier, the settled agricultural region, the centralized industrial city and the decentralized postindustrial city, and our analysis reveals that Buffalo has maintained itself at a critical threshold since the emergence of the automobile city some 70 years ago. Our implied speculation is: how long will this kind of urban form be maintained in the face of seemingly unstoppable technological change?

Suggested Citation

  • Michael Batty & Yichun Xie, 1999. "Self-organized criticality and urban development," Discrete Dynamics in Nature and Society, Hindawi, vol. 3, pages 1-16, January.
  • Handle: RePEc:hin:jnddns:694059
    DOI: 10.1155/S1026022699000151
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    Citations

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    Cited by:

    1. Chen, Yanguang, 2013. "Fractal analytical approach of urban form based on spatial correlation function," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 47-60.
    2. Tadić, Bosiljka & Mitrović Dankulov, Marija & Melnik, Roderick, 2023. "Evolving cycles and self-organised criticality in social dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Fraiman, Daniel, 2022. "A self-organized criticality participative pricing mechanism for selling zero-marginal cost products," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Torres-Rojo, Juan Manuel & Francisco-Cruz, Carlos Alberto & Islas-Aguirre, Juan Francisco & Ramírez-Fuentes, Grodecz Alfredo & Pérez-Sosa, Leonardo, 2020. "A scale invariant model for the expansion of agricultural land and government spending on the agricultural sector," Land Use Policy, Elsevier, vol. 92(C).
    5. 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.
    6. Chen, Yanguang & Zhou, Yixing, 2008. "Scaling laws and indications of self-organized criticality in urban systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 85-98.
    7. 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.
    8. Song, Zhijun & Jin, Wenxuan & Jiang, Guanghui & Li, Sichun & Ma, Wenqiu, 2021. "Typical and atypical multifractal systems of urban spaces—using construction land in Zhengzhou from 1988 to 2015 as an example," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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