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Reinterpreting central place networks using ideas from fractals and self-organized criticality

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  • Yanguang Chen
  • Yixing Zhou

Abstract

The basic rules of central place networks are abstracted and formulated as three geometric series scaling laws, which can be transformed into several power laws associated with fractal structure. The scaling laws might be the Rosetta Stone to understand the complexity of human geographical systems because they take the form of Horton and Strahler’s laws in geomorphology and Gutenberg and Richter’s laws in seismology indicative of fractals and self-organized criticality (SOC). An empirical analysis is conducted with the use of data from southern Germany, given by Christaller. The fractal dimensions, D f , of four systems are calculated as follows: D f is 1.733 for Munich, 1.685 for Nuremberg, 1.837 for Stuttgart, and 1.481 for Frankfurt. SOC theory is employed to interpret the fractality of central places, and the power laws are seen as signatures of feasible optimality, thus yielding further support to the suggestion that optimality of the system as a whole explains the dynamic origin of fractal forms in nature.

Suggested Citation

  • Yanguang Chen & Yixing Zhou, 2006. "Reinterpreting central place networks using ideas from fractals and self-organized criticality," Environment and Planning B: Planning and Design, Pion Ltd, London, vol. 33(3), pages 345-364, May.
  • Handle: RePEc:pio:envirb:v:33:y:2006:i:3:p:345-364
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    Cited by:

    1. Chen, Yanguang, 2014. "Multifractals of central place systems: Models, dimension spectrums, and empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 266-282.
    2. Heitor Reis, A., 2008. "Constructal view of the scaling laws of street networks — the dynamics behind geometry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 617-622.
    3. Guido Ferilli & Pier Luigi Sacco & Massimo Buscema & Giorgio Tavano Blessi, 2015. "Understanding Cultural Geography as a Pseudo-Diffusion Process: The Case of the Veneto Region," Economies, MDPI, Open Access Journal, vol. 3(2), pages 1-28, June.

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