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Self-Organisation in Spatial Systems—From Fractal Chaos to Regular Patterns and Vice Versa

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  • Michal Banaszak
  • Michal Dziecielski
  • Peter Nijkamp
  • Waldemar Ratajczak

Abstract

This study offers a new perspective on the evolutionary patterns of cities or urban agglomerations. Such developments can range from chaotic to fully ordered. We demonstrate that in a dynamic space of interactive human behaviour cities produce a wealth of gravitational attractors whose size and shape depend on the resistance of space emerging inter alia from transport friction costs. This finding offers original insights into the complex evolution of spatial systems and appears to be consistent with the principles of central place theory known from the spatial sciences and geography. Our approach is dynamic in nature and forms a generalisation of hierarchical principles in geographic space.

Suggested Citation

  • Michal Banaszak & Michal Dziecielski & Peter Nijkamp & Waldemar Ratajczak, 2015. "Self-Organisation in Spatial Systems—From Fractal Chaos to Regular Patterns and Vice Versa," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-13, September.
    • Handle: RePEc:plo:pone00:0136248
    DOI: 10.1371/journal.pone.0136248
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    References listed on IDEAS

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    1. Bernard Fingleton (ed.), 2007. "New Directions in Economic Geography," Books, Edward Elgar Publishing, number 3818.
    2. Philip McCann, 2005. "Transport costs and new economic geography," Journal of Economic Geography, Oxford University Press, vol. 5(3), pages 305-318, June.
    3. Bernard Fingleton, 2007. "New Economic Geography: Some Preliminaries," Chapters, in: Bernard Fingleton (ed.), New Directions in Economic Geography, chapter 1, Edward Elgar Publishing.
    4. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    5. Aura Reggiani & Peter Nijkamp (ed.), 2009. "Complexity and Spatial Networks," Advances in Spatial Science, Springer, number 978-3-642-01554-0, Fall.
    6. Aura Reggiani, 2009. "From Complexity to Simplicity," Advances in Spatial Science, in: Aura Reggiani & Peter Nijkamp (ed.), Complexity and Spatial Networks, chapter 0, pages 275-284, Springer.
    7. Brakman,Steven & Garretsen,Harry & van Marrewijk,Charles, 2009. "The New Introduction to Geographical Economics," Cambridge Books, Cambridge University Press, number 9780521875325, December.
    8. Marta C. González & César A. Hidalgo & Albert-László Barabási, 2009. "Understanding individual human mobility patterns," Nature, Nature, vol. 458(7235), pages 238-238, March.
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    Cited by:

    1. Kiyohiro Ikeda & Minoru Osawa & Yuki Takayama, 2022. "Time Evolution of City Distributions in Germany," Networks and Spatial Economics, Springer, vol. 22(1), pages 125-151, March.
    2. Michał Banaszak & Michał Dziecielski & Peter Nijkamp & Waldemar Ratajczak, 2019. "Geography in motion: Hexagonal spatial systems in fuzzy gravitation," Environment and Planning A, , vol. 51(2), pages 393-402, March.
    3. Karima Kourtit & Peter Nijkamp & Soushi Suzuki, 2021. "The science of space: new endeavours in regional science," Asia-Pacific Journal of Regional Science, Springer, vol. 5(1), pages 149-153, February.

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