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Geography in motion: Hexagonal spatial systems in fuzzy gravitation

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Listed:
  • MichaÅ‚ Banaszak
  • MichaÅ‚ Dziecielski
  • Peter Nijkamp
  • Waldemar Ratajczak

Abstract

The dynamics of spatial hierarchical processes displays fascinating images of the evolution of attraction basins of towns. Assuming in the present paper a random character of such complex processes, gravitational modeling is employed to depict changes in the nature of fuzzy boundaries between attraction basins in a hexagonal world, i.e. the geographical pattern central in the renowned and influential Christaller–Lösch central place theory in geography. The paper presents various interesting stylized maps of such stochastic processes. Our findings demonstrate that the collective behavior of actors in geographic space shows a white noise pattern that mirrors a fuzzy gravitation towards large population concentrations. These results support the validity of the conventional central place theory.

Suggested Citation

  • MichaÅ‚ Banaszak & MichaÅ‚ 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.
    • Handle: RePEc:sae:envira:v:51:y:2019:i:2:p:393-402
    DOI: 10.1177/0308518X18790249
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    References listed on IDEAS

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    1. Rikard Forslid & Gianmarco I.P. Ottaviano, 2003. "An analytically solvable core-periphery model," Journal of Economic Geography, Oxford University Press, vol. 3(3), pages 229-240, July.
    2. Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476, April.
    3. Peter Nijkamp & Adam Rose & Karima Kourtit (ed.), 2015. "Regional Science Matters," Springer Books, Springer, edition 127, number 978-3-319-07305-7, January.
    4. Jan Tinbergen, 1961. "The Spatial Dispersion of Production : A Hypothesis," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 97(IV), pages 412-419, December.
    5. Kiyohiro Ikeda & Kazuo Murota & Yuki Takayama, 2017. "Stable Economic Agglomeration Patterns In Two Dimensions: Beyond The Scope Of Central Place Theory," Journal of Regional Science, Wiley Blackwell, vol. 57(1), pages 132-172, January.
    6. 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.
    7. Aura Reggiani & Peter Nijkamp (ed.), 2009. "Complexity and Spatial Networks," Advances in Spatial Science, Springer, number 978-3-642-01554-0.
    8. 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.
    9. Brakman,Steven & Garretsen,Harry & van Marrewijk,Charles, 2009. "The New Introduction to Geographical Economics," Cambridge Books, Cambridge University Press, number 9780521875325, December.
    10. Lucien Benguigui & Efrat Blumenfeld-Lieberthal & Michael Batty, 2009. "Macro and Micro Dynamics of the City Size Distribution," Advances in Spatial Science, in: Aura Reggiani & Peter Nijkamp (ed.), Complexity and Spatial Networks, chapter 0, pages 33-49, Springer.
    11. Czyż Teresa & Hauke Jan, 2015. "Entropy In Regional Analysis," Quaestiones Geographicae, Sciendo, vol. 34(4), pages 69-78, December.
    12. Alan Wilson, 2009. "The “Thermodynamics” of the City," Advances in Spatial Science, in: Aura Reggiani & Peter Nijkamp (ed.), Complexity and Spatial Networks, chapter 0, pages 11-31, Springer.
    13. Haynes, Kingsley E. & Storbeck, James E., 1978. "The entropy paradox and the distribution of urban population," Socio-Economic Planning Sciences, Elsevier, vol. 12(1), pages 1-6.
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