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Group-theoretic spectrum analysis of hexagonal city distributions in Southern Germany and Eastern USA

Author

Listed:
  • Ikeda, Kiyohiro
  • Murota, Kazuo
  • Takayama, Yuki
  • Kamei, Motohiro

Abstract

Hexagonal distributions of cities of various sizes in Southern Germany are envisaged in central place theory. Yet scientific verification of this theory has been lacking. To scientifically support this theory, we propose a group-theoretic double Fourier spectrum analysis procedure that can detect geometrical patterns in population distributions of cities. In addition to hexagonal patterns in the theory, we propose megalopolis patterns. Using this procedure, strong power spectra for megalopolis patterns were detected for population data in Southern Germany. Moreover, a gigantic hexagonal distribution of cities in Eastern USA was found to be an assemblage of megalopolis and hexagonal patterns. The amazing geometrical regularity of this distribution manifests the existence of these patterns in the real world, thereby underpinning central place theory.

Suggested Citation

  • Ikeda, Kiyohiro & Murota, Kazuo & Takayama, Yuki & Kamei, Motohiro, 2016. "Group-theoretic spectrum analysis of hexagonal city distributions in Southern Germany and Eastern USA," MPRA Paper 74567, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:74567
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    References listed on IDEAS

    as
    1. 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.
    2. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    3. Asim Ghosh & Arnab Chatterjee & Anindya S. Chakrabarti & Bikas K Chakrabarti, 2014. "Zipf's law in city size from a resource utilization model," Papers 1403.1822, arXiv.org, revised Oct 2014.
    4. Munz, M & Weidlich, W, 1990. "Settlement Formation: Part II: Numerical Simulation," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 24(3), pages 177-196.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    central place theory; group-theoretic bifurction theory; hexagonal patterns;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General

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