Group-Theoretic Spectrum Analysis of Population Distribution in Southern Germany and Eastern USA

Kiyohiro Ikeda, Yuki Takayama, Mikihisa Onda, Daisuke Murakami

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Self-organization of hexagonal distributions of cities of various sizes in Southern Germany is envisaged in central place theory. Yet scientific verification of this theory has been lacking over the years. To scientifically support this theory, we propose a group-theoretic double Fourier spectrum analysis procedure that can detect self-organizing patterns bifurcating from a uniform state. This procedure is reinforced by the optimization of the choice of an analysis domain and the spatial eigen-decomposition to capture agglomeration effects. Strong power spectra for hexagonal networks of cities were detected by the procedure for population data in Southern Germany. Moreover, a gigantic hexagonal distribution of cities in Eastern USA was found as an assemblage of a series of hexagonal networks. The amazing geometrical regularity observed in this distribution manifests the existence of such distribution in the real world, thereby underpinning central place theory.

Original languageEnglish
Article number18300458
JournalInternational Journal of Bifurcation and Chaos
Issue number14
Publication statusPublished - 2018 Dec 30


  • Bifurcation
  • central place theory
  • city distribution
  • group-theoretic analysis
  • hexagons
  • self-organization
  • spectrum analysis

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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