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Hexagonal distributions of cities in Southern Germany and Eastern USA: Group-theoretic spectrum analysis

Ikeda, Kiyohiro and Murota, Kazuo and Takayama, Yuki and Kamei, Motohiro (2017): Hexagonal distributions of cities in Southern Germany and Eastern USA: Group-theoretic spectrum analysis.

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Abstract

Cities in Southern Germany are envisaged to form hexagonal distributions in central place theory; however, rigorous verification of this theory has been lacking over years. To support this theory, we introduce a group-theoretic Fourier spectrum analysis that can detect geometrical patterns of cities based on the statistical population data. In addition to hexagonal patterns in the theory, we propose a core--satellite pattern. Using this analysis, we detected a strong power spectrum for this pattern for population data in Southern Germany. Moreover, a gigantic hexagonal distribution of cities in Eastern USA was found to be an assemblage of the core--satellite and hexagonal patterns. The amazing geometrical regularity of this distribution implies the existence of such patterns in the real world, thereby underpinning the theory.

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