{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T15:05:17Z","timestamp":1762009517050,"version":"build-2065373602"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,12,30]]},"abstract":"<jats:p> 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. <\/jats:p>","DOI":"10.1142\/s0218127418300458","type":"journal-article","created":{"date-parts":[[2019,1,8]],"date-time":"2019-01-08T02:33:12Z","timestamp":1546914792000},"page":"1830045","source":"Crossref","is-referenced-by-count":8,"title":["Group-Theoretic Spectrum Analysis of Population Distribution in Southern Germany and Eastern USA"],"prefix":"10.1142","volume":"28","author":[{"given":"Kiyohiro","family":"Ikeda","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuki","family":"Takayama","sequence":"additional","affiliation":[{"name":"Institute of Science and Engineering, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikihisa","family":"Onda","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, Tohoku University, Aoba, Sendai 980-8579, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daisuke","family":"Murakami","sequence":"additional","affiliation":[{"name":"Department of Statistical Modeling, The Institute for Statistical Mathematics, Tachikawa, Tokyo 190-8562, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,1,7]]},"reference":[{"key":"S0218127418300458BIB001","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.66.026204"},{"key":"S0218127418300458BIB002","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0136248"},{"volume-title":"Fractal Cities","year":"1994","author":"Batty M.","key":"S0218127418300458BIB003"},{"key":"S0218127418300458BIB004","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/9399.001.0001"},{"key":"S0218127418300458BIB005","first-page":"1309","volume":"11","author":"B\u00e9nard H.","year":"1900","journal-title":"Rev. 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