{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T03:17:50Z","timestamp":1767842270075,"version":"3.49.0"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p> We experimentally demonstrate that both Voronoi diagram and its dual graph Delaunay triangulation are simultaneously constructed \u2014 for specific conditions \u2014 in cultures of plasmodium, a vegetative state of Physarum polycephalum. Every point of a given planar data set is represented by a tiny mass of plasmodium. The plasmodia spread from their initial locations but, in certain conditions, stop spreading when they encounter plasmodia originated from different locations. Thus space loci not occupied by the plasmodia represent edges of Voronoi diagram of the given planar set. At the same time, the plasmodia originating at neighboring locations form merging protoplasmic tubes, where the strongest tubes approximate Delaunay triangulation of the given planar set. The problems are solved by plasmodium only for limited data sets, however the results presented lay a sound ground for further investigations. <\/jats:p>","DOI":"10.1142\/s0218127409024682","type":"journal-article","created":{"date-parts":[[2009,12,15]],"date-time":"2009-12-15T06:45:55Z","timestamp":1260859555000},"page":"3109-3117","source":"Crossref","is-referenced-by-count":92,"title":["ON SIMULTANEOUS CONSTRUCTION OF VORONOI DIAGRAM AND DELAUNAY TRIANGULATION BY <i>PHYSARUM POLYCEPHALUM<\/i>"],"prefix":"10.1142","volume":"19","author":[{"given":"TOMOHIRO","family":"SHIRAKAWA","sequence":"first","affiliation":[{"name":"Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama, Kanagawa 226-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANDREW","family":"ADAMATZKY","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of the West of England, Bristol BS16 1QU, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YUKIO-PEGIO","family":"GUNJI","sequence":"additional","affiliation":[{"name":"Department of Earth and Planetary System Sciences, Graduate School of Science and Technology, Kobe University, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YOSHIHIRO","family":"MIYAKE","sequence":"additional","affiliation":[{"name":"Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Yokohama, Kanagawa 226-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1007\/s00114-007-0276-5"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1142\/S0129626407003150"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1108\/03684920810851168"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408021750"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1145\/116873.116880"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740401059X"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1038\/35035159"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/S0923-2508(01)01259-1"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/S0301-4622(01)00179-X"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1016\/S0301-4622(03)00189-3"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1098\/rspb.2004.2856"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1016\/j.bpc.2007.04.010"},{"key":"p_20","author":"Shirakawa T.","year":"2008","journal-title":"Int. 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