On simultaneous construction of Voronoi diagram and delaunay triangulation by physarum polycephalum

Tomohiro Shirakawa*, Andrew Adamatzky, Yukio Pegio Gunji, Yoshihiro Miyake

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)


We experimentally demonstrate that both Voronoi diagram and its dual graph Delaunay triangulation are simultaneously constructed for specific conditions 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.

Original languageEnglish
Pages (from-to)3109-3117
Number of pages9
JournalInternational Journal of Bifurcation and Chaos
Issue number9
Publication statusPublished - 2009 Sept
Externally publishedYes


  • Delaunay triangulation
  • Pattern formation
  • Physarum polycephalum
  • Plasmodium
  • Unconventional computing
  • Voronoi diagram

ASJC Scopus subject areas

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


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