Pigment color patterns of molluscs as an autonomous process generated by asynchronous automata

Yukio Gunji*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


Pigment color patterns of molluscs are studied from the viewpoint of autonomy. Brownian algebra developed by Spencer-Brown (1969) is extensively used for the expression of cellular-automaton rules. When asynchronous updating is introduced for the transition of cellular automata, various kinds of patterns such as traveling waves, kinks, oscillatory local patterns etc. are generated from the same transitional rule. The type of patterns depends more sensitively on the asynchronous updating relationship rather than the transitional rule itself. Therefore, pattern changes in ontogeny can be explained without any changes in transitional rules or reaction processes. It is proposed that asynchronousness is intrinsic to living systems and that recognition of the intrinsic time is essential in understanding living systems.

Original languageEnglish
Pages (from-to)317-334
Number of pages18
Issue number4
Publication statusPublished - 1990
Externally publishedYes


  • Asynchronous updating
  • Autonomy
  • Brownian algebra
  • Cellular automata
  • Pigmentation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics


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