Time reverse automata patterns generated by Spencer-Brown's modulator: invertibility based on autopoiesis

Yukio Gunji, Takashi Nakamura

Research output: Contribution to journalArticle

13 Citations (Scopus)


In the present paper the self-consistency or operational closure of autopoiesis is described by introducing time explicitly. It is an extension of Spencer-Brown's idea of time, however. The definition of time is segregated into two parts, corresponding to the syntax and semantics of language, respectively. In this context, time reversibility is defined by the formalization of the relationship between time and self-consistency. This idea has also been discussed in the context of designation and/or naming. Here we will discuss it in the context of cellular automata and explain the structure of one-to-many type mappings. Our approach is the first attempt to extend autopoietic systems in terms of dynamics. It illustrates how to introduce an autopoietic time which looks irreversible, but without the concept of entropy.

Original languageEnglish
Pages (from-to)151-177
Number of pages27
Issue number3
Publication statusPublished - 1991



  • Cellular automata
  • Forward- and backward-time
  • Invertibility
  • Local and non-local computation
  • Modulator

ASJC Scopus subject areas

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

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