Q-VFCA: Q-state vector-valued fuzzy cellular automata

Yuki Nishida, Sennosuke Watanabe, Akiko Fukuda, Yoshihide Watanabe

Research output: Contribution to journalArticlepeer-review

Abstract

Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper, we first develop a new fuzzification methodology for q-state CA. It is based on the vector representation of q-state CA, that is, the q-states are assigned to the standard basis vectors of the qdimensional real space and the local rule can be expressed by a tuple of q polynomials. Then, the q-state vector-valued fuzzy CA are defined by expanding the set of the states to the convex hull of the standard basis vectors in the q-dimensional real space. The vector representation of states enables us to enumerate the number-conserving rules of 3-state vector-valued fuzzy CA in a systematic way.

37B15, 68Q80

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2020 Feb 7

Keywords

  • Cellular automata
  • Conservation law
  • Fuzzy cellular automata
  • Number-conserving rule
  • Periodic boundary condition
  • Vector-valued cellular automata

ASJC Scopus subject areas

  • General

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