Period lengths of cellular automata on square lattices with rule 90

Yasuo Kawahara, Satoru Kumamoto, Yoshihiro Mizoguchi, Masaya Nohmi, Hiroshi Ohtsuka, Takayoshi Shoudai

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This paper studies two-dimensional cellular automata ca-90(m,n) having states 0 and 1 and working on a square lattice of size (m-1)x(n-1). All their dynamics, driven by the local transition rule 90, can be simply formulated by representing their configurations with Laurent polynomials over a finite field F2={0,1}. The initial configuration takes the next configuration to a particular configuration whose cells all have the state 1. This paper answers the question of whether the initial configuration lies on a limit cycle or not, and, if that is the case, some properties on period lengths of such limit cycles are studied.

Original languageEnglish
Pages (from-to)1435-1456
Number of pages22
JournalJournal of Mathematical Physics
Issue number3
Publication statusPublished - 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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