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 journalArticle

3 Citations (Scopus)

Abstract

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
Volume36
Issue number3
DOIs
Publication statusPublished - Jan 1 1995
Externally publishedYes

Fingerprint

cellular automata
Square Lattice
Cellular Automata
Configuration
configurations
Limit Cycle
Laurent Polynomials
cycles
Galois field
polynomials
Cell
cells

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Period lengths of cellular automata on square lattices with rule 90. / Kawahara, Yasuo; Kumamoto, Satoru; Mizoguchi, Yoshihiro; Nohmi, Masaya; Ohtsuka, Hiroshi; Shoudai, Takayoshi.

In: Journal of Mathematical Physics, Vol. 36, No. 3, 01.01.1995, p. 1435-1456.

Research output: Contribution to journalArticle

Kawahara, Y, Kumamoto, S, Mizoguchi, Y, Nohmi, M, Ohtsuka, H & Shoudai, T 1995, 'Period lengths of cellular automata on square lattices with rule 90', Journal of Mathematical Physics, vol. 36, no. 3, pp. 1435-1456. https://doi.org/10.1063/1.531132
Kawahara, Yasuo ; Kumamoto, Satoru ; Mizoguchi, Yoshihiro ; Nohmi, Masaya ; Ohtsuka, Hiroshi ; Shoudai, Takayoshi. / Period lengths of cellular automata on square lattices with rule 90. In: Journal of Mathematical Physics. 1995 ; Vol. 36, No. 3. pp. 1435-1456.
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