### 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 F_{2}={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 language | English |
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Pages (from-to) | 1435-1456 |

Number of pages | 22 |

Journal | Journal of Mathematical Physics |

Volume | 36 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1995 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*36*(3), 1435-1456. https://doi.org/10.1063/1.531132

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

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 36, no. 3, pp. 1435-1456. https://doi.org/10.1063/1.531132

}

TY - JOUR

T1 - Period lengths of cellular automata on square lattices with rule 90

AU - Kawahara, Yasuo

AU - Kumamoto, Satoru

AU - Mizoguchi, Yoshihiro

AU - Nohmi, Masaya

AU - Ohtsuka, Hiroshi

AU - Shoudai, Takayoshi

PY - 1995/1/1

Y1 - 1995/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21844517433&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844517433&partnerID=8YFLogxK

U2 - 10.1063/1.531132

DO - 10.1063/1.531132

M3 - Article

AN - SCOPUS:21844517433

VL - 36

SP - 1435

EP - 1456

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

ER -