## 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 - 1995 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics