On Limit Cycles and Transient Lengths of Cellular Automata With Threshod Rules

Abstract

In this paper, we investigate behaviors of 1-D finite cellular automata with triplet local transitions rules of fixed boundary condition. We make the number of limit cycles and transient length clear, and we show 2 theorems, one is for period length of their limit cycles and the other is for their transient length.

On Behaviors of Cellular Automata With Rule Number 57

“…Concerning cellular automata with simple structure, many important results have been reported by Kawahara et al [Kawahara (1991), Kawahara et al (1992), Inokuchi and Sato et al (1996)]. Especially, the author has investigated cellular automata with threshold rules and having limit cycles of period length 3 [Sato (1996a), Sato (1996b), Sato (1998), Sato (1999), Inokuchi and Sato (2000)]. As to cellular automata with threshold rules, Shingai reported that period lengths of limit cycles are 4 or less [Shingai (1978)].…”

Tree Expressions and Their Product Formula

“…Cellular automata are the subjects investigated by many researchers and behaviors of cellular automata with some rules are shown. Kawahara (1991), Lee and Kawahara (1992), Kawahara et al (1995) investigated 1-D and 2-D cellular automata with linear rules 60 and 90, and Inokuchi and Sato (2000) investigated behaviors of 1-D cellular automata with threshold rules and showed that the number of limit cycles and transient lengths.…”