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.
This paper describes the behaviors of one dimensional finite cellular automata with a triplet local transition rule number 57 having the fixed boundary conditions. The behaviors of CA − 57(m) were observed by computer experiments, and some formulae about the limit cycles and the transient length were found out. The purpose of this paper is to prove the above formulae theoretically.
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