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This paper studies two-dimensional cellular automatma $ca-90(m,n)$ having states 0 and 1 and working on a square lattice of size $(m-1) \times (n-1)$. All their dynamics, driven by the local transitio...n 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.show more
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