Period lengths of cellular automata on square lattices with rule 90

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.