Periodicity in One-Dimensional Finite Linear Cellular Automata
Shin-ichi Tadaki, Shinya Matsufuji · Progress of Theoretical Physics · 1993
We investigate the periodic structures of the trajectories in one-dimensional finite linear cellular automata with rule-90, whose time evolutions are described with matrices. The periodicity of the trajectories is found numerically and by use of eigenvalue equations. The period strongly depends on the number of sites. In some cases the null state becomes a limit point.