S. Tadaki, ORBITS IN ONE-DIMENSIONAL FINITE LINEAR CELLULAR-AUTOMATA, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(2), 1994, pp. 1168-1173
Periodicity and relaxation are investigated for the trajectories of th
e states in one-dimensional finite cellular automata with rules 90 and
150 [S. Wolfram, Rev. Mod. Phys. 55, 601 (1983)]. The time evolutions
are described with matrices. An eigenvalue analysis is applied to cla
rify the maximum value of period and relaxation.