Traveling waves and chaotic properties in cellular automata

Traveling wave solutions of cellular automata (CA) with two states and near est neighbors interaction on one-dimensional (1-D) infinite lattice are com puted. Space and time periods and the number of distinct waves have been co mputed for all representative rules, and each velocity ranging from 2 to 22 . This computation shows a difference between spatially extended systems, g enerating only temporal chaos and those producing as well spatial complexit y. In the first case wavelengths are simply related to the velocity of prop agation and the dispersivity is an affine function, while in the second cas e (which coincides with Wolfram class 3), the dispersivity is multiform and its dependence on the velocities is highly random and discontinuous. This property is typical of space-time chaos in CA. (C) 1999 American Institute of Physics. [S1054-1500(99)01004-6].