Limit dynamics of elementary cellular automaton 18

Abstract We study the the asymptotic dynamics of elementary cellular automaton 18 through its limit set, generic limit set and $\mu $ -limit set. The dynamics of rule 18 are characterized by persistent local patterns known as kinks. We characterize the configurations of the generic limit set containing at most two kinks. As a corollary, we show that the three limit sets of rule 18 are distinct.