Abstract

We show that the aperiodic cellular automata studied by Coven (1980), that is the maps F : {0, 1}? ? {0, 1}? induced by block maps f : {0, 1}r+1 ? {0, 1} such that f(x0,x1,...,xr) is equal to (x0 + 1) mod 2 if x1 ... xr = b1 ... br and equal to x0 otherwise, where B = b1 ...br is a given aperiodic word, have the following position in classification of Ku?rka (1994): they are regular, contain equicontinuous points without being equicontinuous, and are chain transitive but not topologically transitive. Therefore they do not have the shadowing property; this answers in the negative a question raised by P. Ku?rka.