Pattern decomposition for tessellation automata

AbstractIn this paper we obtain the following two results about one-dimensional tessellation automata. (1) There is a class of one-dimensional monogenic cellular automata with an arbitrary neighborhood size and arbitrary number of states where any pattern is always decomposed into atomic pieces leaving no residue. (2) For any positive integer q there exists a one-dimensional strongly connected tessellation automation with q states even if we put the restriction that available parallel transformation must be bijective mappings on the set of finite configurations