A completeness property of one-dimensional tessellation automata

摘要

In this paper, it is shown that if k≥3, any finite k-symbols pattern whose lengthis greater than 1 can be generted strictly monotonously from the primitive pattern by some sequence of parallel transformations of a k-symbols scope-n tessellation automaton for any n≥2. It is also shown that any nonzero finite binary pattern can be generated monotonously from the primitive pattern by some sequence of parallel transformations of a binary scope-n tessellation automaton for any n≥3.