A strongly universal cellular automaton on the pentagrid with six states and Moore neighbourhood

Abstract

In this paper, we prove that there is a strongly universal cellular automaton on the pentagrid with six states. For each cell c, Moore neighbourhood consists of the cells which share a vertex with c. Moreover, the rules are rotation invariant. There are 1072 of them. The result is different from arXiv:2306.06728. The present paper deals with the pentagrid and not with the heptagrid, it is not at all the same context although the implementated model is basically the same. The implementation of that model is different from the quoted arXiv paper.

arXiv comment43 pages, 29 figures. arXiv admin note: substantial text overlap with arXiv:2306.06728, arXiv:2304.13575, arXiv:2104.01561, arXiv:2108.13094