A weakly universal cellular automaton on the pentagrid with three states

TL;DR

This paper demonstrates a weakly universal cellular automaton on the pentagrid with three states, rotation invariance, and Moore neighborhood, maintaining infinitely many cycles of non-quiescent states during computation.

Contribution

It introduces the first weakly universal cellular automaton on the pentagrid with minimal states and specific invariance and neighborhood properties.

Findings

Proves weak universality on the pentagrid with three states

Maintains infinite cycles of active states during computation

Ensures rotation invariance and Moore neighborhood usage

Abstract

In this paper, we prove that there is a weakly universal cellular automaton on the pentagrid with three states which is rotation invariant and which uses \`a la Moore neighbourhood. Moreover, at each step of the computation, the set of non quiescent states has always infinitely many cycles.