A weakly universal cellular automaton on the pentagrid with two states

TL;DR

This paper demonstrates the existence of a weakly universal two-state cellular automaton on the pentagrid, improving previous three-state results by reducing the number of states needed for universality.

Contribution

It introduces a two-state weakly universal cellular automaton on the pentagrid, extending prior work with three states and analyzing its properties without rotation invariance.

Findings

Two-state automaton is weakly universal on the pentagrid

The automaton uses e0 la Moore neighborhood

Non quiescent states form infinitely many cycles at each step

Abstract

In this paper, we prove that there is a weakly universal cellular automaton on the pentagrid with two states. This paper improves in some sense a previous result with three states. Both results make use of \textit{\`a la Moore} neighbourhood. However, the result with three states is rotation invariant while that with two states is not. In both cases, at each step of the computation, the set of non quiescent states has always infinitely many cycles.