An outer totalistic weakly universal cellular automaton in the dodecagrid with four states

TL;DR

This paper introduces the first known outer totalistic weakly universal cellular automaton with four states in the hyperbolic 3D dodecagrid, expanding the understanding of universality in complex tessellations.

Contribution

It demonstrates the existence of a weakly universal cellular automaton in the hyperbolic 3D space with a minimal number of states, specifically four, in the dodecagrid tessellation.

Findings

First such automaton in this context

Proves weak universality in hyperbolic 3D space

Uses four states in the cellular automaton

Abstract

In this paper, we prove that there is an outer totalistic weakly universal cellular automaton in the dodecagrid, the tessellation {5,3,4} of the hyperbolic 3D space, with four states. It is the first result in such a context.