A weakly universal cellular automaton in the hyperbolic 3D space with three states

TL;DR

This paper presents a simplified three-state weakly universal cellular automaton in hyperbolic 3D space, improving upon previous five-state models by reducing complexity while maintaining universality.

Contribution

The paper introduces a minimal three-state cellular automaton in hyperbolic 3D space, advancing the understanding of universality with fewer states.

Findings

Successfully constructed a three-state weakly universal cellular automaton

Reduced the number of states from five to three in hyperbolic 3D space

Demonstrated the automaton's universality in hyperbolic 3D geometry

Abstract

In this paper, we significantly improve a previous result by the same author showing the existence of a weakly universal cellular automaton with five states living in the hyperbolic 3D-space. Here, we get such a cellular automaton with three states only.