A weakly universal cellular automaton in the heptagrid with three states

TL;DR

This paper presents a three-state cellular automaton on the heptagrid that is weakly universal, improving upon previous models that required four states, thus advancing the efficiency of such automata.

Contribution

The paper introduces the first three-state weakly universal cellular automaton on the heptagrid, reducing the number of states needed compared to prior models.

Findings

Achieved weak universality with only three states

Improved previous four-state models

Demonstrated planarity and universality in the heptagrid

Abstract

In this paper, we construct a cellular automaton on the heptagrid which is planar, weakly universal and which have three states only. This result improves the best result which was with four states.