A new universal cellular automaton on the ternary heptagrid

TL;DR

This paper introduces a new four-state weakly universal cellular automaton on the ternary heptagrid, improving the state efficiency compared to previous six-state models in hyperbolic plane cellular automata.

Contribution

It presents the first four-state weakly universal cellular automaton on the ternary heptagrid, advancing the minimal state count in hyperbolic cellular automata.

Findings

Achieved the lowest number of states (four) for weakly universal cellular automata on the ternary heptagrid.

Demonstrated universality within the hyperbolic plane cellular automata.

Improved upon previous models requiring six states.

Abstract

In this paper, we construct a new weakly universal cellular automaton on the ternary heptagrid. The previous result, obtained by the same author and Y. Song required six states only. This time, the number of states is four. This is the best result up to date for cellular automata in the hyperbolic plane.