A Particular Universal Cellular Automaton

TL;DR

This paper introduces a new smallest intrinsically universal cellular automaton with 4 states, utilizing particles and collisions to handle infinite interactions, advancing the theoretical understanding of cellular automata universality.

Contribution

It presents a high-level construction of an intrinsically universal cellular automaton with only 4 states, employing particles and collisions for infinite interactions.

Findings

Developed a 4-state universal cellular automaton

Used particles and collisions for infinite interactions

Achieved smallest known universal automaton

Abstract

Signals are a classical tool used in cellular automata constructions that proved to be useful for language recognition or firing-squad synchronisation. Particles and collisions formalize this idea one step further, describing regular nets of colliding signals. In the present paper, we investigate the use of particles and collisions for constructions involving an infinite number of interacting particles. We obtain a high-level construction for a new smallest intrinsically universal cellular automaton with 4 states.