Minimal Glider-Gun in a 2D Cellular Automaton

TL;DR

This paper introduces the Sayab-rule, a minimal 2D cellular automaton with the smallest known glider-gun, enabling simpler analysis of self-organization and universal computation.

Contribution

It presents the Sayab-rule, a new cellular automaton with the smallest glider-gun, facilitating understanding of complex dynamics and logical universality.

Findings

Sayab-rule has the smallest glider-gun to date.

It can implement complex interactions and logic gates.

Demonstrates potential for universal computation in minimal automata.

Abstract

To understand the underlying principles of self-organisation and computation in cellular automata, it would be helpful to find the simplest form of the essential ingredients, glider-guns and eaters, because then the dynamics would be easier to interpret. Such minimal components emerge spontaneously in the newly discovered Sayab-rule, a binary 2D cellular automaton with a Moore neighborhood and isotropic dynamics. The Sayab-rule has the smallest glider-gun reported to date, consisting of just four live cells at its minimal phases. We show that the Sayab-rule can implement complex dynamical interactions and the gates required for logical universality.