The X-rule: universal computation in a non-isotropic Life-like Cellular Automaton

TL;DR

The paper introduces the X-rule, a non-isotropic 2D Life-like cellular automaton capable of universal computation, featuring emergent gliders, stable structures, and logical gates, expanding the scope of cellular automata computational models.

Contribution

It presents the X-rule, a novel non-isotropic Life-like CA demonstrating logic universality with emergent structures and a new search method.

Findings

Emergence of multiple glider types and stable structures

Construction of glider-guns and logical gates

Demonstration of universal computation capabilities

Abstract

We present a new Life-like cellular automaton (CA) capable of logic universality -- the X-rule. The CA is 2D, binary, with a Moore neighborhood and $\lambda$ parameter similar to the game-of-Life, but is not based on birth/survival and is non-isotropic. We outline the search method. Several glider types and stable structures emerge spontaneously within X-rule dynamics. We construct glider-guns based on periodic oscillations between stable barriers, and interactions to create logical gates.