The Variant-Rule, Another Logically Universal Rule

TL;DR

This paper introduces the Variant-rule, a new logical rule derived from the Precursor-rule, demonstrating its ability to support universal computation through newly discovered structures and dynamics, despite some changes in large-scale behaviors.

Contribution

It presents a novel variant of an existing rule, showing how small modifications can preserve core behaviors while enabling universal logical computation.

Findings

Discovered new glider-gun engines and structures.

Built logical gates demonstrating universality.

Showed robustness and fragility in pattern evolution.

Abstract

The Variant-rule derives from the Precursor-rule by interchanging two classes of its 28 isotropic mappings. Although this small mutation conserves most glider types and stable blocks, glider-gun engines are changed, as are most large scale pattern behaviors, illustrating both the robustness and fragility of evolution. We demonstrate these newly discovered structures and dynamics, and utilising two different glider types, build the logical gates required for universality in the logical sence.