X-Rule's Precursor is also Logically Universal

TL;DR

This paper demonstrates that the isotropic Precursor-Rule, a cellular automaton derived from biased rules, is also logically universal, capable of supporting complex structures and computational gates.

Contribution

It shows that the isotropic Precursor-Rule is logically universal, extending the known computational capabilities of related cellular automata.

Findings

Discovered glider-guns and complex structures in the Precursor-Rule.

Built logical gates demonstrating universality.

Confirmed emergent mobile and stable patterns.

Abstract

We re-examine the isotropic Precursor-Rule (of the anisotropic X-Rule) and show that it is also logically universal. The Precursor-Rule was selected from a sample of biased cellular automata rules classified by input-entropy. These biases followed most "Life-Like" constraints --- in particular isotropy, but not simple birth/survival logic. The Precursor-Rule was chosen for its spontaneously emergent mobile and stable patterns, gliders and eaters/reflectors, but glider-guns, originally absent, have recently been discovered, as well as other complex structures from the Game-of-Life lexicon. We demonstrate these newly discovered structures, and build the logical gates required for universality in the logical sense.