X-Rule’s Precursor is Also Logically Universal
José Manuel Gómez Soto and Andrew Wuensche
We re-examine the isotropic Precursor-Rule (of the anisotropic X-Rule [6]) 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 [11]. 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.
Keywords: Universality, cellular automata, glider-gun, logical gates.