English

X-Rule's Precursor is also Logically Universal

Cellular Automata and Lattice Gases 2017-09-11 v1

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.

Cite

@article{arxiv.1611.08829,
  title  = {X-Rule's Precursor is also Logically Universal},
  author = {José Manuel Gómez Soto and Andrew Wuensche},
  journal= {arXiv preprint arXiv:1611.08829},
  year   = {2017}
}

Comments

29 pages, 46 figures

R2 v1 2026-06-22T17:05:21.900Z