English

Isotropic Cellular Automata: the DDLab iso-rule paradigm

Cellular Automata and Lattice Gases 2021-07-14 v2

Abstract

To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule, a concise expression for isotropic CA by the output table for each isotropic neighborhood group, allowing an efficient method of navigating and exploring iso-rule-space. We describe new functions and tools in DDLab to generate iso-groups and iso-rules, for multi-value as well as binary, in one, two and three dimensions. These methods include filing, filtering, mutating, analysing dynamics by input-frequency and entropy, identifying the critical iso-groups for glider-gun/eater dynamics, and automatically classifying iso-rule-space. We illustrate these ideas and methods for two dimensional CA on square and hexagonal lattices.

Keywords

Cite

@article{arxiv.2008.11279,
  title  = {Isotropic Cellular Automata: the DDLab iso-rule paradigm},
  author = {Andrew Wuensche and José Manuel Gómez Soto},
  journal= {arXiv preprint arXiv:2008.11279},
  year   = {2021}
}

Comments

to appear in Journal of Cellular Automata, minor revisions, 32 pages, 31 figures

R2 v1 2026-06-23T18:06:11.441Z