A Language for Particle Interactions in One-dimensional Cellular Automata
Abstract
This is a study of localised structures in one-dimensional cellular automata, with the elementary cellular automaton Rule 54 as a guiding example. A formalism for particles on a periodic background is derived, applicable to all one-dimensional cellular automata. One can compute which particles collide and in how many ways. One can also compute the fate of a particle after an unlimited number of collisions - whether they only produce other particles, or the result is a growing structure that destroys the background pattern. For Rule 54, formulas for the four most common particles are given and all two-particle collisions are found. We show that no other particles arise, which particles are stable and which can be created, provided that only two particles interact at a time. More complex behaviour of Rule 54 requires therefore multi-particle collisions.
Cite
@article{arxiv.1012.0158,
title = {A Language for Particle Interactions in One-dimensional Cellular Automata},
author = {Markus Redeker},
journal= {arXiv preprint arXiv:1012.0158},
year = {2019}
}
Comments
This article is based on arXiv:1007.2920, but has grown considerable and is completely rewritten. Submitted to Complex Systems. 30 pages, 13 figures and 2 tables