An Invitation to Number-Conserving Cellular Automata
Cellular Automata and Lattice Gases
2025-06-02 v3
Abstract
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional number-conserving automata. Here I describe in greater detail how one can simulate the automata on a computer and how to find interesting rules. I show several rules that I have found this way and also some theorems about the space of number-conserving automata.
Cite
@article{arxiv.2308.00060,
title = {An Invitation to Number-Conserving Cellular Automata},
author = {Markus Redeker},
journal= {arXiv preprint arXiv:2308.00060},
year = {2025}
}
Comments
15 pages, 4 figures. (Theorem numbering changed with respect to the previous version.)