English

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.

Keywords

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.)

R2 v1 2026-06-28T11:44:50.964Z