An Invitation to Number-Conserving Cellular Automata

TL;DR

This paper explores number-conserving cellular automata, detailing methods for simulation, rule discovery, and theoretical properties, thereby advancing understanding of these particle-like discrete systems.

Contribution

It provides a detailed simulation approach, methods to find interesting rules, and new theorems about the structure of one-dimensional number-conserving automata.

Findings

Several new rules discovered through simulation

Theorems describing the structure of automata space

Practical methods for automaton simulation and rule identification

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.