An Invitation to Number-Conserving Cellular Automata
Markus Redeker

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.
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Taxonomy
TopicsCellular Automata and Applications · Stochastic processes and statistical mechanics
