Non-uniform cellular automata and distributions of rules

TL;DR

This paper investigates one-dimensional non-uniform cellular automata with various local rules, analyzing how rule combinations affect properties like surjectivity, injectivity, and number conservation using graph-based methods.

Contribution

It introduces a framework for studying rule distributions in non-uniform cellular automata and analyzes key properties using DeBruijn graph variants.

Findings

Surjectivity and injectivity characterized via DeBruijn graphs.

Conditions for number-conserving property identified.

Insights into rule mixing effects on cellular automata properties.

Abstract

In this paper we study $\nu$-CA on one-dimensional lattice defined over a finite set of local rules. The main goal is to determine how the local rules can be mixed to ensure the produced $\nu$-CA has some properties. In a first part, we give some background for the study of $\nu$-CA. Then surjectivity and injectivity are studied using a variant of DeBruijn graphs. The next part is dedicated to the number-conserving property.