Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure

TL;DR

This paper explores how minimal elementary cellular automata's phase space and entropy are affected by vanishing noise, revealing complex modifications that do not always reduce entropy.

Contribution

It provides a detailed analysis of phase space structures of elementary cellular automata under noise, highlighting non-intuitive entropy behaviors.

Findings

Noise alters phase space connections and attractors.

Entropy does not always decrease with vanishing noise.

Complete phase space analysis for small lattice sizes.

Abstract

We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is that this modification not always goes in the sense of decreasing the entropy.