Cold Dynamics in Cellular Automata: a Tutorial

TL;DR

This tutorial explores cellular automata with 'cold dynamics' characterized by zero entropy and stabilization, discussing their properties, differences, and computational capabilities within this specific dynamical regime.

Contribution

It provides a comprehensive overview of 'cold dynamics' in cellular automata, including properties, examples, and their computational limitations and potentials.

Findings

Characterization of cold dynamics properties

Examples of cold cellular automata from literature

Analysis of computational capabilities and limitations

Abstract

This tutorial is about cellular automata that exhibit 'cold dynamics'. By this we mean zero entropy, stabilization of all orbits, trivial asymptotic dynamics, etc. These are purely transient irreversible dynamics, but they capture many examples from the literature. A rich zoo of properties is presented and discussed: nilpotency and asymptotic, generic or mu-variants, unique ergodicity, convergence, bounded-changeness, freezingness. They all correspond to the 'cold dynamics' paradigm in some way, and we study their links and differences by various examples and results from the literature. Besides dynamical considerations, we also focus on computational aspects: we show how such 'cold cellular automata' can still compute under their dynamical constraint, and what are their computational limitation.