Cold Dynamics in Cellular Automata: a Tutorial

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.

Natural Computing, Springer Verlag, 2022

References in corpus (5)

• Monotone cellular automata in a random environment
• A non-ergodic probabilistic cellular automaton with a unique invariant measure
• Ergodicity of some classes of cellular automata subject to noise
• Counter Machines and Distributed Automata: A Story about Exchanging Space and Time
• On Nilpotency and Asymptotic Nilpotency of Cellular Automata