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Cold Dynamics in Cellular Automata: a Tutorial

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Guillaume Theyssier

Cellular Automata and Lattice Gases · Submitted 15 Jun 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

how it is stated · asserted 1.00 read the record →

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arXiv ID2206.08139 (version 1)
Pith IDWDJLGLFC, Pith's permanent record of this paper and its review
CitationGuillaume Theyssier. "Cold Dynamics in Cellular Automata: a Tutorial." arXiv:2206.08139 (2022). https://pith.science/paper/WDJLGLFC
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,860 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.40 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.29 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This tutorial is about cellular automata that exhibit 'cold dynamics'. contribution 0.56 0.19 0.05 asserted 0.97
s1 By this we mean zero entropy, stabilization of all orbits, trivial asymptotic dynamics, etc. background 0.83 0.10 0.05 asserted 0.95
s2 These are purely transient irreversible dynamics, but they capture many examples from the literature. interpretation 0.41 0.16 0.09 asserted 0.99
s3 A rich zoo of properties is presented and discussed: nilpotency and asymptotic, generic or mu-variants, unique ergodicity, convergence, bounded-changeness, freezingness. contribution 1.00 0.39 0.07 asserted 0.99
s4 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. contribution 0.81 0.66 0.13 asserted 0.94
s5 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. contribution 0.97 0.86 0.21 asserted 1.00

What kind of paper the classifier reports this is: review 0.98 · evidence from literature 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 2 sentences without a confident label

Cites as support 1 paper
  • Each time, the nilpotency variant is equivalent to having such asymptotic sets being singletons (see [ref] ).

    Generically Nilpotent Cellular Automata · Variations with partial convergence and measures · 0.96

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