Some results about the chaotic behavior of cellular automata

DOI10.1016/J.TCS.2005.06.038zbMath1085.37007OpenAlexW2057471386MaRDI QIDQ817807

Enrico Formenti, Julien Cervelle, François Blanchard

Publication date: 20 March 2006

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2005.06.038

zbMATH Keywords

cellular automataKolmogorov complexitydeterministic chaostransitivityunconventional topologies

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Cellular automata (computational aspects) (68Q80) Dynamical aspects of cellular automata (37B15) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

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\(m\)-asynchronous cellular automata: from fairness to quasi-fairness ⋮ On one-sided, D-chaotic CA without fixed points, having continuum of periodic points with period 2 topological entropy \(\log(p)\) for any prime \(p\) ⋮ A Curtis-Hedlund-Lyndon theorem for Besicovitch and Weyl spaces ⋮ Conservation of some dynamical properties for operations on cellular automata ⋮ Sand automata as cellular automata ⋮ Progress, gaps and obstacles in the classification of cellular automata ⋮ Classifying 1D elementary cellular automata with the 0-1 test for chaos ⋮ Covering space in the Weyl and Besicovitch topologies ⋮ Generalized Besicovitch and Weyl spaces: topology, patterns, and sliding block codes ⋮ Topological chaos: what may this mean? ⋮ On the directional dynamics of additive cellular automata

Cites Work

• Pattern growth in elementary cellular automata
• Periodic points for onto cellular automata
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• Counting the number of equivalence classes of Borel and coanalytic equivalence relations
• Chaos Without Nonperiodicity
• Languages, equicontinuity and attractors in cellular automata
• Textile systems for endomorphisms and automorphisms of the shift
• Shorter Note: The Converse of Moore's Garden-of-Eden Theorem
• Mathematical Foundations of Computer Science 2003
• Symbolic Dynamics and Transformations of the Unit Interval
• Limit sets of cellular automata associated to probability measures
• Kolmogorov complexity and cellular automata classification
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