Chaotic behaviors of symbolic dynamics about rule 58 in cellular automata
type: Item
instance of: scholarly article
title: Chaotic behaviors of symbolic dynamics about rule 58 in cellular automata
zbMATH Open document ID: 1407.37017
DOI: 10.1155/2014/834268
author: Yangjun Pei
author: Qi Han
author: Chao Liu
author: Dedong Tang
author: Junjian Huang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: The complex dynamical behaviors of rule 58 in cellular automata are investigated from the viewpoint of symbolic dynamics. The rule is Bernoulli \(\sigma_\tau\)-shift rule, which is members of Wolfram's class II, and it was said to be simple as periodic before. It is worthwhile to study dynamical behaviors of rule 58 and whether it possesses chaotic attractors or not. It is shown that there exist two Bernoulli-measure attractors of rule 58. The dynamical properties of topological entropy and topological mixing of rule 58 are exploited on these two subsystems. According to corresponding strongly connected graph of transition matrices of determinative block systems, we divide determinative block systems into two subsets. In addition, it is shown that rule 58 possesses rich and complicated dynamical behaviors in the space of bi-infinite sequences. Furthermore, we prove that four rules of global equivalence class \(\varepsilon_4^3\) of CA are topologically conjugate. We use diagrams to explain the attractors of rule 58, where characteristic function is used to describe that some points fall into Bernoulli-shift map after several times iterations, and we find that these attractors are not global attractors. The Lameray diagram is used to show clearly the iterative process of an attractor.
Mathematics Subject Classification ID: 37B15
Mathematics Subject Classification ID: 68Q80
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7017386
Wikidata QID: Q59069802
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/834268
OpenAlex ID: W2034154591
cites work: Group Properties of Cellular Automata and VLSI Applications
cites work: Design of fast one-pass authenticated and randomized encryption schema using reversible cellular automata
cites work: Elliptic curve based hardware architecture using cellular automata
cites work: Secret image sharing based on cellular automata and steganography
cites work: Non-uniform cellular automata based associative memory: Evolutionary design and basins of attraction
cites work: Q3675526
cites work: Q3150942
cites work: A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART I: THRESHOLD OF COMPLEXITY
cites work: A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part II: Universal Neuron
cites work: A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART III: PREDICTING THE UNPREDICTABLE
cites work: A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART IV: FROM BERNOULLI SHIFT TO 1/f SPECTRUM
cites work: A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART V: FRACTALS EVERYWHERE
cites work: A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART VI: FROM TIME-REVERSIBLE ATTRACTORS TO THE ARROW OF TIME
cites work: Chaos of elementary cellular automata rule 42 of Wolfram’s class II
cites work: Q3654093
cites work: Q5389001
cites work: Complex dynamic behaviors in cellular automata rule 14
cites work: EXTENDING CHUA'S GLOBAL EQUIVALENCE THEOREM ON WOLFRAM'S NEW KIND OF SCIENCE
cites work: Q4264342
cites work: Period Three Implies Chaos
Recommended article: Symbolics dynamics of elementary cellular automata rule 88
Recommended article: Q5389001
Recommended article: On the dynamical behavior of chaotic cellular automata
Recommended article: Some results about the chaotic behavior of cellular automata
Recommended article: Complex dynamics of elementary cellular automata emerging from chaotic rules
Recommended article: Q3971988
Recommended article: On behaviors of cellular automata with rule number 57
Recommended article: Chaotic behaviour of the general symbolic dynamics
Recommended article: Chaotic behavior of one-dimensional cellular automata rule 24
Recommended article: Edge of chaos in rule-changing cellular automata
description: scientific article; zbMATH DE number 7017386