Chaos emerged on the ‘edge of chaos’

Chen, Fangyue; Jin, Weifeng; Chen, Guanrong; Chen, Lin

doi:10.1080/00207160.2012.691971

Cited by 2 publications

(2 citation statements)

References 29 publications

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“…where f : S Z → S Z is the symbolic sequence map [Chen et al, 2012;Zhou, 1997]. (S Z n , F ) is a compact dynamical system.…”

Section: The Fundamental Concepts Of Symbolic Dynamicsmentioning

confidence: 99%

“…In general, gliders are localized structures of nonquiescent and nonether patterns (ether represents a periodic background) translating along the automaton's lattice. Importantly, as gilders are crucial components of conception and simulation of the universal computing model, the concrete rules with a great variety of gliders have captured special attention in a series of CA research work [Martínez et al, 2010a;Cook, 2004;Freire & Gallas, 2007;Chen et al, 2012;Martínez et al, 2014]. It leads to an intriguing possibility: HCAM(43, 74) is an ideal candidate for the universal computing.…”

Section: Introductionmentioning

confidence: 99%

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Glider Collisions in Hybrid Cellular Automaton with Memory Rule (43,74)

Chen

Mart́ınez

2017

Int. J. Bifurcation Chaos

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In the case of one-dimensional cellular automaton (CA), a hybrid CA (HCA) is the member whose evolution of the cells is dependent on nonunique global functions. The HCAs exhibit a wide range of traveling and stationary localizations in their evolution. We focus on HCA with memory (HCAM) because they produce a host of gliders and complicated glider collisions by introducing the hybrid mechanism. In particular, we undertake an exhaustive search of gliders and describe their collisions using quantitative approach in HCAM[Formula: see text]. By introducing the symbol vector space and exploiting the mathematical definition of HCAM, we present an analytical method of complex asymptotic dynamics of the gliders.

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“…where f : S Z → S Z is the symbolic sequence map [Chen et al, 2012;Zhou, 1997]. (S Z n , F ) is a compact dynamical system.…”

Section: The Fundamental Concepts Of Symbolic Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Glider Collisions in Hybrid Cellular Automaton with Memory Rule (43,74)

Chen

Mart́ınez

2017

Int. J. Bifurcation Chaos

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A Symbolic Dynamics Perspective of Conway’s Game of Life

Chen

Guan

et al. 2016

Int. J. Bifurcation Chaos

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An interesting question is whether the intrinsic complexity of the gliders in [Formula: see text]-dimensional cellular automata could be quantitatively analyzed in rigorously mathematical sense. In this paper, by introducing the [Formula: see text]-dimensional symbolic space, some fundamental dynamical properties of [Formula: see text]-dimensional shift map are explored in a subtle way. The purpose of this article is to present an accurate characterization of complex symbolic dynamics of gliders in Conway’s game of life. A series of dynamical properties of gliders on their concrete subsystems are investigated by means of the directed graph representation and transition matrix. More specifically, the gliders here are topologically mixing and possess the positive topological entropy on their subsystems. Finally, it is worth mentioning that the method presented in this paper is also applicable to other gliders in different [Formula: see text] dimensions.

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Chaos emerged on the ‘edge of chaos’

Cited by 2 publications

References 29 publications

Glider Collisions in Hybrid Cellular Automaton with Memory Rule (43,74)

Glider Collisions in Hybrid Cellular Automaton with Memory Rule (43,74)

A Symbolic Dynamics Perspective of Conway’s Game of Life

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