1991
DOI: 10.1103/physrevlett.66.2045
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Evidence for a new phase in the Domany-Kinzel cellular automaton

Abstract: We consider a generalized version (including anisotropy) of the stochastic one-dimensional cellular automaton studied by Domany and Kinzel. It recovers Wolfram-like deterministic cellular automata as particular cases. The phase diagram presents three (and not two, as previously suggested) phases which were detected through the numerical study of both the order parameter and the sensitivity to initial conditions. The various universality classes are exhibited as well.

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Cited by 59 publications
(50 citation statements)
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“…Martins et al [2] and Zebende and Penna [3], thereby economizing computation time. In addition, the growth exponent method can detect the chaotic/non-chaotic boundary much more clearly than the usual Hamming distance, which presents large fluctuations at the transition.…”
Section: Discussionmentioning
confidence: 99%
“…Martins et al [2] and Zebende and Penna [3], thereby economizing computation time. In addition, the growth exponent method can detect the chaotic/non-chaotic boundary much more clearly than the usual Hamming distance, which presents large fluctuations at the transition.…”
Section: Discussionmentioning
confidence: 99%
“…We calculate the Hurst exponent, H, very close to the transition and find, in the symmetric scheme, H = 0.61 (2). As noted by de Sales et al [9] , there is a maximum in the H exponent, marking the phase transition.…”
Section: Frozen-active Transitionmentioning
confidence: 99%
“…The question then is: Are the long time dynamics of the two replicas sensible to small differences in initial conditions? This has been extensively studied in cellular automata (Martins, Verona de Resende, Tsallis andde Magalhães 1991, Hinrichsen, Weitz andDomany 1996), neural networks (Tamarit and Curado 1994), ferromagnetic Ising models (Stanley, Stauffer, Kertesz andHerrmann 1987, Derrida andWeisbuch 1987) and spin glasses (Derrida 1989). The quantities of interest are the Hamming distance at time t between the two replicas:…”
Section: Introductionmentioning
confidence: 99%