Grassberger P.: "Chaos and Diffusion in Deterministic Cellular Automata", Physica 10D, 1984, pp. 145-156  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a finite (usually small) number of possible states for a cell. The transition from one state to the next at discrete time steps in all the cells is what determines the array s behaviour and applications. CAs have been used for studying selfreproduction [8] and modelling of dynamic complex systems [9,10]. Systolic Arrays. In systolic arrays the processing elements are designed to match a particular algorithm. Systolic means that synchronous pipelined computations take place along all dimensions of the array and result in very high computational throughput. The main applications for such ....

Grassberger P.: "Chaos and Diffusion in Deterministic Cellular Automata", Physica 10D, 1984, pp. 145-156

....In these latter ones, statistical measures are often used, together with information theory like measures (entropy, activity, sensitivity to rule change, etc. This leads to definitions of complex behaviors, based on certain values of parameters. Among others, we refer the interested reader to [Gra84, Ped90, LPL90, WL90, CM90, Bin93] In [Svo90] the author presents a classification of chaotic behaviors, based on notions of randomness, complexity measures, computability of initial conditions, and (non)determinism of rules. Finally, in [Jen90] the author studied aperiodicity of some CA ....

Peter Grassberger. Chaos and diffusion in deterministic cellular automata. Physica D, 10:52, 1984.

....is mainly based on union invariant theorems elaborated in [26, 27, 12, 13] that we complement with physical measures of complexity. Related work. In the literature on CA and related models, lots of papers study complexity. Among these ones, let us just mention important approaches developed in [14, 32, 6, 20], as well as the many references cited in [15, 11] However, the notion of chaos is still not well defined in the context of such discretetime discrete space multi dimensional dynamical systems. Several authors propose ways of defining complex behaviors in CA. This is one of the goals of ....

....in the space of CA rules, allowing new classifications, too. In these latter ones, statistical measures are often used, together with information theory measures (entropy, activity, sensitivity to rule change, etc. leading to definitions of complex behaviors, based on certain parameter values [14, 24, 22, 6, 25]. In [28] the author presents a classification of chaotic behaviors, based on notions of randomness, complexity measures, computability of initial conditions, and (non)determinism of rules. Finally, in [19] the author studies aperiodicity of some CA analytically. Closer to our compositional ....

Peter Grassberger. Chaos and diffusion in deterministic cellular automata. Physica D, 10:52, 1984.

....rapidly approach the natural measure under the action of this rule. However, while the natural measure of rule 30 is trivial, that of rule 22 is highly complex. Though correlations show an overall exponential decay, there are intricate fine scale deviations, indicating subtle long range effects [9, 16]. Rule 22 is a representative chaotic or Wolfram class III rule [36] As the radius or number of states of cellular automata increase the fraction of rules which are chaotic approaches 1. Hence the behavior of rule 22 should be representative of a large class of rules. Rule 18. Rule 18 (001,100 ....

....states of cellular automata increase the fraction of rules which are chaotic approaches 1. Hence the behavior of rule 22 should be representative of a large class of rules. Rule 18. Rule 18 (001,100 1, else 0) was one of the first rules to be carefully analyzed as a statistical mechanical system [16, 15, 28]. The space time patterns generated by rule 18 are composed of even and odd domains within which rule 18 behaves like linear rule 90. Eloranta [10] proved that the boundaries between these domains ( defects ) execute a random walk. Jen [24] showed that the defects in the patterns generated by ....

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P. Grassberger, Chaos and diffusion in deterministic cellular automata, Physica D 10:52-58 (1984)

....reach a better understanding of chaos in discrete time multi dimensional systems. 1. Introduction The notion of chaos is still unprecise in discrete time discrete space multi dimensional dynamical systems like, for example, cellular automata (CA) Recently, many authors have tried to formalize it [1, 2, 3, 4]. Classification of CA w.r.t. their asymptotic behavior is a central theme in the field, and should lead to a better understanding of chaotic and related behaviors [5] However, many problems have to be tackled: the asymptotic behavior is easy to study theoretically for very few simple cases only; ....

Grassberger Peter, (1984). Chaos and diffusion in deterministic cellular automata. Physica D, 10:52.

....In the context of elementary cellular automata Rule 18 variations of both of these intriguing phenomena surface. On one hand the rule transforms the randomness in the initial configuration into perfect diffusivity that prevails at all later times. This was discovered in simulations by Grassberger ([G]) and was later analyzed rigorously by e.g. Lind ( L] and Eloranta Nummelin ( EN] On the other hand more ordered configurations are formed through joining of two adjacent phases. This is facilitated by an annihilation mechanism in which neighbouring kinks disappear pairwise. The mechanism ....

Grassberger, P.: Chaos and diffusion in deterministic cellular automata, Physica D 10, 52-58, 1984.

....We give an exact characterization of the movement of a single kink in the elementary cellular automaton Rule 18. It is a random walk with independent increments as well as independent delay times. Its statistical parameters are computed to confirm the earlier simulation results by Grassberger [G]. Keywords: Cellular automaton, kink, random walk 0. Introduction It is quite common in cellular automata that several invariant configurations or phases can be identified. In one dimension the boundaries between these are called kinks or dislocations. In some cases they move in a regular fashion ....

....these are called kinks or dislocations. In some cases they move in a regular fashion like signals carrying information whereas in some cases their motion is highly erratic reflecting the randomness in the initial configuration. The latter situation has been studied empirically by Grassberger in [G] as a model for deterministic diffusion. The canonical case for chaotic kink motion seems to arise in the context of the elementary Rule 18. Knowing this phenomenon would clarify the asymptotic behavior of the system as indicated by Lind [L] Moreover it is likely that by utilizing block ....

Grassberger, P.: Chaos and diffusion in deterministic cellular automata, Physica D 10, 52-58, 1984.

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P. Grassberger. Chaos and diffusion in deterministic cellular automata. Physica D, 10:52, 1984.

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P. Grassberger. Chaos and diffusion in deterministic cellular automata. Physica D, 10:52, 1984.

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P. Grassberger. Chaos and diffusion in deterministic cellular automata. Physica D, 10:52, 1984.

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