Topic
Continuous automaton
About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.
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TL;DR: A continuous cellular automaton that presents self-organized criticality, one-dimensional, totally deterministic, without any embedded randomness, not even in the initial conditions is introduced.
Abstract: We introduce a continuous cellular automaton that presents self-organized criticality. It is one-dimensional, totally deterministic, without any embedded randomness, not even in the initial conditions. This system is in the same universality class as the Oslo rice pile, boundary driven interface depinning and the train model for earthquakes. Although the system is chaotic, in the thermodynamic limit chaos occurs only in a microscopic level.
18 citations
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TL;DR: A procedure to test whether a given ordinary automaton is equivalent to some kth-order Automaton is suggested.
Abstract: A kth-order finite automaton is an automaton whose next state is a function of its most recent k states as well as its present input. A procedure to test whether a given ordinary automaton is equivalent to some kth-order automaton is suggested.
18 citations
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TL;DR: It is shown that there is a cellular automaton with an equicontinuous dynamics along a parabola, but which is sensitive along any linear direction, and it is showed that real numbers that occur as the slope of a limit linear direction with equicontovernmental dynamics in some cellular automata are exactly the computably enumerable numbers.
18 citations
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TL;DR: Deterministic logical-dynamical systems are considered with the dynamical part described by differential equations and the logical part modeling the work of an automaton with memory is described by recursive inclusions.
Abstract: Deterministic logical-dynamical systems are considered with the dynamical part described by differential equations. The logical part modeling the work of an automaton with memory is described by recursive inclusions. Sufficient optimality conditions are obtained for the construction of the logical (automaton) part of the logical-dynamical system.
18 citations
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TL;DR: Motzkin numbers are derived from a special case of Random Domino Automaton – recently proposed a slowly driven system being a stochastic toy model of earthquakes and a generalisation of 1D Drossel–Schwabl forest-fire model.
18 citations