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: In this paper, Park, Steiglitz and Thurston studied the evolution of an arbitrary initial configuration of a certain filter cellular automaton introduced by Park and Stehlitz and found that the interaction properties of these particles are richer than the usual solitons.
43 citations
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TL;DR: In this paper, some rigorous results are obtained for a cellular automaton known as the Greenberg-Hastings Model and it is shown that starting from a nontrivial product measure, the limit exists as 3m→∞ and is Bernoulli shift.
Abstract: In this paper, we obtain some rigorous results for a cellular automaton known as the Greenberg-Hastings Model. The state space is {0, 1, 2} zd. The dynamics are deterministic and discrete time. A site which is 1 changes to 2, a site which is 2 changes to 0, and a site which is 0 changes to a 1 if one of its 2d neighbors is a 1. In one dimension, we compute the exact asymptotic rate at which the system dies out when started at random and compute the topological entropy. In two or more dimensions we show that starting from a nontrivial product measure, the limit exists as 3m~ m and is Bernoulli shift. Finally, we investigate the behavior of the system on a large finite box.
42 citations
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TL;DR: In this article, a cellular automation model of excitable media with improved treatments of diffusion and wave propagation, and slow dynamics of the recovery variable is introduced. But the model is computationally efficient and faithful to the underlying partial differential equations.
42 citations
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TL;DR: This work constructs a three-dimensional self-inspective self-reproducing reversible cellular automaton by extending the two-dimensional version SR8, which canSelf-reproduce various patterns in three- dimensional reversible cellular space without dissipating garbage signals.
Abstract: Due to inevitable power dissipation, it is said that nano-scaled computing devices should perform their computing processes in a reversible manner. This will be a large problem in constructing three-dimensional nano-scaled functional objects. Reversible cellular automata (RCA) are used for modeling physical phenomena such as power dissipation, by studying the dissipation of garbage signals. We construct a three-dimensional self-inspective self-reproducing reversible cellular automaton by extending the two-dimensional version SR8. It can self-reproduce various patterns in three-dimensional reversible cellular space without dissipating garbage signals.
41 citations