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, a discussion of complex dynamics of the elementary cellular automaton rule 54 is presented, and an equation which shows some degree of self-similarity is obtained, showing that rule 54 exhibits Bernoulli shift and is topologically mixing.
Abstract: This work deals with a discussion of complex dynamics of the elementary cellular automaton rule 54. An equation which shows some degree of self-similarity is obtained. It is shown that rule 54 exhibits Bernoulli shift and is topologically mixing on its closed invariant subsystem. Finally, many complex Bernoulli shifts are explored for the finite symbolic sequences with periodic boundary conditions.
2 citations
TL;DR: In this paper, a one-dimensional cellular automaton is introduced as a prototype for memory effects on damage, and the associated Hamming distance as a function of time correctly mimics complex dynamical systems and gradually varies between a noiselike behavior and a plateaulike one.
Abstract: We introduce a one-dimensional cellular automaton as a prototype for memory effects on damage. The associated Hamming distance as a function of time correctly mimics complex dynamical systems and, for different values of the external parameters, gradually varies between a noiselike behavior and a plateaulike one
2 citations
01 Jan 2005
TL;DR: The mathematical structure underlying the time series generated from the elementary cellular automaton of rule 56 is analyzed and its complexity is determined, in which the Dyck language and Catalan numbers emerge naturally.
Abstract: A new approach to study the evolution complexity of cellular automata is proposed and explained thoroughly by an example of elementary cellular automaton of rule 56. Using the tools of distinct excluded blocks, computational search and symbolic dynamics, the mathematical structure underlying the time series generated from the elementary cellular automaton of rule 56 is analyzed and its complexity is determined, in which the Dyck language and Catalan numbers emerge naturally.
2 citations
01 Oct 2015
TL;DR: This paper presents a method for the implementation of a mirror object within the Game of Life cellular automaton, based on quantum states that eliminates self-interference, thereby enabling a continuous progression of translating patterns.
Abstract: This paper presents a method for the implementation of a mirror object within the Game of Life cellular automaton, based on quantum states. While in the nominal case, the application of a regular mirror causes any reflected pattern to degenerate, reflection based on quantum states eliminates self-interference, thereby enabling a continuous progression of translating patterns.
2 citations
TL;DR: The synthesis algorithm carried out the successive transformation of the regular expression into an expression which is presented as the columns of the transition table of the automaton, written down one after the other (starting from the first).
Abstract: The problem is to construct the transition table of an automaton which represents an event from the regular notation of this event [1], [2]. The synthesis algorithm carried out the successive transformation of the regular expression into an expression which is presented as the columns of the transition table of the automaton, written down one after the other (starting from the first). The algorithm includes the following operators. Operator I looks for the letters in the regular notation of the event.
2 citations