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Continuous automaton

About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.


Papers
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Journal ArticleDOI
Maurice Margenstern1, Yu Song1
TL;DR: This paper constructs the first weakly universal cellular automaton on the ternary heptagrid that requires six states only, and provides a universal automaton with less states than in the case of the pentagrid where the best result is nine states.

27 citations

Journal ArticleDOI
TL;DR: It is shown that there exists a simple solution to the density problem in cellular automata, under fixed boundary conditions, in contrast to previously used periodic ones.
Abstract: We show that there exists a simple solution to the density problem in cellular automata, under fixed boundary conditions, in contrast to previously used periodic ones.

27 citations

Journal ArticleDOI
TL;DR: A hierarchy of generative diversity of one‐dimensional cellular automata with binary cell‐states and ternary neighborhoods is built and necessary conditions for a cell‐state transition rule to be on top of the hierarchy are discussed.
Abstract: Purpose – Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space‐time configurations. No one has tried to analyze a generative power of cellular‐automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large‐scale spatially extended systems.Design/methodology/approach – Let all but one cell be in alike state in initial configuration of a one‐dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three‐by‐three cell blocks occurred in the automaton's space‐time configuration.Findings – The paper builds a hierarchy of generative diversity of one‐dimensional cellular automata with binary cell‐states and ternary neighborhoods, discusses necessary conditions for a cell‐state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions.Research limita...

27 citations

Journal ArticleDOI
TL;DR: This work proves that ergodicity is equivalent to nilpotency, and is therefore undecidable, and proposes an efficient perfect sampling algorithm for the invariant measure of an ergodic PCA, based on a bounding process shown to be a PCA.
Abstract: A probabilistic cellular automaton (PCA) can be viewed as a Markov chain. The cells are updated synchronously and independently, according to a distribution depending on a finite neighborhood. We investigate the ergodicity of this Markov chain. A classical cellular automaton is a particular case of PCA. For a one-dimensional cellular automaton, we prove that ergodicity is equivalent to nilpotency, and is therefore undecidable. We then propose an efficient perfect sampling algorithm for the invariant measure of an ergodic PCA. Our algorithm does not assume any monotonicity property of the local rule. It is based on a bounding process which is shown to also be a PCA. Last, we focus on the PCA majority, whose asymptotic behavior is unknown, and perform numerical experiments using the perfect sampling procedure.

27 citations

Journal ArticleDOI
TL;DR: The complex dynamics of a simple stochastic Boolean network is studied and it is shown that the map is chaotic and the route to chaos is period-doubling bifurcations.
Abstract: We study the complex dynamics of a simple stochastic Boolean network. The investigated system is equivalent to a randomly connected Boolean cellular automaton. The dynamical evolution of the cellular automaton is exactly described by a polynomial map with binomial coefficients. We show that the map is chaotic and the route to chaos is period-doubling bifurcations.

26 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
202219
20212
20192
20184
201719