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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.


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Journal Article
TL;DR: This paper introduces a different way to visualize the evolution of continuous cellular automata called Radial Representation and proposes an empirical classification of FCA based on the length of the observed periodic behavior: interestingly, all the minimum periods that the authors observe are of lengths one, two, four, or n (where n is the size of a configuration).
Abstract: Continuous cellular automata (or coupled map lattices) are cellular automata where the state of the cells are real values in [0, 1] and the local transition rule is a real function. The classical observation medium for cellular automata, whether Boolean or continuous, is the space-time diagram, where successive rows correspond to successive configurations in time. In this paper we introduce a different way to visualize the evolution of continuous cellular automata called Radial Representation and we employ it to observe a particular class of continuous cellular automata called fuzzy cellular automata (FCA), where the local rule is the "fuzzification" of the disjunctive normal form that describes the local rule of the corresponding Boolean cellular automata. Our new visualization method reveals interesting dynamics that are not easily observable with the space-time diagram. In particular, it allows us to detect the quick emergence of spatial correlations among cells and to observe that all circular FCA from random initial configurations appear to converge towards an asymptotic periodic behavior. We propose an empirical classification of FCA based on the length of the observed periodic behavior: interestingly, all the minimum periods that we observe are of lengths one, two, four, or n (where n is the size of a configuration).

12 citations

Journal ArticleDOI
TL;DR: This paper proposes another method to obtain a @l-free automaton from a regular expression, whose number of states is bounded above by the size of both the partial derivatives automaton and of the follow automaton.

12 citations

Journal ArticleDOI
TL;DR: A general method to construct a partial difference equation which preserves any time evolution patterns of a cellular automaton is proposed, based on inverse ultradiscretization with filter functions.
Abstract: We propose a general method to construct a partial difference equation which preserves any time evolution patterns of a cellular automaton. The method is based on inverse ultradiscretization with filter functions.

12 citations

Book ChapterDOI
01 Aug 2006
TL;DR: In this paper, it was shown that there is an infinite strict double-dimensional-bit hierarchy for one-dimensional iterative arrays and for two-way cellular automata with inter-cell communication restricted to a constant number of bits independent of the number of states.
Abstract: A d-dimensional cellular automaton with sequential input mode is a d-dimensional grid of interconnected interacting finite automata. The distinguished automaton at the origin, the communication cell, is connected to the outside world and fetches the input sequentially. Often in the literature this model is referred to as iterative array. We investigate d-dimensional iterative arrays and one-dimensional cellular automata operating in real and linear time, whose inter-cell communication is restricted to some constant number of bits independent of the number of states. It is known that even one-dimensional one-bit iterative arrays accept rather complicated languages such as a p |p prim or a 2n |n∈ℕ [16]. We show that there is an infinite strict double dimension-bit hierarchy. The computational capacity of the one-dimensional devices in question is compared with the power of communication-restricted two-way cellular automata. It turns out that the relations are quite different from the relations in the unrestricted case. On passing, we obtain an infinite strict bit hierarchy for real-time two-way cellular automata and, moreover, a very dense time hierarchy for every k-bit cellular automata, i.e., just one more time step leads to a proper superfamily of accepted languages.

12 citations

Journal ArticleDOI
TL;DR: The class of deterministic one-dimensional cellular automata studied recently by Wolfram are considered and it is shown that point attractors under appropriate circumstances provide good approximations to the frequencies of local patterns generated by the discrete rules from which they were derived.

12 citations

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