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Open AccessArticle

Spectrum of Elementary Cellular Automata and Closed Chains of Contours

by Alexander Tatashev 1,2,‡,§ and Marina Yashina 1,2,*,‡,§
1
Department of Higher Mathematics, Moscow Automobile and Road Construction State Technical University (MADI), Moscow 125319, Russia
2
Department of Mathematical Cybernetics and IT, Moscow Technical University of Comminications and Informatics (MTUCI), Moscow 111024, Russia
*
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in Buslaev, A.P.; Tatashev, A.G.; Fomina, M.J.; Yashina, M.V. On Spectra of Wolfram Cellular Automata in Hamming Spaces. In Proceedings of the 6th International Conference on Control, Mechatronics and Automation, Tokyo, Japan, 12–14 October 2018; pp. 123–127.
Current address: Department of Higher Mathematics, Moscow Automobile and Road Construction State Technical University (MADI), 64, Leningradky pr., Moscow 125319, Russia.
§
These authors contributed equally to this work.
Machines 2019, 7(2), 28; https://doi.org/10.3390/machines7020028
Received: 5 February 2019 / Revised: 22 April 2019 / Accepted: 25 April 2019 / Published: 30 April 2019
In this paper, we study the properties of some elementary automata. We have obtained the characteristics of these cellular automata. The concept of the spectrum for a more general class than the class of elementary automata is introduced. We introduce and study discrete dynamical systems which represents the transport of mass on closed chains of contours. Particles on contours move in accordance with given rules. These dynamical systems can be interpreted as cellular automata. Contributions towards this study are as follows. The characteristics of some elementary cellular automata have been obtained. A theorem about the velocity of particles’ movement on the closed chain has been proved. It has been proved that, for any ε > 0 , there exists a chain with flow density ρ < ε such that the average flow particle velocity is less than the velocity of free movement. An interpretation of this system as a transport model is given. The spectrum of a binary closed chain with some conflict resolution rule is studied. View Full-Text
Keywords: cellular automata; spectrum of dynamical system; mass transport dynamical systems cellular automata; spectrum of dynamical system; mass transport dynamical systems
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MDPI and ACS Style

Tatashev, A.; Yashina, M. Spectrum of Elementary Cellular Automata and Closed Chains of Contours . Machines 2019, 7, 28.

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