On linear cellular automata

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Abstract

Wolfram cellular automata are considered and their operation is demonstrated using an example of traffic flow simulation. For the class of one-dimensional elementary cellular automata, the concept of linearity is introduced in the language of Zhegalkin operators. An algorithm for finding linear Zhegalkin operators with multipliers of three variables is presented. The algorithm is implemented in Python.

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About the authors

V. R. Kulikov

Siberian State University

Author for correspondence.
Email: v.r.kulikov@mail.ru
Russian Federation, Krasnoyarsk

А. А. Kytmanov

MIREA – Russian Technological University

Email: aakytm@gmail.com
Russian Federation, Moscow

А. О. Poroshin

Siberian State University

Email: poroshin.012332@gmail.com
Russian Federation, Krasnoyarsk

I. V. Timofeev

Kirensky Institute of Physics, Federal Research Center KSC SB RAS; Siberian State University

Email: tiv@iph.krasn.ru
Russian Federation, Krasnoyarsk; Krasnoyarsk

D. P. Fedchenko

Kirensky Institute of Physics, Federal Research Center KSC SB RAS; Siberian State University

Email: fdp@iph.krasn.ru
Russian Federation, Krasnoyarsk; Krasnoyarsk

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Supplementary files

Supplementary Files
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2. Fig. 1. The rule of the cellular automaton with the Wolfram code W=254.

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3. Fig. 2. The first 50 cycles of a cellular automaton with the Wolfram code W= 30 with a single-point initial state.

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4. Fig. 3. All the rules of the cellular automaton, for which the state of the cell depends only on the states of neighboring cells.

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5. Fig. 4. An element of a transport network modeled using a cellular automaton.

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6. Fig. 5. The result of modeling the congestion of the transport network.

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7. Fig. 6. Actions of Zhegalkin operators with multipliers of two variables.

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8. Fig. 7. Zhegalkin linear operators with multipliers of three variables.

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9. Fig. 8. Algorithm 1

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10. Fig. 9. Algorithm 2

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11. Fig. 10. Algorithm 3

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12. Fig. 11. Algorithm 4

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