- PII
- 10.31857/S0132347424010032-1
- DOI
- 10.31857/S0132347424010032
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume / Issue number 1
- Pages
- 30-39
- 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.
- Keywords
- клеточный автомат код Вольфрама оператор Жегалкина
- Date of publication
- 17.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 10
References
- 1. Neumann J. Theory of self-reproducing automata //Edited by Arthur W. Burks. 1966.
- 2. Цетлин М.Л. Некоторые задачи о поведении конечных автоматов //Доклады Академии наук. Российская академия наук, 1961. Т. 139. № 4. С. 830–833.
- 3. Conway J. et al. The game of life //Scientific American. 1970. Т. 223. № 4. С. 4.
- 4. Batty M. Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies. 2009.
- 5. Ghosh P. et al. Application of Cellular automata and Markov-chain model in geospatial environmental modeling-A review //Remote Sensing Applications: Society and Environment. — 2017. Т. 5. С. 64–77.
- 6. Гасников А. и др. (ред.). Введение в математическое моделирование транспортных потоков. Litres, 2022.
- 7. Fronczak P. et al. Cellular automata approach to modeling self-organized periodic patterns in nanoparticle-doped liquid crystals //Physical Review E. 2022. Т. 106. № 4. С. 44705.
- 8. Janssens K.G.F. An introductory review of cellular automata modeling of moving grain boundaries in polycrystalline materials //Mathematics and Computers in Simulation. 2010. Т. 80. № 7. С. 1361–1381.
- 9. Lemont B. Kier and Paul G. Seybold. Cellular Automata Modeling of Complex Biochemical Systems // Encyclopedia of Complexity and Systems Science, 2015.
- 10. Kozhoridze G., Dor E.B., Sternberg M. Assessing the Dynamics of Plant Species Invasion in Eastern-Mediterranean Coastal Dunes Using Cellular Automata Modeling and Satellite Time-Series Analyses //Remote Sensing. 2022 Т. 14. № 4. С. 1014.
- 11. Wolfram S. Statistical mechanics of cellular automata //Reviews of modern physics. – 1983. Т. 55. № 3. С. 601.
- 12. Wolfram S. et al. A new kind of science. Champaign: Wolfram media, 2002. Т. 5. С. 130.
- 13. Tomassini M., Sipper M., Perrenoud M. On the generation of high-quality random numbers by two-dimensional cellular automata // IEEE Transactions on computers. 2000. Т. 49. № 10. С. 1146–1151.
- 14. Walus K. et al. RAM design using quantum-dot cellular automata // NanoTechnology Conference. 2003. Т. 2. С. 160–163.
- 15. Cagigas-Muniz D. et al. Efficient simulation execution of cellular automata on GPU // Simulation Modelling Practice and Theory. 2022. Т. 118. С. 102519.
- 16. Sato T. Decidability for some problems of linear cellular automata over finite commutative rings // Information Processing Letters. 1993. Т. 46. № 3. С. 151–155.
- 17. Martin A. et al. Reversibility of linear cellular automata // Applied Mathematics and Computation. 2011. Т. 217. № 21. С. 8360-8366.
- 18. Martin del Rey A., Casado Vara R., Hernández Serrano D. Reversibility of symmetric linear cellular automata with radius r = 3 //Mathematics. 2019. Т. 7. № 9. С. 816.
- 19. Жегалкин И.И. Арифметизация символической логики //Математический сборник. 1928. Т. 35. № 3–4. С. 311–377.
- 20. Федченко Д.П., Новиков В.В., Тимофеев И.В. Фотонные топологические изоляторы типа Руднера на языке трехцветных клеточных автоматов // Ученые записки физического факультета МГУ. 2021. № 5. С. 2150302.
- 21. Fedchenko D.P., Kim P.N., Timofeev I.V. Photonic Topological Insulator Based on Frustrated Total Internal Reflection in Array of Coupled Prism Resonators //Symmetry. 2022. Т. 14. № 12. С. 2673.
- 22. Гальперин Г. А., Земляков А. Н. Математические бильярды: Бильярдные задачи и смежные вопросы математики и механики. Наука. Гл. ред. физ.-мат. лит., 1990.
