Evolution of two-dimensional cellular automata. New forms of presentation

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dc.citation.epage90
dc.citation.issue1
dc.citation.journalTitleУкраїнський журнал інформаційних технологій
dc.citation.spage85
dc.citation.volume3
dc.contributor.affiliationДержавний університет інфраструктури та технологій
dc.contributor.affiliationState University of Infrastructure and Technology
dc.contributor.authorБілан, С. М.
dc.contributor.authorBilan, S. M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-03-23T10:27:01Z
dc.date.available2023-03-23T10:27:01Z
dc.date.created2021-10-10
dc.date.issued2021-10-10
dc.description.abstractРозглянуто клітинні автомати та форми відображення їх еволюції. Відомі й широко використовуються форми еволюції елементарних клітинних автоматів, що дало змогу фахівцям моделювати різні динамічні процеси та поведінку систем різного спрямування. В контексті легкої побудови форми еволюції елементарних клітинних автоматів труднощі виникають у представленні форми еволюції двовимірних клітинних автоматів, як синхронних, так і асинхронних. Еволюція двовимірних клітинних автоматів подається множиною станів двовимірних форм клітинних автоматів, що ускладнює сприйняття та визначення динаміки зміни станів. В статті запропоновано подання еволюції двовимірних клітинних автоматів у вигляді масивів двійкових кодів для кожної клітини поля. Кожний часовий такт зміни станів визначається станом логічної “1” або “0”, причому кожний наступний стан визначається збільшенням двійкового розряду на одиницю. Тобто формується двійковий код у бік старших розрядів. Отриманий двійковий код зумовлює код кольору, який призначається відповідній клітині на кожному кроці ітерації еволюції. Внаслідок такого кодування формується двовимірна матриця кольорів (кольорове зображення), яка за кольоровою структурою (розташування кольорів на двовимірному масиві) указує на еволюцію двовимірного клітинного автомата. Для представлення еволюції використано кодування Волфрама, яке збільшує кількість правил для двовимірного клітинного автомата. Правила використано для сусідства фон Неймана без урахування власного стану аналізованої клітини. Відповідно до отриманого двовимірного масиву кодів формується дискретне кольорове зображення. Колір кожного пікселя такого зображення кодується отриманим еволюційним кодом відповідної клітини двовимірного клітинного автомата з тими самими координатами. Запропонований підхід дає змогу простежувати поведінку клітинного автомата в часі залежно від його початкових станів.
dc.description.abstractThe paper considers cellular automata and forms of reflection of their evolution. Forms of evolution of elementary cellular automata are known and widely used, which allowed specialists to model different dynamic processes and behavior of systems in different directions. In the context of the easy construction of the form of evolution of elementary cellular automata, difficulties arise in representing the form of evolution of two-dimensional cellular automata, both synchronous and asynchronous. The evolution of two-dimensional cellular automata is represented by a set of states of two-dimensional forms of cellular automataon, which is displayed in different colors on a two-dimensional image The paper proposes the evolution of two-dimensional cel the own state of the analyzed cell. In accordance with the obtained two-dimensional array of codes, a discrete color image is formed. The color of each pixel of such an image is encoded by the obtained evolution code of the corresponding cell of the two-dimensional cellular automaton with the same coordinates. The bitness of the code depends on the number of time steps of evolution. The proposed approach allows us to trace the behavior of the cellular automaton in time depending on its initial states. Experimental analysis of various rules for the von Neumann neighborhood made it possible to determine various rules that allow the shift of an image in different directions, as well as various affine transformations over images. Using this approach, it is possible to describe various dynamic processes and natural phenomena.
dc.format.extent85-90
dc.format.pages6
dc.identifier.citationBilan S. M. Evolution of two-dimensional cellular automata. New forms of presentation / S. M. Bilan // Ukrainian Journal of Information Technology. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 3. — No 1. — P. 85–90.
dc.identifier.citationenBilan S. M. (2021) Evolution of two-dimensional cellular automata. New forms of presentation. Ukrainian Journal of Information Technology (Lviv), vol. 3, no 1, pp. 85-90.
dc.identifier.doihttps://doi.org/10.23939/ujit2021.03.085
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/57765
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofУкраїнський журнал інформаційних технологій, 1 (3), 2021
dc.relation.ispartofUkrainian Journal of Information Technology, 1 (3), 2021
dc.relation.references[1] ACRI. (2016). Effects of Agents Fear, Desire and Knowledge on Their Success When Crossing a CA Based Highway, at ABSim-CA Second International Workshop on Agent-Based Simulation & Cellular Automata, at the 12th International Conference on Cellular Automata for Research and Industry. ACRI 2016, Proceedings (September 05-08, 2016), Fez (Morocco), Sept. 05-08, 2016, Talk given on September 8. Retrieved from: http://acri2016.complexworld.net
dc.relation.references[2] Adamatzky, A. (2010). Game of life Cellular automata. Springer-Verlag London, 579. https://doi.org/10.1007/978-1-84996-217-9
dc.relation.references[3] Adamatzky, A. (2018). Cellular automata. A volume in the Enciclopedia of cjmplexity and systems science. Second edition. Springer Science + business media LLC, part of springer Nature. https://doi.org/10.1007/978-1-4939-8700-9
dc.relation.references[4] Bidlo, M. & Vasicek, Z. (2013). Evolution of cellular automata with conditionally matching rules. 2013 IEEE Congress on Evolutionary Computation, 1178–1185. https://doi.org/10.1109/CEC.2013.6557699
dc.relation.references[5] Bidlo, M. (2016). On Routine Evolution of Complex Cellular Automata IEEE Transactions on Evolutionary Computation, 20, 742–754. https://doi.org/10.1109/TEVC.2016.2516242
dc.relation.references[6] Bidlo, M. (2019). Comparison of Evolutionary Development of Cellular Automata Using Various Representations inproceedings, MENDEL, Soft Computing Journal, 25(1), 95–102. https://doi.org/10.13164/mendel.2019.1.095
dc.relation.references[7] Bilan, S. M. (2018). Formation Methods, Models, and Hardware Implementation of Pseudorandom Number Generators: Emerging Research and Opportunities. IGI Global. https://doi.org/10.4018/978-1-5225-2773-2
dc.relation.references[8] Bilan, S. M., & Al-Zoubi, S. I. (2019). Handbook of Research on Intelligent Data Processing and Information Security Systems. Edited by Hershey, USA: IGI Global. https://doi.org/10.4018/978-1-7998-1290-6
dc.relation.references[9] Bilan, S. M., Bilan, M. M., & Motornyuk, R. L. (2021). New Methods and Paradigms for Modeling Dynamic Processes Based on Cellular Automata. IGI Global. https://doi.org/10.4018/978-1-7998-2649-1
dc.relation.references[10] Bilan, Stepan, Elhoseny, Mohamed, & Hemanth, D. Jude (Eds.). (2020). Biometric Identification Technologies Based on Modern Data Mining Methods. Springer. https://doi.org/10.1007/978-3-030-48378-4
dc.relation.references[11] Breukelaar, R. & B¨ack, T. (2005). Using a genetic algorithm to evolve behavior in multi dimensional cellular automata. In Proceedings of the 2005 Genetic and Evolutionary Computation Conference, GECCO 2005. ACM, 107–114. https://doi.org/10.1145/1068009.1068024
dc.relation.references[12] Chavoya, A. & Duthen, Y. (2007). Use of a genetic algorithm to evolve an extended artificial regulatory network for cell pattern generation. In GECCO 07: Proceedings of the 9th annual conference on Genetic and evolutionary computation, 1062–1062, New York, NY, USA. ACM. https://doi.org/10.1145/1276958.1277167
dc.relation.references[13] Chen, Y., Wang, C., Li, H., Yap, J. B. H., Tang, R., & Xu, B. (2020). Cellular automaton model for social forces interaction in building evacuation for sustainable society. Sustainable Cities and Society, 53, 101913. https://doi.org/10.1016/j.scs.2019.101913
dc.relation.references[14] Elmenreich, W. & Fehervari, I. (2011). Evolving self-organizing cellular automata based on neural network genotypes. In Proc. of the 5th International Conference on Self-organizing Systems. Springer, 16–25. https://doi.org/10.1007/978-3-642-19167-1_2
dc.relation.references[15] Ershov, N. & Kravchuk, A. (2014). Discrete modeling using stochastic cellular automata. Bulletin of the Peoples Friendship University of Russia. Series: Mathematics, Computer Science, Physics, 2, 359–362.
dc.relation.references[16] Gardner, M. (1970). The fantastic combinations of John Conways new solitaire game “Life”. Scientific American, 4, 120–123. https://doi.org/10.1038/scientificamerican1070-120
dc.relation.references[17] Mauri, Giancarlo, El Yacoubi, Samira, Dennunzio, Alberto, Nishinari, Katsuhiro, & Manzoni, Luca (Eds.). (2018). Lecture Notes in Computer Science. 13th International Conference on Cellular Automata for Research and Industry, ACRI 2018, Como, Italy. (September 17–21, 2018), Proceedings, 11115, Springer. https://doi.org/10.1007/978-3-319-99813-8
dc.relation.references[18] Michal Bidlo, Zdenek Vasicek. (2021). Evolution of Cellular Automata Using Instruction-Based Approach. WCCI 2012 IEEE World Congress on Computational Intelligence. Australia, 1–8. https://doi.org/10.1109/CEC.2012.6256475
dc.relation.references[19] Mohammad, Ali Javaheri Javid. (2021). Aesthetic evaluation of cellular automata cjnfigurations using spatial complexity and Kolmogorov complexity. Romero et al. (Eds.). EvoMUSART, Springer, 147–160. https://doi.org/10.1007/978-3-030-72914-1_10
dc.relation.references[20] Motornyuk, R. L., & Bilan, S. (2019). The Moving Object Detection and Research Effects of Noise on Images Based on Cellular Automata With a Hexagonal Coating Form and Radon Transform. Handbook of Research on Intelligent Data Processing and Information Security Systems. Edited by Bilan, S. M., & Al-Zoubi, S. I. Hershey, USA: IGI Global, 330–359. https://doi.org/10.4018/978-1-7998-1290-6.ch013
dc.relation.references[21] Rocha, L. M. & Hordijk, W. (2005). Material representations: from the genetic code to the evolution of cellular automata. Artif Life. 2005 Winter-Spring, 11(1-2), 189–214. https://doi.org/10.1162/1064546053278964
dc.relation.references[22] Verykokou, S., Ioannidis, C., Athanasiou, G., Doulamis, N., & Amditis, A. (2018). 3D reconstruction of disaster scenes for urban search and rescue. Multimedia Tools and Applications, 77(8), 9691–9717. https://doi.org/10.1007/s11042-017-5450-y
dc.relation.references[23] Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3). https://doi.org/10.1103/RevModPhys.55.601
dc.relation.references[24] Wolfram, S. (2002). A new kind of science. Wolfram Media
dc.relation.references[25] Yuta, Kariyado, Camilo, Arevalo, & Julian, Villegas. (2021). Auralization of three-dimensional cellular automata. Romero et al. (Eds.). EvoMUSART, Springer, 161–170. https://doi.org/10.1007/978-3-030-72914-1_11
dc.relation.referencesen[1] ACRI. (2016). Effects of Agents Fear, Desire and Knowledge on Their Success When Crossing a CA Based Highway, at ABSim-CA Second International Workshop on Agent-Based Simulation & Cellular Automata, at the 12th International Conference on Cellular Automata for Research and Industry. ACRI 2016, Proceedings (September 05-08, 2016), Fez (Morocco), Sept. 05-08, 2016, Talk given on September 8. Retrieved from: http://acri2016.complexworld.net
dc.relation.referencesen[2] Adamatzky, A. (2010). Game of life Cellular automata. Springer-Verlag London, 579. https://doi.org/10.1007/978-1-84996-217-9
dc.relation.referencesen[3] Adamatzky, A. (2018). Cellular automata. A volume in the Enciclopedia of cjmplexity and systems science. Second edition. Springer Science + business media LLC, part of springer Nature. https://doi.org/10.1007/978-1-4939-8700-9
dc.relation.referencesen[4] Bidlo, M. & Vasicek, Z. (2013). Evolution of cellular automata with conditionally matching rules. 2013 IEEE Congress on Evolutionary Computation, 1178–1185. https://doi.org/10.1109/CEC.2013.6557699
dc.relation.referencesen[5] Bidlo, M. (2016). On Routine Evolution of Complex Cellular Automata IEEE Transactions on Evolutionary Computation, 20, 742–754. https://doi.org/10.1109/TEVC.2016.2516242
dc.relation.referencesen[6] Bidlo, M. (2019). Comparison of Evolutionary Development of Cellular Automata Using Various Representations inproceedings, MENDEL, Soft Computing Journal, 25(1), 95–102. https://doi.org/10.13164/mendel.2019.1.095
dc.relation.referencesen[7] Bilan, S. M. (2018). Formation Methods, Models, and Hardware Implementation of Pseudorandom Number Generators: Emerging Research and Opportunities. IGI Global. https://doi.org/10.4018/978-1-5225-2773-2
dc.relation.referencesen[8] Bilan, S. M., & Al-Zoubi, S. I. (2019). Handbook of Research on Intelligent Data Processing and Information Security Systems. Edited by Hershey, USA: IGI Global. https://doi.org/10.4018/978-1-7998-1290-6
dc.relation.referencesen[9] Bilan, S. M., Bilan, M. M., & Motornyuk, R. L. (2021). New Methods and Paradigms for Modeling Dynamic Processes Based on Cellular Automata. IGI Global. https://doi.org/10.4018/978-1-7998-2649-1
dc.relation.referencesen[10] Bilan, Stepan, Elhoseny, Mohamed, & Hemanth, D. Jude (Eds.). (2020). Biometric Identification Technologies Based on Modern Data Mining Methods. Springer. https://doi.org/10.1007/978-3-030-48378-4
dc.relation.referencesen[11] Breukelaar, R. & B¨ack, T. (2005). Using a genetic algorithm to evolve behavior in multi dimensional cellular automata. In Proceedings of the 2005 Genetic and Evolutionary Computation Conference, GECCO 2005. ACM, 107–114. https://doi.org/10.1145/1068009.1068024
dc.relation.referencesen[12] Chavoya, A. & Duthen, Y. (2007). Use of a genetic algorithm to evolve an extended artificial regulatory network for cell pattern generation. In GECCO 07: Proceedings of the 9th annual conference on Genetic and evolutionary computation, 1062–1062, New York, NY, USA. ACM. https://doi.org/10.1145/1276958.1277167
dc.relation.referencesen[13] Chen, Y., Wang, C., Li, H., Yap, J. B. H., Tang, R., & Xu, B. (2020). Cellular automaton model for social forces interaction in building evacuation for sustainable society. Sustainable Cities and Society, 53, 101913. https://doi.org/10.1016/j.scs.2019.101913
dc.relation.referencesen[14] Elmenreich, W. & Fehervari, I. (2011). Evolving self-organizing cellular automata based on neural network genotypes. In Proc. of the 5th International Conference on Self-organizing Systems. Springer, 16–25. https://doi.org/10.1007/978-3-642-19167-1_2
dc.relation.referencesen[15] Ershov, N. & Kravchuk, A. (2014). Discrete modeling using stochastic cellular automata. Bulletin of the Peoples Friendship University of Russia. Series: Mathematics, Computer Science, Physics, 2, 359–362.
dc.relation.referencesen[16] Gardner, M. (1970). The fantastic combinations of John Conways new solitaire game "Life". Scientific American, 4, 120–123. https://doi.org/10.1038/scientificamerican1070-120
dc.relation.referencesen[17] Mauri, Giancarlo, El Yacoubi, Samira, Dennunzio, Alberto, Nishinari, Katsuhiro, & Manzoni, Luca (Eds.). (2018). Lecture Notes in Computer Science. 13th International Conference on Cellular Automata for Research and Industry, ACRI 2018, Como, Italy. (September 17–21, 2018), Proceedings, 11115, Springer. https://doi.org/10.1007/978-3-319-99813-8
dc.relation.referencesen[18] Michal Bidlo, Zdenek Vasicek. (2021). Evolution of Cellular Automata Using Instruction-Based Approach. WCCI 2012 IEEE World Congress on Computational Intelligence. Australia, 1–8. https://doi.org/10.1109/CEC.2012.6256475
dc.relation.referencesen[19] Mohammad, Ali Javaheri Javid. (2021). Aesthetic evaluation of cellular automata cjnfigurations using spatial complexity and Kolmogorov complexity. Romero et al. (Eds.). EvoMUSART, Springer, 147–160. https://doi.org/10.1007/978-3-030-72914-1_10
dc.relation.referencesen[20] Motornyuk, R. L., & Bilan, S. (2019). The Moving Object Detection and Research Effects of Noise on Images Based on Cellular Automata With a Hexagonal Coating Form and Radon Transform. Handbook of Research on Intelligent Data Processing and Information Security Systems. Edited by Bilan, S. M., & Al-Zoubi, S. I. Hershey, USA: IGI Global, 330–359. https://doi.org/10.4018/978-1-7998-1290-6.ch013
dc.relation.referencesen[21] Rocha, L. M. & Hordijk, W. (2005). Material representations: from the genetic code to the evolution of cellular automata. Artif Life. 2005 Winter-Spring, 11(1-2), 189–214. https://doi.org/10.1162/1064546053278964
dc.relation.referencesen[22] Verykokou, S., Ioannidis, C., Athanasiou, G., Doulamis, N., & Amditis, A. (2018). 3D reconstruction of disaster scenes for urban search and rescue. Multimedia Tools and Applications, 77(8), 9691–9717. https://doi.org/10.1007/s11042-017-5450-y
dc.relation.referencesen[23] Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3). https://doi.org/10.1103/RevModPhys.55.601
dc.relation.referencesen[24] Wolfram, S. (2002). A new kind of science. Wolfram Media
dc.relation.referencesen[25] Yuta, Kariyado, Camilo, Arevalo, & Julian, Villegas. (2021). Auralization of three-dimensional cellular automata. Romero et al. (Eds.). EvoMUSART, Springer, 161–170. https://doi.org/10.1007/978-3-030-72914-1_11
dc.relation.urihttp://acri2016.complexworld.net
dc.relation.urihttps://doi.org/10.1007/978-1-84996-217-9
dc.relation.urihttps://doi.org/10.1007/978-1-4939-8700-9
dc.relation.urihttps://doi.org/10.1109/CEC.2013.6557699
dc.relation.urihttps://doi.org/10.1109/TEVC.2016.2516242
dc.relation.urihttps://doi.org/10.13164/mendel.2019.1.095
dc.relation.urihttps://doi.org/10.4018/978-1-5225-2773-2
dc.relation.urihttps://doi.org/10.4018/978-1-7998-1290-6
dc.relation.urihttps://doi.org/10.4018/978-1-7998-2649-1
dc.relation.urihttps://doi.org/10.1007/978-3-030-48378-4
dc.relation.urihttps://doi.org/10.1145/1068009.1068024
dc.relation.urihttps://doi.org/10.1145/1276958.1277167
dc.relation.urihttps://doi.org/10.1016/j.scs.2019.101913
dc.relation.urihttps://doi.org/10.1007/978-3-642-19167-1_2
dc.relation.urihttps://doi.org/10.1038/scientificamerican1070-120
dc.relation.urihttps://doi.org/10.1007/978-3-319-99813-8
dc.relation.urihttps://doi.org/10.1109/CEC.2012.6256475
dc.relation.urihttps://doi.org/10.1007/978-3-030-72914-1_10
dc.relation.urihttps://doi.org/10.4018/978-1-7998-1290-6.ch013
dc.relation.urihttps://doi.org/10.1162/1064546053278964
dc.relation.urihttps://doi.org/10.1007/s11042-017-5450-y
dc.relation.urihttps://doi.org/10.1103/RevModPhys.55.601
dc.relation.urihttps://doi.org/10.1007/978-3-030-72914-1_11
dc.rights.holder© Національний університет „Львівська політехніка“, 2021
dc.subjectклітинний автомат
dc.subjectзображення
dc.subjectоколиця клітин
dc.subjectеволюція
dc.subjectCellular automata
dc.subjectimage
dc.subjectcell neighborhood
dc.subjectevolution
dc.subject.udc004.932
dc.titleEvolution of two-dimensional cellular automata. New forms of presentation
dc.title.alternativeЕволюція двовимірних клітинних автоматів. Нові форми подання
dc.typeArticle

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Ukrainian Journal of Information Technology. – 2021. – Vol. 3, No. 1