A detailed study on implementing new approaches in the Game of Life
DOI:
https://doi.org/10.56294/dm202395Keywords:
Game of Life, Cellular Automata, AlgorithmsAbstract
In 1952, Alan Turing who is considered as a father of Computer Science, based on his previous scientific research on the theory of computation, he emphasized how important is the analysis of pattern formation in nature and developed a theory. In his theory, he described specific patterns in nature that could be formed from basic chemical systems. Turing in his previous studies in the theory of computation, he had constantly worked on symmetrical patterns that could be formed simultaneously and realized the necessity for further analysis of pattern formation in biological problems. However, it was until the late 1960s, when John Conway was the first to introduce the "Game of Life", an innovative mathematical game based on cellular automata, having a purpose to utilize the fundamental entities, called as cells, in two possible states described as "dead" or "alive". This paper tries to contribute to a better understanding of the "Game of Life" by implementing algorithmic approaches of this problem in PASCAL and Python programming languages. Also, inside the paper numerous variations and extensions of the Conway's Game of Life are proposed that introduce new ideas and concepts. Furthermore, several machine learning algorithms to learn patterns from large sets of Game of Life simulations and generate new rules or strategies are described in detail
References
1.Bays, C. (2010). Introduction to Cellular Automata and Conway’s Game of Life. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_1
2. Caballero, L., Hodge, B. and Hernandez, S. (2016) “Conway's ‘Game of life’ and the epigenetic principle,” Frontiers in Cellular and Infection Microbiology, 6. Available at: https://doi.org/10.3389/fcimb.2016.00057.
3. Wainwright, R. (2010). Conway’s Game of Life: Early Personal Recollections. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_2
4. Rendell, P. (2002). Turing Universality of the Game of Life. In: Adamatzky, A. (eds) Collision-Based Computing. Springer, London. https://doi.org/10.1007/978-1-4471-0129-1_18
5. Rendell P. Conway’s Game Life Turing Machine http://www.rendell.uk.co/gol
6. Turing A.M. On computable numbers, with applications to the entscheidungsproblem Proc. London Math. Soc. 42 (1937 230–265.
7. M. Gardner. Mathematical games: The fantastic combinations of John Conway's new solitaire Game 'Life'. Scientific American, 1970. 5, 11
8. Yurii Rogozhin. Small universal Turing machines. Theor. Comput. Sci., 168(2): 215-240, November 1996. ISSN 0304-3975. 2, 13, 46
9. Smith. Universality of Wolfram's 2, 3 Turing Machine, 2007. the Wolfram 2,3 Turing Machine Research Prize. 55, 185
10. S. Wolfram. Universality and complexity in cellular automata. Physica, 10D: 1-35, 1984. 4, 6, 13, 55, 185, 200
11. Martin Gardner, Mathematical games: The fantastic combinations of john conway’s new solitaire game “life”, Scientific American 223 (1970), 120–123.
12. Kazakov, Dimitar & Sweet, Matthew. (2004). Evolving the Game of Life. Lecture Notes in Computer Science. 3394. 10.1007/978-3-540-32274-0_9.
13. Hirte, R. (2022). John Horton Conway’s Game of Life, An overview and examples.
14. John von Neumann, Theory of self-reproducing automata, Edited by Arthur W. Burks(1966).
15. Christopher G Langton, Self-reproduction in cellular automata, Physica D: Nonlinear Phenomena 10 (1984), no. 1-2, 135–144.
16. Zaks, R. (1981). Introduction to Pascal (including UCSD Pascal). SYBEX Inc..
17. Triantafyllou, S.A. (2023). A Quantitative Research About MOOCs and EdTech Tools for Distance Learning. In: Auer, M.E., El-Seoud, S.A., Karam, O.H. (eds) Artificial Intelligence and Online Engineering. REV 2022. Lecture Notes in Networks and Systems, vol 524. Springer, Cham. https://doi.org/10.1007/978-3-031-17091-1_52
18. Triantafyllou, S.A. (2022). TPACK and Toondoo Digital Storytelling Tool Transform Teaching and Learning. In: Florez, H., Gomez, H. (eds) Applied Informatics. ICAI 2022. Communications in Computer and Information Science, vol 1643. Springer, Cham. https://doi.org/10.1007/978-3-031-19647-8_24
19. Adamatzky, A. (Ed.). (2010). Game of life cellular automata (Vol. 1). London: Springer.
20. Triantafyllou, S. A. (2022). "Work in progress: Educational Technology and Knowledge Tracing Models," 2022 IEEE World Engineering Education Conference (EDUNINE), 2022, pp. 1-4, https://doi.org/10.1109/EDUNINE53672.2022.9782335.
21. Triantafyllou, S. A. (2022). Magic squares in order 4K+2. 2022 30th National Conference with International Participation (TELECOM). https://doi.org/10.1109/TELECOM56127.2022.10017312
22. Rennard, J. P. (2002). Implementation of logical functions in the Game of Life. In Collisionbased computing (pp. 491-512). London: Springer London.
23. Triantafyllou, S.A. (2023). A Detailed Study on the 8 Queens Problem Based on Algorithmic Approaches Implemented in PASCAL Programming Language. In: Silhavy, R., Silhavy, P. (eds) Software Engineering Research in System Science. CSOC 2023. Lecture Notes in Networks and Systems, vol 722. Springer, Cham. https://doi.org/10.1007/978-3-031-35311-6_18
24. Springer, J. M., & Kenyon, G. T. (2021). It's hard for neural networks to learn the game of life. In 2021 International Joint Conference on Neural Networks (IJCNN) (pp. 1-8). IEEE.
25. Durand, B., & Róka, Z. (1999). The game of life: universality revisited. In Cellular Automata: a Parallel Model (pp. 51-74). Dordrecht: Springer Netherlands.
26. Rendell, P. (2011). A universal turing machine in conway's game of life. In 2011 International Conference on High Performance Computing & Simulation (pp. 764-772). IEEE.
27. Rodríguez-Pérez JA. Strengthening the Implementation of the One Health Approach in the Americas: Interagency Collaboration, Comprehensive Policies, and Information Exchange. Seminars in Medical Writing and Education 2022;1:11-11. https://doi.org/10.56294/mw202211.
28. Farhaoui, Y.and All, Big Data Mining and Analytics, 2023, 6(3), pp. I–II, DOI: 10.26599/BDMA.2022.9020045
29. Gonzalez-Argote D, Gonzalez-Argote J. Generation of graphs from scientific journal metadata with the OAI-PMH system. Seminars in Medical Writing and Education 2023;2:43-43. https://doi.org/10.56294/mw202343.
30. Farhaoui, Y. , "Big data analytics applied for control systems" Lecture Notes in Networks and Systems, 2018, 25, pp. 408–415. https://doi.org/10.1007/978-3-319-69137-4_36
31. Rodríguez FAR, Flores LG, Vitón-Castillo AA. Artificial intelligence and machine learning: present and future applications in health sciences. Seminars in Medical Writing and Education 2022;1:9-9. https://doi.org/10.56294/mw20229.
32. Alaoui, S.S., and all. "Hate Speech Detection Using Text Mining and Machine Learning", International Journal of Decision Support System Technology, 2022, 14(1), 80. DOI: 10.4018/IJDSST.286680
33. Alaoui, S.S.,and All "Data openness for efficient e-governance in the age of big data", International Journal of Cloud Computing, 2021, 10(5-6), pp. 522–532, https://doi.org/10.1504/IJCC.2021.120391
34. Vidal AAR de C. Modelamiento y análisis del comportamiento de la variable: Generación de Energía Eléctrica, en el sector eléctrico peruano utilizando la metodología Box and Jenkins, para la predicción de este recurso. Sincretismo 2020;1.
35. Tarik, A., and all."Recommender System for Orientation Student" Lecture Notes in Networks and Systems, 2020, 81, pp. 367–370. https://doi.org/10.1007/978-3-030-23672-4_27
36. Sossi Alaoui, S., and all. "A comparative study of the four well-known classification algorithms in data mining", Lecture Notes in Networks and Systems, 2018, 25, pp. 362–373. https://doi.org/10.1007/978-3-319-69137-4_32
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