Abstract
In this study we present some advanced experiments dealing with the evolutionary design of multi-state uniform cellular automata. The generic square calculation problem in one-dimensional automata will be treated as one of the case studies. An analysis of the evolutionary experiments will be proposed and properties of the resulting cellular automata will be discussed. It will be demonstrated that various approaches to the square calculations in cellular automata exist, some of which substantially overcome the known solution. The second case study deals with a non-trivial pattern development problem in two-dimensional automata. Some of the results will be presented which indicate that an exact behaviour can be automatically designed even for cellular automata working with more than ten cell states. A discussion for both case studies is included and potential areas of further research are highlighted.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
References
Basanta, D., Bentley, P., Miodownik, M., Holm, E.: Evolving cellular automata to grow microstructures. Genetic Programming. Lecture Notes in Computer Science, vol. 2610, pp. 1–10. Springer, Berlin Heidelberg (2003)
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 4, 2nd edn. A K Peters/CRC Press, Boca Raton (2004)
Bidlo, M.: Investigation of replicating tiles in cellular automata designed by evolution using conditionally matching rules. In: 2015 IEEE International Conference on Evolvable Systems (ICES), Proceedings of the 2015 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 1506–1513. IEEE Computational Intelligence Society (2015)
Bidlo, M.: Evolution of generic square calculations in cellular automata. In: Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 3: ECTA, pp. 94–102. SciTePress - Science and Technology Publications (2016)
Bidlo, M.: On routine evolution of complex cellular automata. IEEE Trans. Evol. Comput. 20(5), 742–754 (2016)
Bidlo, M., Vasicek, Z.: Evolution of cellular automata with conditionally matching rules. In: 2013 IEEE Congress on Evolutionary Computation (CEC 2013), pp. 1178–1185. IEEE Computer Society (2013)
Codd, E.F.: Cellular Automata. Academic Press, New York (1968)
Durand, B., Rka, Z.: The game of life: universality revisited. Mathematics and Its Applications. Cellular Automata, vol. 460, pp. 51–74. Springer, Netherlands (1999)
Elmenreich, W., Fehérvári, I.: Evolving self-organizing cellular automata based on neural network genotypes. In: Proceedings of the 5th International Conference on Self-organizing Systems, pp. 16–25. Springer (2011)
Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
Ilachinski, A.: Cellular Automata: A Discrete Universe. World Scientific, Singapore (2001)
Lindgren, K., Nordahl, M.G.: Universal computation in simple one-dimensional cellular automata. Complex Syst. 4(3), 299–318 (1990)
Mardiris, V., Sirakoulis, G., Karafyllidis, I.: Automated design architecture for 1-d cellular automata using quantum cellular automata. IEEE Trans. Comput. 64(9), 2476–2489 (2015)
Ninagawa, S.: Solving the parity problem with rule 60 in array size of the power of two. J. Cell. Autom. 8(3–4), 189–203 (2013)
Perrier, J.-Y., Sipper, M.: Toward a viable, self-reproducing universal computer. Phys. D 97(4), 335–352 (1996)
Rendell, P.: A universal turing machine in Conway’s game of life. In: 2011 International Conference on High Performance Computing and Simulation (HPCS), pp. 764–772 (2011)
Rendell, P.: A fully universal turing machine in Conway’s game of life. J. Cell. Autom. 9(1–2), 19–358 (2013)
Sahoo, S., Choudhury, P.P., Pal, A., Nayak, B.K.: Solutions on 1-d and 2-d density classification problem using programmable cellular automata. J. Cell. Autom. 9(1), 59–88 (2014)
Sahu, S., Oono, H., Ghosh, S., Bandyopadhyay, A., Fujita, D., Peper, F., Isokawa, T., Pati, R.: Molecular implementations of cellular automata. In: Cellular Automata for Research and Industry. Lecture Notes in Computer Science, vol. 6350. Springer, Berlin (2010)
Sipper, M.: Quasi-uniform computation-universal cellular automata. Advances in Artificial Life. ECAL 1995. Lecture Notes in Computer Science, vol. 929, pp. 544–554. Springer, Berlin (1995)
Sridharan, K., Pudi, V.: Design of Arithmetic Circuits in Quantum Dot Cellular Automata Nanotechnology. Springer International Publishing, Switzerland (2015)
Stefano, G.D., Navarra, A.: Scintillae: how to approach computing systems by means of cellular automata. Cellular Automata for Research and Industry. Lecture Notes in Computer Science, vol. 7495, pp. 534–543. Springer, Berlin (2012)
Suzudo, T.: Searching for pattern-forming asynchronous cellular automata - an evolutionary approach. Cellular Automata. Lecture Notes in Computer Science, vol. 3305, pp. 151–160. Springer, Berlin (2004)
Tempesti, G.: A new self-reproducing cellular automaton capable of construction and computation. In: Advances in Artificial Life, Proceedings of the 3rd European Conference on Artificial Life. Lecture Notes in Artificial Intelligence, vol. 929, pp. 555–563. Springer, Berlin (1995)
von Neumann, J.: The Theory of Self-reproducing Automata (Burks, A.W. (ed.)). University of Illinois Press, Urbana (1966)
Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)
Yuns, J.B.: Achieving universal computations on one-dimensional cellular automata. Cellular Automata for Research and Industry. Lecture Notes in Computer Science, vol. 6350, pp. 660–669. Springer, Berlin (2010)
Acknowledgements
This work was supported by The Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II), project IT4Innovations excellence in science – LQ1602, and from the Large Infrastructures for Research, Experimental Development and Innovations project “IT4Innovations National Supercomputing Center – LM2015070”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Bidlo, M. (2019). Advances in the Evolution of Complex Cellular Automata. In: Merelo, J.J., et al. Computational Intelligence. IJCCI 2016. Studies in Computational Intelligence, vol 792. Springer, Cham. https://doi.org/10.1007/978-3-319-99283-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-99283-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99282-2
Online ISBN: 978-3-319-99283-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)