Abstract
It is speculated that there is a relationship between 1/f noise and computational universality in two-dimensional cellular automata. We use genetic algorithms to find two-dimensional cellular automata which have 1/f spectrum. Spectrum is calculated from the evolution of the state of cell from a random initial configuration. The fitness function is constructed in consideration of the spectral similarity to 1/f spectrum. The result shows that the rule with the third highest fitness in the experiment has 1/f spectrum and it behaves like the Game of Life, although two rules with the highest and the second highest fitness do not have 1/f spectrum.
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Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 2. Academic Press, New York (1982)
Ninagawa, S., Yoneda, M., Hirose, S.: 1/f Fluctuation in the ”Game of Life”. Physica D 118, 49–52 (1988)
Keshner, M.S.: 1/f Noise. Proc. IEEE 70, 211–218 (1982)
Mitchell, M., Hraber, P.T., Crutchfield, J.P.: Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations. Complex Systems 7, 89–130 (1993)
Mitchell, M., Crutchfield, J.P., Hraber, P.T.: Evolving Cellular Automata to Perform Computations: Mechanisms and Impediments. Physica D 75, 361–391 (1994)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C, 2nd edn., ch. 13. Cambridge University Press, Cambridge (1992)
Li, W.: Power Spectra of Regular Languages and Cellular Automata. Complex Systems 1, 107–130 (1987)
Langton, C.: Computation at the Edge of Chaos: Phase Transitions and Emergent Computation. Physica D 42, 12–37 (1990)
Ninagawa, S.: Cascade Process in the Transient Behavior of the ”Game of Life”. In: Proceedings of the Seventh International Symposium on Artificial Life and Robotics, vol. 16, pp. 124–127 (2002)
Ninagawa, S.: 1/f Fluctuation and Transient Behavior in the Game of Life. IPSJ Journal 43, 2017–2020 (2002) (in Japanese)
Cook, M.: Universality in Elementary Cellular Automata. Complex Systems 15, 1–40 (2004)
Ninagawa, S., Hirose, S., Hase, H., Yoneda, M.: Classification of One-dimensional Cellular Automata by Spectral Analysis. Trans. of the IEICE D-1 80, 856–865 (1997) (in Japanese)
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© 2005 Springer-Verlag Berlin Heidelberg
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Ninagawa, S. (2005). Evolving Cellular Automata by 1/f Noise. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds) Advances in Artificial Life. ECAL 2005. Lecture Notes in Computer Science(), vol 3630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11553090_46
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DOI: https://doi.org/10.1007/11553090_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28848-0
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