Abstract
The investigations carried out about the relationships between the generic dynamic behavior of cellular automata (CA) and their computational abilities have established a very active research area. Evolutionary methods have been used to look for CA with predefined computational abilities; one in particular that has been widely studied is the ability to solve the density classification task (DCT). The majority of these studies are focused on the one-dimensional CA. It has recently been shown that the use of a heuristic guided by parameters that estimate the dynamic behavior of 1D CA can improve the evolutionary search for DCT. The present work shows the application of three parameters previously published in the one-dimensional context generalized to the two-dimensional space: sensitivity, neighborhood dominance and activity propagation were used to evolve CA able to perform the two-dimensional version of the density classification task. The results obtained show that the parameters can effectively help a genetic algorithm in searching for 2D CA. A new rule was found which performed better than others previously published for the 2D DCT.
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Andre, D., Bennett III, F., Koza, J.: Discovery by Genetic Programming of a Cellular Automata Rule that is Better than any Known Rule for the Majority Classification Problem. In: Proceedings of Genetic Programming 1996. Stanford University, Stanford (1996)
Bedau, M., McCaskill, J., Packard, N., Rasmussen, S., Adami, C., Green, D., Ikegami, T., Kaneko, K., Ray, T.: Open Problems in Artificial Life. Artificial Life 6(4), 363–376 (2000)
Binder, P.: A Phase Diagram for Elementary Cellular Automata. Complex Systems 7, 241–247 (1993)
Capcarrère, M., Sipper, M., Tomassini, M.: Two-state, r=1, cellular automata that classifies density. Physical Review Letters 77(24), 4969–4971 (1996)
Culik II, K., Hurd, L., Yu, S.: Computation Theoretic Aspects of Cellular Automata. Physica D 45, 357–378 (1990)
Fukś, H.: Solution of the density classification problem with two cellular automata rules. Physics Review E 55, 2081R–2084R (1997)
Goldberg, D.: Genetic algorithm in search, optimization and machine learning. Addison-Wesley, Reading (1989)
Juillé, H., Pollack, J.: Coevolving the “Ideal” Trainer: Application to the Discovery of Cellular Automata Rules. In: Proceedings of Genetic Programming Conference, Madison, vol. 3 (1998)
Land, M., Belew, R.: No Perfect Two-State Cellular Automata for Density Classification Exists. Physical Review Letters 74(25), 5148–5150 (1995)
Langton, C.: Computation at the Edge of Chaos: Phase Transitions and Emergent Computation. Physica D 42, 12–37 (1990)
Li, W., Packard, N.: The Structure of Elementary Cellular Automata Rule Space. Complex Systems 4, 281–297 (1990)
Mitchell, M., Hraber, P., Crutchfield, J.: Evolving Cellular Automata to Perform Computations: Mechanisms and Impediments. Physica D 75, 361–391 (1994)
Mitchell, M.: Computation in Cellular Automata: A Selected Review. In: Nonstandard Computation. VCH Verlagsgesellschaft, Weinheim (1996)
Morales, F., Crutchfield, J., Mitchell, M.: Evolving two-dimensional cellular automata to perform density classification: a report on work in progress. Parallel Computing 27, 571–585 (2000)
Oliveira, G., de Oliveira, P., Omar, N.: Evolving Solutions of the Density Classification Task in 1D Cellular Automata, Guided by Parameters that Estimate their Dynamic Behavior. In: Bedau, M.A., Mc Caskill, J.S., Packard, N.H., Rasmussen, S. (eds.) Proceeding of Artificial Life VII, pp. 428–436 (2000)
Oliveira, G., de Oliveira, P., Omar, N.: Definition and Applications of a Five-Parameter Characterization of One-Dimensional Cellular Automata Rule Space. Artificial Life 7(3), 277–301 (2001)
Oliveira, G., de Oliveira, P., Omar, N.: Searching for one-dimensional cellular automata in the absence of a priori information. In: Kelemen, J., Sosík, P. (eds.) ECAL 2001. LNCS (LNAI), vol. 2159, pp. 262–271. Springer, Heidelberg (2001)
Oliveira, G., de Oliveira, P., Omar, N.: Improving Genetic Search for One-Dimensional Cellular Automata, Using Heuristics Related to Their Dynamic Behavior Forecast. In: Proc. of the 2001 IEEE Conference on Evolutionary Computation, Seoul, South Korea, pp. 348–355. IEEE Press, Piscataway (2001)
Oliveira, G., Siqueira, S.: Parameter Characterization of Two-Dimensional Cellular Automata Rule Space. Submitted to Physica D (2005)
Packard, N.: Adaptation toward the Edge of Chaos. In: Dynamic Patterns in Complex Systems, pp. 293–301. World Scientific, Singapore (1988)
Reynaga, R., Amthauer, E.: Two-dimensional cellular automata of radius one for density classification task ρ =1/2. Pattern Recognition Letters 24, 2849–2856 (2003)
Sipper, M., Capcarrère, M., Ronald, E.: A simple cellular automaton that solves the density and ordering problems. International Journal of Modern Physics 9(7), 899–902 (1998)
Werfel, J., Mitchell, M., Crutchfield, J.: Resource Sharing and Coevolution in Evolving Cellular Automata. IEEE Transactions on Evolutionary Computation 4(4), 388–393 (2000)
Wolfram, S.: Computation Theory of Cellular Automata. Communication in Mathematical Physics 96, 15–57 (1984)
Wuensche, A.: Classifying Cellular Automata Automatically: Finding gliders, filtering, and relating space-time patterns, attractor basins and the Z parameter. Complexity 4(3), 47–66 (1999)
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de Oliveira, G.M.B., Siqueira, S.R.C. (2005). Using Dynamic Behavior Prediction to Guide an Evolutionary Search for Designing Two-Dimensional Cellular Automata. 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_50
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DOI: https://doi.org/10.1007/11553090_50
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