Abstract
Here we extend previous results in which a genetic algorithm (GA) is used to evolve three dimensional cellular automata (CA) to perform a non-trivial collective behavior (NTCB) task. Under a fitness function that is defined as an averaged area in the iterative map, the GA discovers CA rules with quasiperiod-3(QP3) collective behavior and others with period-3. We describe the generational progression of the GA and the synchronization necessary to maintain the global behavior is shown using a generalized space-time diagram that reveals the existence of propagating structures inside the system.
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References
C. H. Bennet, G. Grinstein, Yu He C. Jayaprakash and D. Mukamel. Stability of temporally periodic states of classical many-body systems. Phys. Rev. A, 41:1932–1935, 1990.
H. Chaté and P. Manneville. Collective behaviors in spatially extended systems with local interactions and synchronous updating. Progress Theor. Phys., 87(1):1–60, 1992.
J. P. Crutchfield and M. Mitchell. The evolution of emergent computation. Proceedings of the National Academy of Science U.S.A., 92:10742–10746, 1995.
R. Das, J. P. Crutchfield, M. Mitchell, and J. E. Hanson. Evolving globally synchronized cellular automata. In L. J. Eshelman, editor, Proceedings of the Sixth International Conference on Genetic Algorithms, pages 336–343, San Francisco, CA, 1995. Morgan Kaufmann.
R. Das, M. Mitchell, and J. P. Crutchfield. A genetic algorithm discovers particle-based computation in cellular automata. In Y. Davidor, H.-P. Schwefel, and R. Männer, editors, Parallel Problem Solving from Nature—PPSN III, volume 866, pages 344–353, Berlin, 1994. Springer-Verlag (Lecture Notes in Computer Science).
F. Jiménez-Morales, J.P. Crutchfield and M. Mitchell. Evolving two-dimensional cellular automata to perform density classification: A report on work in progress. In R. Serra, S. Bandini and F. Suggi Liverani, editors, Cellular Automata: Research Towards Industry, pages 3–14, London, 1998. Springer-Verlag.
H. Chaté, G. Grinstein and P. Lei-Hang Tan. Long-range correlations in systems with coherent(quasi)periodic oscillations. Phys.Rev.Lett., 74:912–915, 1995.
J. E. Hanson and J. P. Crutchfield. Computational mechanics of cellular automata: An example. Physica D, 103:169–189, 1997.
J. Hemmingsson. A totalistic three-dimensional cellular automaton with quasiperiodic behaviour. Physica A, 183:225–261, 1992.
F. Jiménez-Morales and J. J. Luque. Collective behaviour of a probabilistic cellular automaton with two absorbing phases. Phys. Lett. A, 181:33–38, 1993.
F. Jiméenez-Morales. Evolving three-dimensional cellular automata to perform a quasiperiod-3(p3) collective behavior task. Phys. Rev. E, (4):4934–4940, 1999.
C. G. Langton. Computation at the edge of chaos: Phase transitions and emergent computation. Physica D, 42:12–37, 1990.
M. Mitchell, J. P. Crutchfield, and P. T. Hraber. Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D, 75:361–391, 1994.
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Jiménez-Morales, F. (2000). The Evolution of 3-d C.A. to Perform a Collective Behavior Task. In: Miller, J., Thompson, A., Thomson, P., Fogarty, T.C. (eds) Evolvable Systems: From Biology to Hardware. ICES 2000. Lecture Notes in Computer Science, vol 1801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46406-9_10
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DOI: https://doi.org/10.1007/3-540-46406-9_10
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