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The Evolution of 3-d C.A. to Perform a Collective Behavior Task

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Evolvable Systems: From Biology to Hardware (ICES 2000)

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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

  1. 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.

    Article  MathSciNet  Google Scholar 

  2. 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.

    Article  Google Scholar 

  3. 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.

    Article  MATH  Google Scholar 

  4. 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.

    Google Scholar 

  5. 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).

    Google Scholar 

  6. 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.

    Google Scholar 

  7. 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.

    Article  Google Scholar 

  8. J. E. Hanson and J. P. Crutchfield. Computational mechanics of cellular automata: An example. Physica D, 103:169–189, 1997.

    Article  MathSciNet  Google Scholar 

  9. J. Hemmingsson. A totalistic three-dimensional cellular automaton with quasiperiodic behaviour. Physica A, 183:225–261, 1992.

    Article  Google Scholar 

  10. 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.

    Article  Google Scholar 

  11. F. Jiméenez-Morales. Evolving three-dimensional cellular automata to perform a quasiperiod-3(p3) collective behavior task. Phys. Rev. E, (4):4934–4940, 1999.

    Article  Google Scholar 

  12. C. G. Langton. Computation at the edge of chaos: Phase transitions and emergent computation. Physica D, 42:12–37, 1990.

    Article  MathSciNet  Google Scholar 

  13. M. Mitchell, J. P. Crutchfield, and P. T. Hraber. Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D, 75:361–391, 1994.

    Article  MATH  Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67338-5

  • Online ISBN: 978-3-540-46406-8

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