A Genetic Algorithm to Study a P3 Non-trivial Collective Task

F. Jiménez-Morales, J. L. Guisado

2012

Abstract

Here we report new results of a genetic algorithm (GA) used to evolve one dimensional Cellular Automata (CA) to perform a P3 non-trivial collective behavior task. For this task the goal is to find a CA rule that reaches one final configuration in which the concentration of active cells oscillates among three different values. Though the majority of the best evolved rules belong to the II Wolfram’s class, the GA also finds rules of the III and IV classes. The different computational mechanisms used by each rule to synchronize the entire lattice are analyzed by means of the spatio-temporal patterns generated.

References

  1. Bennet, C. H., Grinstein, G., He, Y., Jayaprakash, C., and Mukamel, D. (1990). Stability of temporally periodic states of classical many-body systems. Phys. Rev. A, 41:1932-1935.
  2. Chaté, H. and P.Manneville (1992). Collective behaviors in spatially extended systems with local interactions and synchronous updating. Progress Theor. Phys., 87(1):1-60.
  3. Crutchfield, J. P. and Mitchell, M. (1995). The evolution of emergent computation. Proceedings of the National Academy of Science U.S.A., 92:10742-10746.
  4. Das, R., Crutchfield, J. P., Mitchell, M., and Hanson, J. E. (1995). Evolving globally synchronized cellular automata. In Eshelman, L. J., editor, Proceedings of the Sixth International Conference on Genetic Algorithms, pages 336-343, San Francisco, CA. Morgan Kaufmann.
  5. Das, R., Mitchell, M., and Crutchfield, J. P. (1994). A genetic algorithm discovers particle-based computation in cellular automata. In Davidor, Y., Schwefel, H.- P., and Männer, R., editors, Parallel Problem Solving from Nature-PPSN III, volume 866, pages 344-353, Berlin. Springer-Verlag (Lecture Notes in Computer Science).
  6. Hanson, J. E. and Crutchfield, J. P. (1997). Computational mechanics of cellular automata: An example. Physica D, 103:169-189.
  7. Jiménez-Morales, F. (1999). Evolving three-dimensional cellular automata to perform a quasiperiod-3(p3) collective behavior task. Phys. Rev. E, 60(4):4934-4940.
  8. Jiménez-Morales, F. (2000). The evolution of 3-d c.a. to perform a collective behavior task. In Miller, J., Thompson, A., P.Thompson, and Fogarty, T. C., editors, Evolvable Systems: From Biology to Hardware ICES-2000, LNCS 1801, pages 90-102, Berlin. Springer-Verlag.
  9. Jiménez-Morales, F., Mitchell, M., and Crutchfield, J. (2002). Evolving one dimensional cellular automata to perform non-trivial collective behavior task: One case study. In Sloot, P., Tan, C. K., Dongarra, J., and Hoekstra, A., editors, Computational Science ICSS2002, LNCS 2331, pages 793-802, Berlin. SpringerVerlag.
  10. Jiménez-Morales, F. and Tomassini, M. (2004). Globally synchronized oscillations in an one-dimensional cellular automaton. Int. Jour. Modern Physics C, 15(3):409-425.
  11. Langton, C. G. (1990). Computation at the edge of chaos: Phase transitions and emergent computation. Physica D, 42:12-37.
  12. Mitchell, M., Crutchfield, J. P., and Hraber, P. T. (1994). Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D, 75:361 - 391.
  13. Mitchell, M., Hraber, P. T., and Crutchfield, J. P. (1993). Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems, 7:89 - 130.
  14. Wolfram, S. (1984). Universality and complexity in cellular automata. Physica D, 10:1.
  15. Wolfram, S. (1994). Cellular Automata and Complexity. Addison-Wesley, USA, first edition.
Download


Paper Citation


in Harvard Style

Jiménez-Morales F. and L. Guisado J. (2012). A Genetic Algorithm to Study a P3 Non-trivial Collective Task . In Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012) ISBN 978-989-8565-33-4, pages 250-256. DOI: 10.5220/0004179502500256


in Bibtex Style

@conference{ecta12,
author={F. Jiménez-Morales and J. L. Guisado},
title={A Genetic Algorithm to Study a P3 Non-trivial Collective Task},
booktitle={Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)},
year={2012},
pages={250-256},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004179502500256},
isbn={978-989-8565-33-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2012)
TI - A Genetic Algorithm to Study a P3 Non-trivial Collective Task
SN - 978-989-8565-33-4
AU - Jiménez-Morales F.
AU - L. Guisado J.
PY - 2012
SP - 250
EP - 256
DO - 10.5220/0004179502500256