Abstract
Here we present preliminary results in which a genetic algorithm (GA) is used to evolve one-dimensional binary-state cellular automata (CA) to perform a non-trivial task requiring collective behavior. Using a fitness function that is an average area in the iterative map, the GA discovers rules that produce a period-3 oscillation in the concentration of 1s in the lattice. We study one run in which the final state reached by the best evolved rule consists of a regular pattern plus some defects. The structural organization of the CA dynamics is uncovered using the tools of computational mechanics. PACS: 82.20Wt Computational modeling; simulation.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
T. Bohr, G. Grinstein, Y. He, and C. Jayaprakash. Coherence, Chaos, and Broken Symmetry in Classical, Many-Body Dynamical Systems. Phys. Rev. Lett., 58:2155–2158, 1987.
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.
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).
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 quasiperi-odic behaviour. Physica A, 183:225–261, 1992.
W. Hordijk. Dynamics, Emergent Computation, and Evolution in Cellular Automata. Ph.D. dissertation, Univ. New Mexico, 1999.
F. Jiménez-Morales and K. Hassan. Non-trivial collective behavior in three-dimensional totalistic illegal cellular automata with high connectivity. Physics Letters A, 240:151–159, 1998.
F. Jiménez-Morales. Evolving three-dimensional cellular automata to perform a quasiperiod-3(p3) collective behavior task. Phys. Rev. E, 60(4):4934–4940, 1999.
C. G.Langton. Studying Artificial Life with Cellular Automata. Physica D, 22:120–149, 1986.
M. Mitchell, J. P. Crutchfield, and P. T. Hraber. Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D, 75:361–391, 1994.
M. Sipper. Evolution of Parallel Cellular Machines. Springer, Germany, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Jiménez-Morales, F., Mitchell, M., Crutchfield, J.P. (2002). Evolving One Dimensional Cellular Automata to Perform a Non-Trivial Collective Behavior Task: One Case Study. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46043-8_80
Download citation
DOI: https://doi.org/10.1007/3-540-46043-8_80
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43591-4
Online ISBN: 978-3-540-46043-5
eBook Packages: Springer Book Archive