Skip to main content
SpringerLink
Log in

Enhancing the Computational Mechanics of Cellular Automata

  • Chapter
Nature Inspired Cooperative Strategies for Optimization (NICSO 2011)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 387))

  • 652 Accesses

Abstract

Cellular Automata are discrete dynamical systems having the ability to generate highly complex behavior starting from a simple initial configuration and set of update rules. However, the discovery of rules exhibiting a high degree of global self-organization for certain tasks is not easily achieved. In this paper, a fast compression based technique is proposed, capable of detecting promising emergent space-time patterns of cellular automata. This information can be used to automatically guide the evolutionary search toward more complex, better performing rules. Results are presented for the most widely studied cellular automata computation problem, the Density Classification Task, where incorporation of the proposed method almost always pushes the search beyond the simple block-expanding rules.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andre, D., Bennett III, F.H., Koza, J.R.: Discovery by genetic programming of a cellular automata rule that is better than any known rule for the majority classification problem. In: Proceedings of the First Annual Conference on Genetic Programming, GECCO 1996, pp. 3–11. MIT Press, Cambridge (1996)

    Google Scholar 

  2. Chira, C., Gog, A., Lung, R., Iclanzan, D.: Complex Systems and Cellular Automata Models in the Study of Complexity. In: Studia Informatica series, vol. LV(4), pp. 33–49 (2010)

    Google Scholar 

  3. Das, R., Mitchell, M., Crutchfield, J.P.: A genetic algorithm discovers particle-based computation in cellular automata. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 344–353. Springer, Heidelberg (1994)

    Google Scholar 

  4. de Oliveira, P.P.B., Bortot, J.C., Oliveira, G.: The best currently known class of dynamically equivalent cellular automata rules for density classification. Neurocomputing 70(1-3), 35–43 (2006)

    Article  Google Scholar 

  5. Ferreira, C.: Gene Expression Programming: A New Adaptive Algorithm for Solving Problems. Complex Systems 13(2), 87–129 (2001)

    MathSciNet  MATH  Google Scholar 

  6. Gacs, P., Kurdyumov, G.L., Levin, L.A.: One-dimensional uniform arrays that wash out finite islands. Probl. Perdachi. Inform. 14, 92–98 (1978)

    Google Scholar 

  7. Gog, A., Chira, C.: Cellular Automata Rule Detection Using Circular Asynchronous Evolutionary Search. In: Corchado, E., Wu, X., Oja, E., Herrero, Á., Baruque, B. (eds.) HAIS 2009. LNCS, vol. 5572, pp. 261–268. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Juille, H., Pollack, J.B.: Coevolving the ideal trainer: Application to the discovery of cellular automata rules. In: Koza, J.R., Banzhaf, W., Chellapilla, K., Deb, K., Dorigo, M., Fogel, D.B., Garzon, M.H., Goldberg, D.E., Iba, H., Riolo, R. (eds.) Genetic Programming 1998: Proceedings of the Third Annual Conference, University of Wisconsin, Madison, Wisconsin, USA, pp. 519–527. Morgan Kaufmann, San Francisco (1998)

    Google Scholar 

  9. Juille, H., Pollack, J.B.: Coevolutionary learning and the design of complex systems. Advances in Complex Systems 2(4), 371–394 (2000)

    Article  Google Scholar 

  10. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  11. Land, M., Belew, R.K.: No perfect two-state cellular automata for density classification exists. Physical Review Letters 74(25), 5148–5150 (1995)

    Article  Google Scholar 

  12. Mariano, A.S., de Oliveira, G.M.B.: Evolving one-dimensional radius-2 cellular automata rules for the synchronization task. In: AUTOMATA 2008 Theory and Applications of Cellular Automata, pp. 514–526. Luniver Press (2008)

    Google Scholar 

  13. Mitchell, M., Hraber, P.T., Crutchfield, J.P.: Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems 7, 89–130 (1993)

    MATH  Google Scholar 

  14. Mitchell, M., Crutchfield, J.P., Das, R.: Evolving cellular automata with genetic algorithms: A review of recent work. In: Proceedings of the First International Conference on Evolutionary Computation and Its Applications (EvCA 1996), Russian Academy of Sciences (1996)

    Google Scholar 

  15. Mitchell, M., Thomure, M.D., Williams, N.L.: The role of space in the Success of Coevolutionary Learning. In: Proceedings of ALIFE X - The Tenth International Conference on the Simulation and Synthesis of Living Systems (2006)

    Google Scholar 

  16. Jiménez Morales, F., Crutchfield, J.P., Mitchell, M.: Evolving two-dimensional cellular automata to perform density classification: a report on work in progress. Parallel Comput. 27, 571–585 (2001)

    Article  MATH  Google Scholar 

  17. Oliveira, G.M.B., Martins, L.G.A., de Carvalho, L.B., Fynn, E.: Some investigations about synchronization and density classification tasks in one-dimensional and two-dimensional cellular automata rule spaces. Electron. Notes Theor. Comput. Sci. 252, 121–142 (2009)

    Article  Google Scholar 

  18. Packard, N.H.: Adaptation toward the edge of chaos. In: Dynamic Patterns in Complex Systems, pp. 293–301. World Scientific, Singapore (1988)

    Google Scholar 

  19. Pagie, L., Mitchell, M.: A comparison of evolutionary and coevolutionary search. Int. J. Comput. Intell. Appl. 2(1), 53–69 (2002)

    Article  Google Scholar 

  20. Tomassini, M., Venzi, M.: Evolution of Asynchronous Cellular Automata for the Density Task. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 934–943. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  21. Wolz, D., de Oliveira, P.P.B.: Very effective evolutionary techniques for searching cellular automata rule spaces. Journal of Cellular Automata 3, 289–312 (2008)

    MathSciNet  MATH  Google Scholar 

  22. Wolfram, S. (ed.): Theory and Applications of Cellular Automata. Advanced series on complex systems, vol. 1. World Scientific Publishing, Singapore (1986)

    MATH  Google Scholar 

  23. Zhao, Y., Billings, S.A.: Identification of the Belousov-Zhabotinsky Reaction using Cellular Automata Models. International Journal of Bifurcation and Chaos 17(5), 1687–1701 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  24. Cook, M.: Universality in elementary cellular automata. Complex Systems 15(1), 1–40 (2004)

    MathSciNet  MATH  Google Scholar 

  25. Wuensche, A.: Classifying cellular automata automatically: finding gliders, filtering, and relating space-time patterns, attractor basins, and the z parameter. Complex 4, 47–66 (1999)

    Article  MathSciNet  Google Scholar 

  26. Wolfram, S.: Computation theory of cellular automata. Communications in Mathematical Physics 96(1), 15–57 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hanson, J., Crutchfield, J.: The attractorbasin portrait of a cellular automaton. Journal of Statistical Physics 66(5), 1415–1462 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  28. Hanson, J., Crutchfield, J.: Computational mechanics of cellular automata. PhD thesis, University of California, Berkeley, CA (1993)

    Google Scholar 

  29. Steiglitz, K., Kamal, I., Watson, A.: Embedding computation in one-dimensional automata by phase coding solitons. IEEE Trans. Comput. 37, 138–145 (1988)

    Article  MathSciNet  Google Scholar 

  30. Aizawa, Y., Nishikawa, I., Kaneko, K.: Soliton turbulence in one-dimensional cellular automata. Phys. D 45, 307–327 (1990)

    Article  MATH  Google Scholar 

  31. Crutchfield, J., Mitchell, M.: The evolution of emergent computation. Proceedings of the National Academy of Sciences 92(23), 10742 (1995)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Sapientia Hungarian University of Transylvania, 540485, Tg-Mureş, CP 4, OP 9, Romania

    David Iclănzan

  2. Department of Computer Science, Babeş-Bolyai University, Kogălniceanu no. 1, Cluj-Napoca, 400084, Romania

    Anca Gog & Camelia Chira

Authors
  1. David Iclănzan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anca Gog
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Camelia Chira
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science and A.I.E.T.S. Ingenieria Informatica y de Telecomunicación, University of Granada, C/ Periodista Daniel Saucedo Aranda s/n,, 18071, Granada, Spain

    David Alejandro Pelta

  2. School of Computer Science, University of Nottingham, Jubilee Campus Wollaton Road, NG8 1BB, Nottingham, UK

    Natalio Krasnogor

  3. Center for Cognitive and Neural Studies, Babes-Bolyai University of Cluj Napoca, (Coneural), Str. Ciresilor 29, 400487, Cluj-Napoca, Romania

    Dan Dumitrescu

  4. Department of Computer Science, Babes-Bolyai University, Kogalniceanu 1, 400084, Cluj-Napoca, Romania

    Camelia Chira

  5. Faculty of Economics and Business Administration, Babes-Bolyai University of Cluj Napoca, Str. Teodor Mihali Nr. 58-60, 400591, Cluj Napoca, Romania

    Rodica Lung

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Iclănzan, D., Gog, A., Chira, C. (2011). Enhancing the Computational Mechanics of Cellular Automata. In: Pelta, D.A., Krasnogor, N., Dumitrescu, D., Chira, C., Lung, R. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2011). Studies in Computational Intelligence, vol 387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24094-2_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24094-2_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24093-5

  • Online ISBN: 978-3-642-24094-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation