Skip to main content

Evolving Sequential Combinations of Elementary Cellular Automata Rules

  • Conference paper
Advances in Artificial Life (ECAL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3630))

Included in the following conference series:

Abstract

Performing computations with cellular automata, individually or arranged in space or time, opens up new conceptual issues in emergent, artificial life type forms of computation, and opens up the possibility of novel technological advances. Here, a methodology for combining sequences of elementary cellular automata is presented, in order to perform a given computation. The problem at study is the well-known density classification task that consists of determining the most frequent bit in a binary string. The methodology relies on an evolutionary algorithm, together with analyses driven by background knowledge on dynamical behaviour of the rules and their parametric estimates, as well as those associated with the formal behaviour characterisation of the rules involved. The resulting methodology builds upon a previous approach available in the literature, and shows its efficacy by leading to 2 rule combinations already known, and to additional 26, apparently unknown so far.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  • Kanoh, Wu, Y.: Evolutionary design of rule changing cellular automata. In: Palade, V., Howlett, R.J., Jain, L. (eds.) KES 2003. LNCS, vol. 2773, pp. 258–264. Springer, Heidelberg (2003), www.kslab.is.tsukuba.ac.jp/kanoh/kslab/study2/kanoh_KES2003.pdf

    Chapter  Google Scholar 

  • Wolfram, S.: A New Kind of Science. Wolfram Media, Champaign (2002)

    MATH  Google Scholar 

  • Lee, K.M., Xu, H., Chau, H.F.: Parity problem with a cellular automaton solution. Physical Review E 64, 026702/1–026702/4 (2001)

    Google Scholar 

  • Chau, H.F., Siu, L.W., Yan, K.K.: One dimensional n-ary density classification using two cellular automaton rules. International Journal of Modern Physics C 10(5), 883–889 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Chau, H.F., Yan, K.K., Wan, K.Y., Siu, L.W.: Classifying rational densities using two one-dimensional cellular automata. Physical Review E 57(2), 1367–1369 (1998)

    Article  Google Scholar 

  • Mitchell, M.: An Introduction to Genetic Algorithms. Bradford Book, Reprint edition (1998)

    MATH  Google Scholar 

  • Fukś, H.: Solution of the density classification problem with two cellular automata rules. Physics Review E 55, 2081R–2084R, (1997)

    Article  Google Scholar 

  • Sipper, M., Capcarrère, M.S., Ronald, E.: A simple cellular automaton that solves the density and ordering problems. International Journal of Modern PhysicsC 9(7), 899–902 (1998)

    Article  Google Scholar 

  • Mitchell, M., Crutchfield, J.P., Das, R.: Evolving cellular automata to perform computations. In: Back, T., Fogel, D., Michalewicz, Z. (eds.) Handbook of Evolutionary Computation. Oxford University Press, Oxford (1998)

    Google Scholar 

  • de Oliveira, P.P.B., Vaiano, R.B.: Searching for a cellular automaton to solve the parity problem (in Portuguese). Unpublished manuscript under review (2005)

    Google Scholar 

  • Oliveira, G.M.B., de Oliveira, P.P.B., Omar, N.: Definition and applications of a five-parameter characterization of one-dimensional cellular rule space. Artificial Life Journal 7(3), 277–301 (2001)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Li, W.: Parameterizations of Cellular Automata Rule Space. SFI Technical Report: Preprints, Santa Fe, NM, USA (1991)

    Google Scholar 

  • Land, M.W.S., Belew, R.K.: No two-state CA for density classification exists. Physical Review Letters 74(25), 5148 (1995)

    Article  Google Scholar 

  • Mitchell, M.: An Introduction to Genetic Algorithms. Bradford Book, Reprint edition (1998)

    Google Scholar 

  • Bandini, S., Mauri, G., Serra, R.: Cellular automata: From a theoretical paralell computational model to its application to complex systems. Parallel Computing 27, 539–553 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Mitchell, M.: Computation in cellular automata: A selected review. In: Nonstandard Computation. VCH Verlagsgesellschaft, Weinheim (1996)

    Google Scholar 

  • Sarkar, P.: A brief history of cellular automata. ACM Computing Surveys 32(1), 80–107 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Martins, C.L.M., de Oliveira, P.P.B. (2005). Evolving Sequential Combinations of Elementary Cellular Automata Rules. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds) Advances in Artificial Life. ECAL 2005. Lecture Notes in Computer Science(), vol 3630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11553090_47

Download citation

  • DOI: https://doi.org/10.1007/11553090_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28848-0

  • Online ISBN: 978-3-540-31816-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics