The Evolution of Computation in Co-evolving Demes of Non-uniform Cellular Automata for Global Synchronisation

  • Vesselin K. Vassilev
  • Julian F. Miller
  • Terence C. Fogarty
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1674)


We study the evolution of computation performed by non-uniform cellular automata in which global information processing appears at two different levels of self-organisation. In our model, the first level of self-organisation is characterised by interactions among cellular macrostructures or computational demes which compete for room in a finite grid of cells. This level is related to the formation, evolution and extinction of macrostructures, and it is designed in a completely local manner. The second level of self-organisation refers to the interactions among the cells within the demes. The model, derived from the cellular programming approach, allows global computation to occur as a result of many local interactions among computational demes of interacting cells. The study reveals some of the mechanisms by which co-evolving demes of non-uniform cellular automata perform non-trivial computation, such as the synchronisation tasks.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. Y. Vichniac, P. Tamayo, and H. Hartman. Annealed and quenched inhomogeneous cellular automata. J. Stat. Phys., 45:875–883, 1986.CrossRefMathSciNetGoogle Scholar
  2. 2.
    H. Gutowitz. Cellular Automata: Theory and Experiment. MIT Press, Cambridge, MA, 1991.MATHGoogle Scholar
  3. 3.
    M. Sipper. Non-uniform cellular automata: Evolution in rule space and formation of complex structures. In R. A. Brooks and P. Maes, eds., Artificial Life IV, pp. 394–399. MIT Press, Cambridge, MA, 1994.Google Scholar
  4. 4.
    P. Hogeweg. Mirror beyond mirror, puddles of life. In C. Langton, ed., Artificial Life, pp. 297–316. Addison-Wesley, Reading, MA, 1988.Google Scholar
  5. 5.
    K. Lindgren and M. G. Nordahl. Artificial food webs. In C. G. Langton, ed., Artificial Life III, pp. 73–103. Addison-Wesley, Reading, MA, 1994.Google Scholar
  6. 6.
    A. R. Johnson. Evolution of a size-structured, predator-prey community. In C. G. Langton, ed., Artificial Life III, pp. 105–129. Addison-Wesley, Reading, MA, 1994.Google Scholar
  7. 7.
    J. von Neumann. Theory of Self-Reproducing Automata. Univ. of Illinois, 1966.Google Scholar
  8. 8.
    S. Wolfram. Theory and Applications of Cellular Automata. World Scientific, 1986.Google Scholar
  9. 9.
    T. Toffoli and N. Margolus. Cellular Automata Machines. MIT Press, Cambridge, MA, 1987.Google Scholar
  10. 10.
    M. Mitchell. Computation in cellular automata: A selected review. In H. G. Schuster and T. Gramss, eds., Nonstandard Computation. VCH Verlagsgesellschaft, Weinheim, 1996.Google Scholar
  11. 11.
    M. Sipper. Simple + parallel + local = cellular computing. In A. E. Eiben, T. Bäck, M. Schoenauer, and H.-P. Schwefel, eds., PPSN V, pp. 653–662. Springer, Berlin, 1998.Google Scholar
  12. 12.
    S. Forrest. Emergent computation: Self-organizing, collective, and cooperative phenomena in natural and artificial computing networks. Physica D, 42:1–11, 1990.CrossRefMathSciNetGoogle Scholar
  13. 13.
    J. P. Crutchfield and M. Mitchell. The evolution of emergent computation. Proc. Natl. Acad. Sci. U.S.A, 92:10742–10746, 1995.MATHCrossRefGoogle Scholar
  14. 14.
    M. Mitchell, J. P. Crutchfield, and P. T. Hraber. Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D, 75:361–391, 1994.MATHCrossRefGoogle Scholar
  15. 15.
    R. Das, J. P. Crutchfield, M. Mitchell, and J. E. Hanson. Evolving globally synchronised cellular automata. In L. J. Eshelman, ed., Proc. 6th ICGA, pp. 336–343. Morgan Kaufmann, San Francisco, CA, 1995.Google Scholar
  16. 16.
    M. Land and R. Belew. No perfect two-state cellular automata for density classification exists. Phys. Rev. Lett., 74(25):5148–5150, 1995.CrossRefGoogle Scholar
  17. 17.
    M. Sipper. Co-evolving non-uniform cellular automata to perform computations. Physica D, 92:193–208, 1996.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    M. Sipper. Evolution of Parallel Cellular Machines: The Cellular Programming Approach. Springer, Berlin, 1997.Google Scholar
  19. 19.
    S. Wright. Stohastic processes in evolution. In J. Gurland, ed., Stohastic Models in Medicine and Biology, pp. 199–241. Univ. of Wisconsin, Madison, WI, 1964.Google Scholar
  20. 20.
    W. N. Martin, J. Lienig, and J. P. Cohoon. Island (migration) models: Evolutionary algorithms based on punctuated equilibra. In Th. Bäck, D. B. Fogel, and Z. Michalewicz, eds., Handbook of Evol. Comp., chap. C6.3:l. Oxford University Press, New York, NY, 1997.Google Scholar
  21. 21.
    V. K. Vassilev, J. F. Miller, and T. C. Fogarty. Co-evolving demes of non-uniform cellular automata for synchronisation. In A. Stoica, D. Keymeulen, and J. Lohn, eds., Proc. 1st NASA/DoD Worksh. Evol. Hard.. IEEE Computer Society Press, Piscataway, NJ, 1999. To appear (available via Scholar
  22. 22.
    J. Holland. Adaptation in Natural and Artificial Systems. MIT Press, Cambridge, MA, 1992. 2nd edition.Google Scholar
  23. 23.
    G. Nicolis and I. Prigogine. Self-Organization in Nonequilibrium Systems. Wiley Interscience, New York, NY, 1977.MATHGoogle Scholar
  24. 24.
    C. G. Langton. Computation at the edge of chaos: Phase transitions and emergent computation. Physica D, 42:12–37, 1990.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Vesselin K. Vassilev
    • 1
  • Julian F. Miller
    • 1
  • Terence C. Fogarty
    • 1
  1. 1.School of ComputingNapier UniversityEdinburghUK

Personalised recommendations