Advertisement

Evolving the Game of Life

  • Dimitar Kazakov
  • Matthew Sweet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3394)

Abstract

It is difficult to define a set of rules for a cellular automaton (CA) such that creatures with life-like properties (stability and dynamic behaviour, reproducton and self-repair) can be grown from a large number of initial configurations. This work describes an evolutionary framework for the search of a CA with these properties. Instead of encoding them directly into the fitness function, we propose one, which maximises the variance of entropy across the CA grid. This fitness function promotes the existence of areas on the verge of chaos, where life is expected to thrive. The results are reported for the case of CA in which cells are in one of four possible states. We also describe a mechanism for fitness sharing that successfully speeds up the genetic search, both in terms of number of generations and CPU time.

Keywords

Genetic Algorithm Cellular Automaton Inductive Logic Programming Game Board Tile Size 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    De Jong, K.: An Analysis of the Behaviour of a Class of Genetic Adaptive Systems. PhD thesis, University of Michigan (1975)Google Scholar
  2. 2.
    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)zbMATHGoogle Scholar
  3. 3.
    Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989)zbMATHGoogle Scholar
  4. 4.
    Holland, J.: Adaption in natural and artificial systems. University of Michigan Press (1975)Google Scholar
  5. 5.
    Hollstien, R.: Artificial Genetic Adaption in Computer Control Systems. PhD thesis, University of Michigan (1971)Google Scholar
  6. 6.
    Mahfoud, S.: Niching Methods for Genetic Algorithms. PhD thesis, University of Illinois, Urbana-Champaign (1995)Google Scholar
  7. 7.
    Dawkins, R.: The Extended Phenotype. Oxford University Press, Oxford (1982)Google Scholar
  8. 8.
    Falconer, D.: Introduction to Quantitative Genetics, 2nd edn. Longman, London (1981)Google Scholar
  9. 9.
    Packard, N.H.: Adaptation towards the Edge of Chaos. In: Dynamic Patterns in Complex Systems. World Scientific, Singapore (1988)Google Scholar
  10. 10.
    Sapin, E., Bailleux, O., Chabrier, J.: Research of complex forms in the cellular automata by evolutionary algorithms. In: Proc. of the 6th Intl. Conf. on Artificial Evolution, Marseille (2003)Google Scholar
  11. 11.
    Wolfram, S.: Statistical mechanics of cellular automata. Reviews of Modern Physics 55 (1983)Google Scholar
  12. 12.
    Wolfram, S.: Universality and complexity in cellular automata. Physica D 10, 1–35 (1984)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Basanta, D.: Evolving automata to grow patterns. Symposium on Evolvability and Interaction (2003)Google Scholar
  14. 14.
    Wolfram, S., Packard, N.: Two-dimensional cellular automata. Statistical Physics 38, 901–946 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Muggleton, S., Raedt, L.D.: Inductive logic programming: Theory and methods. Journal of Logic Programming 19, 20, 629–679 (1994)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Dimitar Kazakov
    • 1
  • Matthew Sweet
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkHeslington, YorkUK

Personalised recommendations