Natural Computing

, Volume 9, Issue 3, pp 513–543 | Cite as

Stochastic automated search methods in cellular automata: the discovery of tens of thousands of glider guns

Article

Abstract

This paper deals with the spontaneous emergence of glider guns in cellular automata. An evolutionary search for glider guns with different parameters is described and other search techniques are also presented to provide a benchmark. We demonstrate the spontaneous emergence of an important number of novel glider guns discovered by an evolutionary algorithm. An automatic process to identify guns leads to a classification of glider guns that takes into account the number of emitted gliders of a specific type. We also show it is possible to discover guns for many other types of gliders. Significantly, all the found automata can be candidate to an automatic search for collision-based universal cellular automata simulating Turing machines in their space-time dynamics using gliders and glider guns.

Keywords

Emergence of complexity Evolutionary algorithm Universality Cellular automata Glider gun Classification 

References

  1. Adamatzky A (1998) Universal dymical computation in multi-dimensional excitable lattices. Int J Theor Phys 37:3069–3108MATHCrossRefMathSciNetGoogle Scholar
  2. Andre D, Koza JR, Bennett FH III, Keane MA (1999) Genetic programming III: Darwinian invention and problem solving. Morgan Kaufmann, San Francisco, CAMATHGoogle Scholar
  3. Banks ER (1971) Information and transmission in cellular automata. PhD thesis, MITGoogle Scholar
  4. Bays C (1987) Candidates for the game of life in three dimensions. Complex Syst 1:373–400MATHMathSciNetGoogle Scholar
  5. Berlekamp E, Conway JH, Guy R (1982) Winning ways for your mathematical plays. Academic Press, New YorkMATHGoogle Scholar
  6. Das R, Crutchfield JP, Mitchell M, Hanson JE (1995) Evolving globally synchronized cellular automata. In: Proceedings of the sixth international conference on genetic algorithms, pp 336–343Google Scholar
  7. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13:533–549MATHCrossRefMathSciNetGoogle Scholar
  8. Heudin JC (1996) A new candidate rule for the game of two-dimensional life. Complex Syst 10:367–381MATHMathSciNetGoogle Scholar
  9. Holland JH (1975) Adaptation in natural and artificial systems. University of MichiganGoogle Scholar
  10. Hordijk W, Crutchfield JP, Mitchell M (1998) Mechanisms of emergent computation in cellular automata. In: Eiben AE, BSck T, Schoenauer M, Schwefel H-P (eds) Parallel problem solving from nature-V, vol 866. Springer-Verlag, London, UK, pp 344–353Google Scholar
  11. Kennedy J, Eberhart C (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE conference on neural networksGoogle Scholar
  12. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge, MAMATHGoogle Scholar
  13. Langton CL (1990) Computation at the edge of chaos. Physica D 42:12–37Google Scholar
  14. Lindgren K, Nordahl M (1990) Universal computation in simple one dimensional cellular automata. Complex Syst 4:299–318MATHMathSciNetGoogle Scholar
  15. Lohn JD, Reggia JA (1997) Automatic discovery of self-replicating structures in cellular automata. IEEE Trans Evol Comput 1:165–178CrossRefGoogle Scholar
  16. Margolus N (1984) Physics-like models of computation. Physica D 10:81–95CrossRefMathSciNetGoogle Scholar
  17. Martinez GJ, Adamatzky A, McIntosh HV (2006) Phenomenology of glider collisions in cellular automaton rule 54 and associated logical gates. Chaos, Solitons & Fractals 28(1):100–111MATHCrossRefMathSciNetGoogle Scholar
  18. Mitchell M, Hraber PT, Crutchfield JP (1993) Revisiting the edge of chaos: evolving cellular automate to perform computations. Complex Syst 7:89–130MATHGoogle Scholar
  19. Mitchell M, Crutchfield JP, Hraber PT (1994) Evolving cellular automata to perform computations: mechanisms and impediments. Physica D 75:361–391MATHCrossRefGoogle Scholar
  20. Morita K, Tojima Y, Katsunobo I, Ogiro T (2002) Universal computing in reversible and number-conserving two-dimensional cellular spaces. In: Adamatzky A (ed) Collision-based computing. Springer-Verlag, London, UK, pp 161–199Google Scholar
  21. Packard NH (1988) Adaptation toward the edge of chaos. In: Kelso JAS, Mandell AJ, Shlesinger MF (eds) Dynamic patterns in complex systems, pp 293–301Google Scholar
  22. Resnick M, Silverman B (1996) Exploring emergence. http://llk.media.mit.edu/projects/emergence/
  23. Sapin E, Bailleux O, Chabrier JJ (2003) Research of a cellular automaton simulating logic gates by evolutionary algorithms. In: EuroGP03 Lecture Notes in Computer Science, vol 2610, pp 414–423Google Scholar
  24. Sapin E, Bailleux O, Chabrier JJ (2004a) Research of complex forms in the cellular automata by evolutionary algorithms. In: EA03 Lecture Notes in Computer Science, vol 2936, pp 373–400Google Scholar
  25. Sapin E, Bailleux O, Chabrier JJ, Collet P (2004b) A new universal automata discovered by evolutionary algorithms. In: Gecco2004 Lecture Notes in Computer Science, vol 3102, pp 175–187Google Scholar
  26. Sapin E, Bailleux O, Chabrier JJ, Collet P (2006) Demonstration of the universality of a new cellular automaton. In: Adamatzky A et al (eds) IJUC 2(3):79–103Google Scholar
  27. Sapin E, Bailleux O, Chabrier J (2007) Research of complexity in cellular automata through evolutionary algorithms. Complex Syst 17(3):231–241MathSciNetGoogle Scholar
  28. Sipper M (1997) Evolution of parallel cellular machines. In: Stauffer D (ed) Annual reviews of computational physics, V. World Scientific, Singapore, pp 243–285Google Scholar
  29. Urfas J, Rechtman R, Enciso A (1997) Sensitive dependence on initial conditions for cellular automata. Chaos Interdiscip J Nonlinear Sci 7(4):688–693CrossRefGoogle Scholar
  30. Ventrella JJ (2006) A particle swarm selects for evolution of gliders in non-uniform 2d cellular automata. In: Artificial Life X: proceedings of the 10th international conference on the simulation and synthesis of living systems, pp 386–392Google Scholar
  31. Von Neumann J (1966) Theory of self-reproducing automata. University of Illinois Press, Urbana, ILGoogle Scholar
  32. Wolfram S (1984) Universality and complexity in cellular automata. Physica D 10:1–35CrossRefMathSciNetGoogle Scholar
  33. Wolfram S (2002) A new kind of science. Wolfram Media, Inc., Illinois, USAMATHGoogle Scholar
  34. Wolfram S, Packard NH (1985) Two-dimensional cellular automata. J Stat Phys 38:901–946MATHCrossRefMathSciNetGoogle Scholar
  35. Wolz D, de Oliveira PB (2008) Very effective evolutionary techniques for searching cellular automata rule spaces. J Cell Autom 3(4):289–312MATHMathSciNetGoogle Scholar
  36. Wuensche A (2005) Discrete dynamics lab (ddlab). http://www.ddlab.org
  37. Wuensche A, Adamatzky A (2008) On spiral glider-guns in hexagonal cellular automata: activator-inhibitor paradigm. Int J Mod Phys C 17(7):1009–1026CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Faculty of Computing, Engineering and Mathematical SciencesUniversity of the West of EnglandBristolUK
  2. 2.Laboratoire d’Informatique du LittoralUniversité du LittoralCalaisFrance

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