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Emergent Complexity in Conway’s Game of Life

  • Chapter
Game of Life Cellular Automata

Abstract

It is shown that both small, finite patterns and random infinite very low density (“sparse”) arrays of the Game of Life can produce emergent structures and processes of great complexity, through ramifying feedback networks and cross-scale interactions. The implications are discussed: it is proposed that analogous networks and interactions may have been precursors to natural selection in the real world.

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References

  1. Axtell, R.: U.S. firm sizes are Zipf distributed. Science 293, 1818–1820 (2001)

    Article  Google Scholar 

  2. Bak, P., Chen, K., Creutz, M.: Self-organized criticality in the “Game of Life”. Nature 342, 780–781 (1989)

    Article  Google Scholar 

  3. Barabási, A.-L.: Linked: The New Science of Networks. Perseus, Cambridge (2002)

    Google Scholar 

  4. Barrow, J.D., Tipler, F.J.: The Anthropic Cosmological Principle. Oxford University Press, Oxford (1986)

    Google Scholar 

  5. Bell, D.I.: Highlife: an interesting variant of Life. Available from http://www.tip.net.au/~dbell/ (1994)

  6. Berlekamp, E., Conway, J.H., Guy, R.: Winning Ways, vol. 2. Academic Press, San Diego (1982)

    MATH  Google Scholar 

  7. Braga, G., Catteneo, G., Flocchini, P., Quaranta Vogliotti, Q.: Pattern growth in elementary cellular automata. Theor. Comput. Sci. 145, 1–26 (1995)

    Article  MATH  Google Scholar 

  8. Carroll, G.R.: National city-size distributions. Prog. Hum. Geogr. 6, 1–43 (1982)

    Article  Google Scholar 

  9. Casti, J.L.: Would-Be Worlds: How Simulation Is Changing the Frontiers of Science. Wiley, New York (1997)

    Google Scholar 

  10. Chang, T., Tam, S.W.Y., Wu, C.-C., Consolini, G.: Complexity, forced and/or self-organised criticality, and topological phase transitions in space plasmas. Space Sci. Rev. 107, 425–445 (2003)

    Article  Google Scholar 

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

    MATH  Google Scholar 

  12. Dhar, A., Lakdawala, P., Mandal, G.: Role of initial conditions in the classification of the rule-space of cellular-automata dynamics. Phys. Rev. E 51(4, Pt. A), 3032–3037 (1995)

    Article  Google Scholar 

  13. Fleck, J.: Artefact activity: the coevolution of artefacts, knowledge and organization in technological innovation. In: Ziman, J. (ed.) Technological Innovation as an Evolutionary Process, pp. 248–266. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  14. Fu, L.-L.: Interaction of mesoscale variability with large-scale waves in the Argentine basin. J. Phys. Oceanogr. 37, 787–797 (2007)

    Article  Google Scholar 

  15. Gardner, M.: Wheels, Life and Other Mathematical Amusements. Freeman, New York (1983)

    MATH  Google Scholar 

  16. Gönerup, O., Crutchfield, J.P.: Hierarchical self-organization in the finitary process soup. Santa Fe Institute working paper 06-03-008 (2006)

    Google Scholar 

  17. Gotts, N.M.: Emergent phenomena in large sparse random arrays of Conway’s “Game of Life”. Int. J. Syst. Sci. 31(7), 873–894 (2000)

    Article  MATH  Google Scholar 

  18. Gotts, N.M.: Self-organised construction in sparse random arrays of Conway’s Game of Life. In: Griffeath, D., Moore, C. (eds.) New Constructions in Cellular Automata. Santa Fe Institute. Studies in the Sciences of Complexity, pp. 1–53. Oxford University Press, Oxford (2003)

    Google Scholar 

  19. Gotts, N.M.: Ramifying feedback networks, cross-scale interactions, and emergent quasi individuals in Conway’s Game of Life. Artif. Life 15(3), 351–375 (2009)

    Article  Google Scholar 

  20. Gotts, N.M., Callahan, P.B.: Emergent structures in sparse fields of Conway’s “Game of Life”. In: Adami, C., Belew, R.K., Kitano, H., Taylor, C. (eds.) Artificial Life VI: Proceedings of the Sixth International Conference on Artificial Life, pp. 104–113. MIT, Cambridge (1998)

    Google Scholar 

  21. Hanson, J.E., Crutchfield, J.P.: Computational mechanics of cellular automata: an example. Physica D 103(1–4), 169–189 (1997)

    Article  MathSciNet  Google Scholar 

  22. Holling, C.S., Peterson, F., Marples, P., Sendzimir, J., Redford, K., Gunderson, L., Lambert, D.: Self-organization in ecosystems: lumpy geometries, periodicities and morphologies. In: Walker, B.H., Steffen, W.L. (eds.) Global Change and Terrestrial Ecosystems, pp. 346–384. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  23. Kauffman, S.A.: The Origins of Order: Self-organization and Selection in Evolution. Oxford University Press, Oxford (1993)

    Google Scholar 

  24. Koonin, E.V., Martin, W.: On the origin of genomes and cells within inorganic compartments. Trends Genet. 21, 649–654 (2005)

    Article  Google Scholar 

  25. Langton, C.G.: Self-reproduction in cellular automata. Physica D 10, 134–144 (1984)

    Article  Google Scholar 

  26. Martin, W., Russell, M.J.: On the origins of cells: a hypothesis for the evolutionary transitions from abiotic geochemistry to chemoautotrophic prokaryotes, and from prokaryotes to nucleated cells. Philos. Trans. R. Soc. Lond. A: Biol. Sci. 358, 59–85 (2002)

    Article  Google Scholar 

  27. Maynard Smith, J., Szathmáry, E.: The Major Transitions in Evolution. Freeman, New York (1995)

    Google Scholar 

  28. Pargellis, A.N.: The evolution of self-replicating computer organisms. Physica D 98, 111–127 (1996)

    Article  MATH  Google Scholar 

  29. Peters, D.P.C., Pielke, R.A. Sr., Bestelmeyer, B.T., Allen, C.D., Munson-McGee, S., Havstad, K.M.: Cross-scale interactions, nonlinearities, and forecasting catastrophic events. Proc. Natl. Acad. Sci. USA 101(42), 15130–15135 (2004). www.pnas.org_cgi_doi_10.1073_pnas.0403822101

    Article  Google Scholar 

  30. Peterson, G.D., Allen, C.R., Holling, C.S.: Ecological resilience, biodiversity and scale. Ecosyst. 1, 6–18 (1998)

    Article  Google Scholar 

  31. Poundstone, W.: The Recursive Universe. Morrow, New York (1985)

    Google Scholar 

  32. Shante, V.K.S., Kirkpatrick S.: An introduction to percolation theory. Adv. Phys. 20, 325–357 (1971)

    Article  Google Scholar 

  33. Silver, S.: Personal communication (1998)

    Google Scholar 

  34. Simon, H.A.: The Sciences of the Artificial, 3rd edn. MIT, Cambridge (1996)

    Google Scholar 

  35. Theraulaz, G., Bonabeau, E.: A brief history of stigmergy. Artif. Life 5(2), 97–116 (1999)

    Article  Google Scholar 

  36. Tjardes, T., Neugebauer, E.: Sepsis research in the next millennium: concentrate on the software rather than the hardware. Shock 17(1), 1–8 (2002)

    Article  Google Scholar 

  37. von Neumann, J.: The Theory of Self-reproducing Automata. University of Illinois, Urbana (1966)

    Google Scholar 

  38. Winfree, A.T.: When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias. Princeton University Press, Princeton (1987)

    Google Scholar 

  39. Wolfram, S.: Universality and complexity in cellular automata. Physica D 10, 1–35 (1984)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Integrated Land Use Systems, Macaulay Land Use Research Institute, Aberdeen, AB15 8QH, UK

    Nick Gotts

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  1. Nick Gotts
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Correspondence to Nick Gotts .

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Editors and Affiliations

  1. Fac. of Computing, Engineering and, Mathematical Sciences (CEMS), University of the West of England, Coldharbour Lane, Bristol, BS16 1QY, United Kingdom

    Andrew Adamatzky

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Gotts, N. (2010). Emergent Complexity in Conway’s Game of Life. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_20

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  • DOI: https://doi.org/10.1007/978-1-84996-217-9_20

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-216-2

  • Online ISBN: 978-1-84996-217-9

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