Literature Review/Related Work

  • Paul RendellEmail author
Part of the Emergence, Complexity and Computation book series (ECC, volume 18)


This chapter reviews the relevant literature on Conway’s Game of Life, universality and Turing machines. Conway’s book Winning Ways contains the proof for universality of Conway’s Game of Life with descriptions of the parts required to build universal computing machine. Buckingham and Niemiec’s build a adder in Conway’s Game of Life. Dean Hickerson’s sliding block memory in Conway’s Game of Life is an implementation of the memory unit described in Conway’s Winning Ways. Paul Chapman’s counter machine is an implementation of Conway’s universal computing machine.


Prime Number Turing Machine Counter Module Instruction Instruction Initial Pattern 
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.


  1. 1.
    Hickerson, D.: Sliding Block Memory. (1990)
  2. 2.
    Berlekamp, E., Conway, J., Guy, R.: What is life. Winning Ways for your Mathematical Plays. vol. 2, chapter 25. Academic Press, London (1982)Google Scholar
  3. 3.
    Chapman, P.: Life Universal Computer. (2002)
  4. 4.
    Goucher, A.P.: Universal computation and construction in GoL cellular automata. In: Adamatzky, A. (ed.) Game of Life Cellular Automata, chapter, pp. 505–517. Springer (2010)Google Scholar
  5. 5.
    Goucher, A.P.: Game of Life News August 2009: Completed Universal Computer/Constructor. (2009)
  6. 6.
    Rogozhin, Y.: Small universal Turing machines. Theor. Comput. Sci. 168(2), 215–240 (1996). ISSN 0304-3975MathSciNetCrossRefGoogle Scholar
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    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Englewood Cliffs (1967)Google Scholar
  8. 8.
    Neary, T., Woods, D.: Small weakly universal Turing machines. In: Proceedings of the 17th International Conference on Fundamentals of Computation Theory, FCT’09, pp. 262–273. Springer, Berlin (2009). ISBN 3-642-03408-X, 978-3-642-03408-4Google Scholar
  9. 9.
    Wolfram, S.: A New Kind of Science. Wolfram Media Inc., Champaign (2002)Google Scholar
  10. 10.
    Cook, M.: Universality in elementary cellular automata. Complex Syst. 15(1), 1–40 (2004)Google Scholar
  11. 11.
    Wolfram, S.: Universality and complexity in cellular automata. Physica 10D, 1–35 (1984)MathSciNetGoogle Scholar
  12. 12.
    Smith, A.: Universality of Wolfram’s 2, 3 Turing Machine, 2007. The Wolfram 2, 3 Turing Machine Research PrizeGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of the West of EnglandBristolUK

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