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A Simple Universal Turing Machine for the Game of Life Turing Machine

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Game of Life Cellular Automata

Abstract

In this chapter we present a simple universal Turing machine which is small enough to fit into the design limits of the Turing machine build in Conway’s Game of Life by the author. That limit is 8 symbols and 16 states. By way of comparison we also describe one of the smallest known universal Turing machines due to Rogozhin which has 6 symbols and 4 states.

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References

  1. Britton, S.: Java applet Turing machine simulator. http://ironphoenix.org/tril/tm/

  2. Gardner, M.: Mathematical Games articles in Scientific American: On cellular automata, self-reproduction, and the game “life” (February, 1971); The fantastic combinations of John Conway’s new solitaire game “life” (October, 1970)

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  4. Golly, an open source, cross-platform application for exploring Conway’s Game of Life and other cellular automata. http://golly.sourceforge.net/

  5. Hashlife, an algorithm for computing the long-term fate of a given starting configuration in Conway’s Game of Life and related cellular automata. http://en.wikipedia.org/wiki/Hashlife

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  7. Rendell, P.: Conway’s Game Life Turing machine. www.rendell-attic.org/gol

  8. Rendell, P.: Java applet Turing machine simulator. http://www.rendell-attic.org/gol/TMapplet

  9. Rogozhin, Y.: Small universal Turing machines. Theor. Comput. Sci. 168, 215–240 (1996)

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  10. Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. In: Proc. London Mathematical Society (1936)

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Correspondence to Paul Rendell .

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© 2010 Springer-Verlag London Limited

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Rendell, P. (2010). A Simple Universal Turing Machine for the Game of Life Turing Machine. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_26

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  • DOI: https://doi.org/10.1007/978-1-84996-217-9_26

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-216-2

  • Online ISBN: 978-1-84996-217-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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