Conclusions and Discussion

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


This chapter provides a summary and of the Game of Life Turing machine work, the Demonstration of universality and the Quadratic Assignment Problem solution. This project aims were to prove universal computation in the Game of Life cellular automaton by using a Turing machine construction with the object of providing a more demonstrable proof than using a counter machine construction.This has been done, starting with the finite state Turing machine described in Chap.  4 and adding the universal Turing machine described in Chap.  5 then by providing infinite capability through the stack constructor patterns described in Chap.  8.The result of running the symbol doubler Turing machine within the universal Turing machine are shown in Fig. 11.1. This shows how easy it is to verify the result of the computation. In addition some and original work has done during the process if optimizing the order of transitions described in Chap.  6. This uncovered the possibility that the NP-Hard quadratic assignment problem may have a subclass of problems for which optimal solutions all have large basins of attraction .


Turing machineTuring Machine stackStack transitionsTransition Cellular automatonCellular Automaton Universal Turing 
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  1. 1.
    Berlekamp, E., Conway, J., Guy, R.: What is life (Chapter 25). Winning Ways for Your Mathematical Plays, vol. 2. Academic Press, London (1982)Google Scholar
  2. 2.
    Silver, S.: Stephen Silver’s Life Lexicon., pre (2000)
  3. 3.
    Trevorrow, A., Rokicki, T.: An open source, cross-platform application for exploring Conway’s Game of Life and other cellular automata. (2005)
  4. 4.
    HP laptop with a 2.67 GHz Dual Core 64bit Intel processor and 3 Gb of RAM running Windows 7Google Scholar
  5. 5.
    Gosper, R.: Exploiting regularities in large cellular spaces. Phys. D: Nonlinear Phenom. 10, 75–80 (1984)CrossRefGoogle Scholar
  6. 6.
    McIntosh, G.: Youtube video of minecraft implementation of universal Turing machine program. (2011)

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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