Wolfram’s Two State Three Symbol UTM

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


The smallest known universal Turing machine is Wolfram’s two state three symbol machine described in Chap.  3. This is small enough to fit in the author’s original Turing machine in Conway’s Game of Life which has three states and three symbols. Wolfram’s two state three symbol machine was proved to be weakly universal by Smith. The coding of the Turing machine tape for universal Turing machine behaviour creates a tape much larger than can be demonstrated in Conway’s Game of Life. This chapter presents Wolfram’s two state three symbol machine built in Conway’s Game of Life with a short section of blank tape .


Artificial Intelligence Nonlinear Dynamics State Machine State Version Computational Intelligence 
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    Rendell, P.: Conway’s Game of Life Turing machine. (2000)
  3. 3.
    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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