Abstract
This chapter describes a Turing machine built from patterns in the Conway’s Game of Life cellular automaton. It outlines the architecture of the construction, the structure of its parts and explains how the machine works. It also illustrates the principle choices made during the design0 [17]. Background information about Turing machines, minimal universal Turing machines (those that simulate any other Turing machine) and non-erasing Turing machines can be found in [20,7,15,14,18]. The importance of Turing machines is the existence of universal Turing machines. Thus a machine that can simulate any Turing machine can simulate a universal Turing machine. It has been proved that Turing machines can be simulated by many types of machine: cellular automata (as one can see in this and other chapters of this book), random access machines [4], register machines [1] and others. In particular Minsky [16] describes a register machine which can simulate a Turing machine. The registers have the unusual property of being able to store positive numbers of any size. Remarkably, a long time ago Conway described [1] a method of constructing a register of this form in the Game of Life. This is discussed later in this chapter.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berlekamp E.R., Conway J.H. and Guy R. Winning Ways for Your Mathematical Plays, vol 2 (Academic Press, 1982).
Bontes J.G. Life32 Win32 PC Program for Conway’s Game Life http://life32.1ifepatterns.net/
Callahan P. Java Applet was written by Paul Callahan. http://www.radicaleye.com/lifepage/
Cook S. and Reckhow K.R. Time bounded random access machines J. Comput. System Sci. 7 (1973) 354–375.
Cook S.A. Characterizations of pushdown machines in terms of time-bounded computers J. Ass. Comput. Mach. 18 (1971) 14–18.
Hoperoft J.E. and Ullman J.D. Introduction to Automata Theory, Languages and Computation (Addison-Wesley, 1979).
Hoperoft J.E. Turing machines Scientific American 250 (1984) 86–98.
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).
Gardner M. Wheels, Life and Other Mathematical Amusements (Freeman, 1983).
Ginsburg S., Greibach S.A. and Harrison M.A. One-way stack automata J.Assoc. Comput. Mach. 14 (1967) 389–418.
Gruska J. Foundations of Computing (Thomson International Computer Press, 1997).
Korec I. Small universal register machines Theor. Comput. Sci. 168 (1996) 267–301.
Leithner D. and Rott P. Dieter and Peter’s Gun Collection http://www.mindspring.com/%7Ealanh/guns.zip and http://www.mindspring.com/%7Ealanh/guns2.zip
Margenstern M. Nonerasing Turing machines: A frontier between a decidable halting problem and universality Theoret. Comput. Sci. 129 (1994) 419–424.
Margenstern M. On quasi-unilateral universal Turing machines Theor. Comput. Sci. 257 (2001) 153–166.
Minsky M.L. Computation: Finite and Infinite Machines (Prentice-Hall, 1967).
Rendell P. Conway’s Game Life Turing Machine http://www.rendell.uk.co/gol
Rogozhin Y. Small universal Turing machines Theor. Comput. Sci. 168 (1996) 215–240.
Silver S. Stephen Silver’s Life Lexicon http://www.argentum.freeserve.co.uk/lex_home.htm
Turing A.M. On computable numbers, with applications to the entscheidungsproblem Proc. London Math. Soc. 42 (1937 230–265.
Wojna A. Counter machines Information Processing Lett. 71 (1999) 193–197.
Wójtowicz M. Mirek’s Cellebration (MCell) http://www.mirwoj.opus.chelm.pl
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag London
About this chapter
Cite this chapter
Rendell, P. (2002). Turing Universality of the Game of Life. In: Adamatzky, A. (eds) Collision-Based Computing. Springer, London. https://doi.org/10.1007/978-1-4471-0129-1_18
Download citation
DOI: https://doi.org/10.1007/978-1-4471-0129-1_18
Publisher Name: Springer, London
Print ISBN: 978-1-85233-540-3
Online ISBN: 978-1-4471-0129-1
eBook Packages: Springer Book Archive