Abstract
John Horton Conway’s Game of Life is a simple two-dimensional, two state cellular automaton (CA), remarkable for its complex behaviour. That behaviour is known to be very sensitive to a change in the CA rules. Here we continue our investigations into its sensitivity to changes in the lattice, by the use of an aperiodic Penrose tiling lattice.
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References
Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 2: Games in Particular. Academic Press, San Diego (1982)
de Bruijn, N.G.: Algebraic theory of Penrose’s non-periodic tilings of the plane I and II. Indag. Math. (Proc.) 84, 39–66 (1981)
de Bruijn, N.G.: Remarks on Penrose tilings. In: Graham, R.L., Nesetrilm, J. (eds.) The Mathematics of P. Erdös, vol. 2, pp. 264–283. Springer, Berlin (1996)
Gardner, M.: Mathematical games: The fantastic combinations of John Conway’s new solitaire game “life”. Sci. Am. 223(4), 120–123 (1970)
Gardner, M.: Mathematical games: Extraordinary non-periodic tiling that enriches the theory of tiles. Sci. Am. 236(1), 110–121 (1977)
Grünbaum, B., Shephard, G.C.: Tilings and Patterns. Freeman, New York (1987)
Hill, M., Stepney, S., Wan, F.: Penrose Life: ash and oscillators. In: Capcarrere, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds.) Advances in Artificial Life: ECAL 2005, Canterbury, UK, September 2005. LNAI, vol. 3630, pp. 471–480. Springer, Berlin (2005)
Knuth, D.E.: The Art of Computer Programming: Seminumerical Algorithms, vol. 2, 3rd edn. Addison–Wesley, Reading (1998)
Niemiec, M.D.: Life page. http://home.interserv.com/~mniemiec/lifepage.htm (1998)
Owens, N., Stepney, S.: Investigations of Game of Life cellular automata rules on Penrose tilings: lifetime and ash statistics. In: Automata 2008, Bristol, UK, June 2008, pp. 1–34. Luniver Press, Beckington (2008)
Owens, N., Stepney, S.: Investigations of the Game of Life cellular automata rules on Penrose tilings: lifetime, ash and oscillator statistics. J. Cell. Autom. 5(3), 207–255 (2010)
Penrose, R.: Pentaplexity. Eureka 39, 16–32 (1978)
Rendell, P.: Turing universality of the Game of Life. In: Adamatzky, A. (ed.) Collision-Based Computing. Springer, Berlin (2002)
Senechal, M.: Quasicrystals and Geometry. Cambridge University Press, Cambridge (1995)
Silver, S.: Life lexicon, release 25. http://www.argentum.freeserve.co.uk/lex.htm (2006)
Socolar, J.E.S., Steinhardt, P.J.: Quasicrystals. II. Unit-cell configurations. Phys. Rev. B 34, 617–647 (1986)
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Owens, N., Stepney, S. (2010). The Game of Life Rules on Penrose Tilings: Still Life and Oscillators. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_18
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DOI: https://doi.org/10.1007/978-1-84996-217-9_18
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