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Penrose Life: Ash and Oscillators

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Advances in Artificial Life (ECAL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3630))

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Abstract

We compare the long term behaviour of Conway’s Game of Life cellular automaton, from initial random configurations, on a bounded rectangular grid and a bounded Penrose tiling grid. We investigate the lifetime to stability, the final ‘ash’ density, and the number and period of final oscillators. Penrose grids have similar qualitative behaviour but different quantitative behaviour, with shorter lifetimes, lower ash densities, and higher ocurrence of long-period oscillators.

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References

  1. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays games in particular, vol. 2. Academic Press, London (1982)

    MATH  Google Scholar 

  2. Flammenkamp, A.: Achim’s game of life page (2004), http://wwwhomes.uni-bielefeld.de/achim/gol.html

  3. Gardner, M.: Mathematical games: The fantastic combinations of John Conway’s new solitaire game “life”. Scientific American 223(4), 120–123 (1970)

    Article  Google Scholar 

  4. Gardner, M.: Mathematical games: extraordinary non-periodic tiling that enriches the theory of tiles. Scientific American 236(1), 110–121 (1977)

    Article  Google Scholar 

  5. Gosper, R.W.: Exploiting regularities in large cellular spaces. Physica D 10, 75–80 (1984)

    Article  Google Scholar 

  6. Grünbaum, B., Shephard, G.C.: Tilings and Patterns. W. H. Freeman, New York (1987)

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  7. Penrose, R.: Pentaplexity. Eureka 39, 16–32 (1978)

    Google Scholar 

  8. Rendell, P.: Turing Universaility of the Game of Life. In: Adamatzky, A. (ed.) Collision-Based Computing. Springer, Heidelberg (2002)

    Google Scholar 

  9. Silver, S.: Life lexicon, release 24 (February 2005), http://www.argentum.freeserve.co.uk/lex.htm

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© 2005 Springer-Verlag Berlin Heidelberg

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Hill, M., Stepney, S., Wan, F. (2005). Penrose Life: Ash and Oscillators. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds) Advances in Artificial Life. ECAL 2005. Lecture Notes in Computer Science(), vol 3630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11553090_48

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  • DOI: https://doi.org/10.1007/11553090_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28848-0

  • Online ISBN: 978-3-540-31816-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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