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Growth and Decay in Life-Like Cellular Automata

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Game of Life Cellular Automata

Abstract

Since the study of life began, many have asked: is it unique in the universe, or are there other interesting forms of life elsewhere? Before we can answer that question, we should ask others: What makes life special? If we happen across another system with life-like behavior, how would we be able to recognize it? We are speaking, of course, of the mathematical systems of cellular automata, of the fascinating patterns that have been discovered and engineered in Conway’s Game of Life, and of the possible existence of other cellular automaton rules with equally complex behavior to that of Life.

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References

  1. Adamatzky, A., Martínez, G.J., Mora, J.C.S.T.: Phenomenology of reaction–diffusion binary-state cellular automata. Int. J. Bifurc. Chaos Appl. Sci. Eng. 16(10), 2985–3006 (2006). http://uncomp.uwe.ac.uk/genaro/Papers/Papers_on_CA_files/rdca.pdf

    Article  MATH  Google Scholar 

  2. Baldwin, J.T., Shelah, S.: On the classifiability of cellular automata. Theor. Comput. Sci. 230(12), 117–129 (2000). doi:10.1016/S0304-3975(99)00042-0. arXiv:math.LO/9801152

    Article  MATH  MathSciNet  Google Scholar 

  3. Bell, D.I.: Day & Night — An interesting variant of Life. http://www.tip.net.au/~dbell/articles/HighLife.zip (1994). Unpublished article

  4. Bell, D.I.: HighLife — An interesting variant of Life. http://www.tip.net.au/~dbell/articles/HighLife.zip (1994). Unpublished article

  5. Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 4, 2nd edn. AK Peters, Wellesley (2004)

    MATH  Google Scholar 

  6. Chaté, H., Manneville, P.: Criticality in cellular automata. Physica D 45, 122–135 (1990). doi:10.1016/0167-2789(90)90178-R. Special issue of Physica D, reprinted as: Gutowitz, H. (ed.) Cellular Automata: Theory and Experiment. MIT/North-Holland, Cambridge/Amsterdam (1991)

    Article  MATH  MathSciNet  Google Scholar 

  7. Culik, K. II, Yu S.: Undecidability of CA classification schemes. Complex Syst. 2, 177–190 (1988)

    MATH  MathSciNet  Google Scholar 

  8. Due, B.: Outer totalistic cellular automata meta-pixel. http://otcametapixel.blogspot.com/ (2006). See also Dave Greene’s “metafier” script, and several examples of metafied patterns, included as part of the Golly cellular automaton software. Retrieved November 1, 2009. Unpublished web page

  9. Eppstein, D.: Gliders in life-like cellular automata. http://fano.ics.uci.edu/ca/. Web database of spaceships in life-like cellular automaton rules

  10. Eppstein, D.: Searching for spaceships. In: More Games of No Chance. MSRI Publications, vol. 42, pp. 433–453. Cambridge University Press, Cambridge (2002). arXiv:cs.AI/0004003. http://www.msri.org/publications/books/Book42/files/eppstein.pdf

    Google Scholar 

  11. Eppstein, D.: B35/S236. http://www.ics.uci.edu/~eppstein/ca/b35s236/ (2003). Unpublished web site

  12. Flammenkamp, A.: Most seen natural occurring ash objects in Game of Life. http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html (2004). Retrieved November 1, 2009. Unpublished web page

  13. Gardner, M.: Mathematical Games: The fantastic combinations of John Conway’s new solitaire game “Life”. Sci. Am. 223, 120–123 (1970)

    Article  Google Scholar 

  14. Gotts, N.M.: Self-organized construction in sparse random arrays of Conway’s Game of Life. In: New Constructions in Cellular Automata, pp. 1–53. Oxford University Press, London (2003)

    Google Scholar 

  15. Gravner, J.: Growth phenomena in cellular automata. In: New Constructions in Cellular Automata, pp. 161–181. Oxford University Press, London (2003)

    Google Scholar 

  16. Gravner, J., Griffeath, D.: Cellular automaton growth on Z 2: theorems, examples, and problems. Adv. Appl. Math. 21(2), 241–304 (1998). doi:10.1006/aama.1998.0599. http://psoup.math.wisc.edu/extras/r1shapes/r1shapes.html

    Article  MATH  MathSciNet  Google Scholar 

  17. Gravner, J., Griffeath, D.: Asymptotic densities for Packard Box rules. Nonlinearity 22, 1817–1846 (2009). doi:10.1088/0951-7715/22/8/003. http://psoup.math.wisc.edu/papers/box.pdf

    Article  MATH  MathSciNet  Google Scholar 

  18. Griffeath, D., Moore, C.: Life without Death is P-complete. Complex Syst. 10, 437–447 (1996). http://psoup.math.wisc.edu/java/lwodpc/lwodpc.html

    MATH  MathSciNet  Google Scholar 

  19. Lafusa, A., Bossomaier, T.: Localisation of critical transition phenomena in cellular automata rule-space. In: Recent Advances in Artificial Life. World Scientific, Singapore (2005). doi:10.1142/9789812701497_0010

    Google Scholar 

  20. Li, W., Packard, N.H., Langton, C.G.: Transition phenomena in cellular automata rule space. Physica D 45, 77–94 (1990). doi:10.1016/0167-2789(90)90175-O. Special issue of Physica D, reprinted as: Gutowitz, H. (ed.) Cellular Automata: Theory and Experiment. MIT/North-Holland, Cambridge/Amsterdam (1991)

    Article  MATH  MathSciNet  Google Scholar 

  21. Martínez, G.J., Adamatzky, A., McIntosh, H.V.: Localization dynamics in a binary two-dimensional cellular automaton: the Diffusion Rule. arXiv:0908.0828. J. Cell. Autom. (2008, in press)

  22. McIntosh, H.V.: Wolfram’s class IV automata and a good life. Physica D 45, 105–121 (1990). doi:10.1016/0167-2789(90)90177-Q. Special issue of Physica D, reprinted as: Gutowitz, H. (ed.) Cellular Automata: Theory and Experiment. MIT/North-Holland, Cambridge/Amsterdam (1991)

    Article  MATH  MathSciNet  Google Scholar 

  23. Nivasch, G.: The 17c/45 caterpillar spaceship. http://www.yucs.org/~gnivasch/life/article_cat/ (2005). Retrieved November 8, 2009. Unpublished web page

  24. Nivasch, G.: The photon/XOR system. http://yucs.org/~gnivasch/life/photonXOR/ (2007). Retrieved November 8, 2009. Unpublished web page

  25. Packard, N.H.: Lattice models for solidification and aggregation. Inst. for Advanced Study preprint (1984). Reprinted in: Wolfram, S. (ed.) Theory and Applications of Cellular Automata, pp. 305–310. World Scientific, Singapore (1986)

    Google Scholar 

  26. Toffoli, T., Margolus, N.: Cellular Automata Machines: A New Environment for Modeling, pp. 6–7. MIT Press, Cambridge (1987)

    Google Scholar 

  27. Trevorrow, A., Rokicki, T.: Golly. http://golly.sourceforge.net/ (2009). Multiplatform open-source software, version 2.1

  28. Wolfram, S.: University and complexity in cellular automata. Physica D 10, 1–35 (1984). doi:10.1016/0167-2789(84)90245-8. Reprinted in: Cellular Automata and Complexity, pp. 115–157. Addison–Wesley, Reading (1994)

    Article  MathSciNet  Google Scholar 

  29. Wolfram, S., Packard, N.H.: Two-dimensional cellular automata. J. Stat. Phys. 38, 901–946 (1985). doi:10.1007/BF01010423. Reprinted in: Cellular Automata and Complexity, pp. 211–249. Addison–Wesley, Reading (1994)

    Article  MATH  MathSciNet  Google Scholar 

  30. Wootters, W.K., Langton, C.G.: Is there a sharp phase transition for deterministic cellular automata? Physica D 45, 75–104 (1990). doi:10.1016/0167-2789(90)90176-P. Special issue of Physica D, reprinted as: Gutowitz, H. (ed.) Cellular Automata: Theory and Experiment. MIT/North-Holland, Cambridge/Amsterdam (1991)

    Article  Google Scholar 

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Eppstein, D. (2010). Growth and Decay in Life-Like Cellular Automata. In: Adamatzky, A. (eds) Game of Life Cellular Automata. Springer, London. https://doi.org/10.1007/978-1-84996-217-9_6

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  • DOI: https://doi.org/10.1007/978-1-84996-217-9_6

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-216-2

  • Online ISBN: 978-1-84996-217-9

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