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Growth and Decay in Life-Like Cellular Automata

  • David Eppstein

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.

Keywords

Dead Cell Cellular Automaton Random Initial Condition Single Live Cell Rule Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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 MATHCrossRefGoogle Scholar
  2. 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 MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bell, D.I.: Day & Night — An interesting variant of Life. http://www.tip.net.au/~dbell/articles/HighLife.zip (1994). Unpublished article
  4. 4.
    Bell, D.I.: HighLife — An interesting variant of Life. http://www.tip.net.au/~dbell/articles/HighLife.zip (1994). Unpublished article
  5. 5.
    Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways for Your Mathematical Plays, vol. 4, 2nd edn. AK Peters, Wellesley (2004) MATHGoogle Scholar
  6. 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) MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Culik, K. II, Yu S.: Undecidability of CA classification schemes. Complex Syst. 2, 177–190 (1988) MATHMathSciNetGoogle Scholar
  8. 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. 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. 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. 11.
    Eppstein, D.: B35/S236. http://www.ics.uci.edu/~eppstein/ca/b35s236/ (2003). Unpublished web site
  12. 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. 13.
    Gardner, M.: Mathematical Games: The fantastic combinations of John Conway’s new solitaire game “Life”. Sci. Am. 223, 120–123 (1970) CrossRefGoogle Scholar
  14. 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. 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. 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 MATHCrossRefMathSciNetGoogle Scholar
  17. 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 MATHCrossRefMathSciNetGoogle Scholar
  18. 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 MATHMathSciNetGoogle Scholar
  19. 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. 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) MATHCrossRefMathSciNetGoogle Scholar
  21. 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. 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) MATHCrossRefMathSciNetGoogle Scholar
  23. 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. 24.
    Nivasch, G.: The photon/XOR system. http://yucs.org/~gnivasch/life/photonXOR/ (2007). Retrieved November 8, 2009. Unpublished web page
  25. 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. 26.
    Toffoli, T., Margolus, N.: Cellular Automata Machines: A New Environment for Modeling, pp. 6–7. MIT Press, Cambridge (1987) Google Scholar
  27. 27.
    Trevorrow, A., Rokicki, T.: Golly. http://golly.sourceforge.net/ (2009). Multiplatform open-source software, version 2.1
  28. 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) CrossRefMathSciNetGoogle Scholar
  29. 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) MATHCrossRefMathSciNetGoogle Scholar
  30. 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) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversity of CaliforniaIrvineUSA

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