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Abstract: A still Life is a subset S of the square lattice Z fixed under the transition rule of Conway's Game of Life, i.e. a subset satisfying the following three conditions: 1. No element of Z \Gamma S has exactly three neighbors in S; 2. Every element of S has at least two neighbors in S; 3. Every element of S has at most three neighbors in S. (Update)
Context of citations to this paper: More
...be alive or become alive according to the rules. There has been work done on computational and theoretical aspects of stilllifes. Elkies [6] has shown for the in nite board the maximum density is 1=2. For nite size boards, no exact formula is known for the maximum density....
Cited by: More
Constraint Programming and Hybrid Formulations for Life - Bosch, Trick (2002) (Correct)
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0.8: The still-Life density problem and its generalizations - Elkies (1997) (Correct)
0.3: Searching for Spaceships - Eppstein (2002) (Correct)
0.0: Efficient Coding Schemes for the Hard-Square Model - Roth, Siegel, Wolf (1999) (Correct)
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BibTeX entry: (Update)
N.D. Elkies, The still-Life density problem and its generalizations [pages 228-253 in Voronoi's Impact on Modern Science, Book 1 (P. Engel, H. Syta, eds.; Institute of Math., Kyiv, 1998)]. http://citeseer.ist.psu.edu/elkies98stilllife.html More
@misc{ elkies98stilllife,
author = "N. Elkies",
title = "The still-Life density problem and its generalizations [pages 228-253 in
Voronoi's Impact on Modern Science",
text = "N.D. Elkies, The still-Life density problem and its generalizations [pages
228-253 in Voronoi's Impact on Modern Science, Book 1 (P. Engel, H. Syta,
eds.; Institute of Math., Kyiv, 1998)].",
year = "1998",
url = "citeseer.ist.psu.edu/elkies98stilllife.html" }
Citations (may not include all citations):860 The Theory of Error-Correcting Codes (context) - MacWilliams, Sloane - 1977
116 Winning Ways For Your Mathematical Plays (context) - Berlekamp, Conway et al. - 1982
47 Undecidability and nonperiodicity for tilings of the plane (context) - Robinson - 1971
3 Tight bounds on periodic cell configurations in Life - Buckingham, Callahan - 1997
2 The Four-Color Problem: Assaults amd Conquest (context) - Saaty, Kainen - 1977
1 edubrownnewcell automata html (context) - on, cell et al. - 1996
1 mail communication (context) - Kuperberg - 1994
Documents on the same site (http://www.math.harvard.edu/~elkies/math_pubs.html): More
The still-Life density problem and its generalizations - Elkies (1997) (Correct)
Explicit Modular Towers - Elkies (1998) (Correct)
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