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The die hard Methuselah lives for 130 generations before all cells die.
In cellular automata, a methuselah is a small "seed" pattern of initial live cells that take a large number of generations in order to stabilize. More specifically, Martin Gardner defines them as patterns of fewer than ten live cells which take longer than 50 generations to stabilize,[1] although some patterns that are larger than ten cells have also been called methuselahs. Patterns that grow forever are not considered methuselahs.
[edit] In Conway's Game of Life
In Conway's Game of Life, the smallest methuselah is the R-pentomino,[2] a pattern of five cells first considered by Conway himself,[3] that takes 1103 generations before stabilizing with 116 cells. The acorn,[4] a pattern of seven live cells developed by Charles Corderman, takes 5206 generations to stabilize and produce a 633-cell pattern referred to as its "oak." Some other examples of methuselahs are called bunnies[5] and rabbits.[6] The longest-lived methuselah known to date is referred to as "lidka"[7], was discovered by Andrzej Okrasinski and David Bell, has an initial population of 13 and a final population of 1623, and takes 29055 generations to stabilize.[8]
[edit] References
- ^ Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 246, W.H. Freeman.
- ^ Silver, Stephen (28 February 2006). "R-pentomino". Life Lexicon. http://www.argentum.freeserve.co.uk/lex_r.htm#rpentomino. Retrieved on 2008-12-24.
- ^ Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 219, 223, W.H. Freeman.
- ^ Silver, Stephen (28 February 2006). "Acorn". Life Lexicon. http://www.argentum.freeserve.co.uk/lex_a.htm#acorn. Retrieved on 2008-12-24.
- ^ Silver, Stephen (28 February 2006). "Bunnies". Life Lexicon. http://www.argentum.freeserve.co.uk/lex_b.htm#bunnies. Retrieved on 2008-12-24.
- ^ Silver, Stephen (28 February 2006). "Rabbits". Life Lexicon. http://www.argentum.freeserve.co.uk/lex_r.htm#rabbits. Retrieved on 2008-12-24.
- ^ Silver, Stephen (28 February 2006). "Lidka". Life Lexicon. http://www.argentum.freeserve.co.uk/lex_l.htm#lidka. Retrieved on 2009-03-13.
- ^ Koenig, H (14 July 2005). "New Record Methuselah". Game of Life News. http://gameoflife-news.blogspot.com/2005/07/new-record-methuselah.html. Retrieved on 2008-12-24.
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