Methuselah

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A methuselah is, roughly speaking, a pattern that takes a large number of generations in order to stabilize and becomes much larger than its initial configuration at some point during its evolution. In particular, patterns that grow forever are not methuselahs. Their exact definition is not completely agreed upon, and some definitions place restrictions on the number of cells in the initial pattern.

Martin Gardner defined them as patterns of fewer than ten cells that take longer than 50 generations to stabilize.[1]

Examples

The smallest methuselah is the R-pentomino, a pattern of five cells first considered by John Conway,[2] that takes 1103 generations before stabilizing. The acorn, a pattern of seven cells developed by Charles Corderman, takes 5206 generations to stabilize. Some other popular examples include bunnies, die hard and rabbits.

The longest-lived small methuselah known to date, 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.[3]

See also

References

  1. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 246, W.H. Freeman. 
  2. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 219, 223, W.H. Freeman. 
  3. Koenig, H (July 14, 2005). "New Record Methuselah". Game of Life News. Retrieved on January 24, 2009.