Methuselah

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A methuselah is, roughly speaking, a pattern that takes a large number of generations in order to stabilize (known as its lifespan) 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 most definitions place restrictions on the number of cells in the initial pattern.

Martin Gardner defined methuselahs as patterns of fewer than ten cells that take longer than 50 generations to stabilize,[1] though some sources allow for more cells or require a longer lifespan.

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 B-heptomino, bunnies, die hard and rabbits.

Acorn
B-heptomino
R-pentomino
Rabbits

The longest-lived methuselah known to date, 40514M, was discovered by knightlife. It has an initial population of 18, a final population of 3735, takes 40514 generations to stabilize, and fits within a 78×54 bounding box.

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. 

External links

Methuselah at the Life Lexicon