Methuselah (cellular automaton)

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For other uses of "Methuselah", see Methuselah (disambiguation).

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 [1], a pattern of five cells first considered by Conway himself,[2] that takes 1103 generations before stabilizing. The acorn [2], a pattern of seven live cells developed by Charles Corderman, takes 5206 generations to stabilize and produce an "oak." Some other examples of methuselahs are called bunnies [3] and rabbits [4]. The longest-lived 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 [5].

[edit] 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. 
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