Methuselah

From LifeWiki
Jump to: navigation, search

A methuselah is 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. There is no consensus on the exact definition.

R-pentomino
Generation 1103 of R-pentomino(excluding six gliders).

Martin Gardner defined methuselahs as patterns of fewer than ten cells that take longer than 50 generations to stabilize,[1]. Some other interpretations allow for more cells while requiring a longer lifespan, or characterize the size of an initial configuration by the size of its bounding box instead of the number of cells.

The time when a pattern is considered to have stabilized is commonly agreed upon to be the first generation such that the pattern can be resolved into still lifes, oscillators and escaping spaceships, provided such a generation exists. For infinitely growing patterns, no agreed-upon definition is known, although the Life Lexicon describes a particular ark as stabilizing at generation 736692[2]. Most interpretations exclude such patterns.

Patterns with excessively large bounding boxes, such as a glider heading towards an arbitrarily distant block in the most trivial case, are generally implicitly excluded.

Examples

The smallest and most well-known methuselah is the R-pentomino, a pattern of five cells first considered by John Conway[3] that takes 1103 generations before stabilizing as a pattern of eight blocks, six gliders, four beehives, four blinkers, one boat, one loaf, and one ship. This methuselah is particularly notable since almost all other patterns of similar size stabilize within 10 generations.

Martin Gardner gave the first well-known definition of a methuselah along with some examples. Among the examples are pi-heptomino, thunderbird, B-heptomino and acorn[4]. The acorn, a pattern of seven cells developed by Charles Corderman, takes 5206 generations to stabilize.

Because they are very active, frequently-appearing methuselahs can be used as conduit objects. Known methuselahs of this type include B-heptomino, century, Herschel, pi-heptomino, queen bee, R-pentomino, and wing (also known as Block and glider).

Acorn
B-heptomino
Pi-heptomino

See also

References

  1. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 246, W.H. Freeman. 
  2. Stephen Silver (March 30, 2011). "Life Lexicon". Retrieved on March 14, 2016.
  3. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 219, 223, W.H. Freeman. 
  4. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 246, W.H. Freeman. 

External links