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A110910 Configurations in the evolution of a line of n cells in Conway's Game of Life, with 0=infinity. For periodic evolutions, a(n)=(preperiod length)+(period length). For non-periodic evolutions, a(n)=0. 0
1, 2, 2, 2, 3, 8, 13, 15, 49, 22, 17, 17, 16, 26, 29, 41, 34, 25, 21, 26, 21, 21, 36, 31, 29, 95, 25, 29, 34, 38, 105, 150, 61, 582, 43, 58, 92, 108, 263, 277, 50, 212, 59, 53, 57, 99, 55, 170, 196, 812, 105, 54, 53, 85, 59, 81, 0, 418, 63, 63, 314, 117, 118, 170, 236, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
If nothing catches up with an outbound glider, then a(n)=0 for n>=1000 because when you watch the horizontal 1000-line evolve in a simulator, around the 490th generation, gliders fly away from the left and right corners _before_ the non-chaotic growing in the middle has finished, so you will see the same local picture in the 490th generation of longer lines.
REFERENCES
Berlekamp/Conway/Guy, Winning Ways ..., 2nd ed, vol. 4, chapter 25
LINKS
EXAMPLE
a(0)=1 because there is only the empty configuration. a(10)=2+15 because the 10-line needs two steps to become a pentadecathlon. a(56)=0 because the 56-line sends four gliders to outer space.
PROG
(Haskell)
{- program for verification of periodic cases. The non-periodic cases listed here evolve into a periodic kernel plus gliders whose paths ahead do not intersect each other or the kernel (gliders marching in single file are not counted as intersecting). Replace leading dots with spaces before running! -}
import Data.Set
main = print [if n `elem` known then 0 else a n | n<-[0..105]]
known = [56, 71, 72, 75, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 96, 98, 100, 102, 103, 105]
a n = count empty (iterate evolve (fromList [(x, 0) | x<-[1..n]]))
neighbors (x, y) = fromList
................. [(x+u, y+v) | u<-[ -1, 0, 1], v<-[ -1, 0, 1], (u, v)/=(0, 0)]
evolve life =
. let fil f = Data.Set.filter
............. (\x-> f (size (life `intersection` neighbors x)))
. in (life `difference` fil (\k-> k<2 || k>3) life) `union` fil (== 3)
.... (unions (Prelude.map neighbors (elems life)) `difference` life)
count o (x:xs) | x `member` o = 0
.............. | otherwise = 1 + count (o `union` singleton x) xs
CROSSREFS
Sequence in context: A270371 A351108 A184311 * A119532 A010583 A306343
KEYWORD
nonn,uned
AUTHOR
Paul Stoeber (pstoeber(AT)uni-potsdam.de), Oct 03 2005
STATUS
approved

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Last modified May 23 10:34 EDT 2024. Contains 372760 sequences. (Running on oeis4.)