0,0 → 1,351 |
#Life 1.05 |
#D Irrational 5 |
#D Population growth is linear with an irrational multiplier. |
#D Each middleweight spaceship produced by the puffers either hits a |
#D boat or is deleted by a glider. Denoting the first possibility by |
#D 1 and the second by 0, we obtain a sequence beginning 101011011010... |
#D If we prepend 101, we obtain the Fibonacci string sequence, defined |
#D by starting with 1 and then repeatedly replacing each 0 by 1 and each |
#D 1 by 10: 1 -> 10 -> 101 -> 10110 -> 10110101 -> ... (See Knuth's |
#D "The art of computer programming, vol. 1", exercise 1.2.8.36 for |
#D another definition.) The density of 1's in this sequence is |
#D (sqrt(5)-1)/2, which implies that the population in gen t is |
#D asymptotic to (8 - 31 sqrt(5)/10) t. More specifically, the |
#D population in gen 20 F[n] - 92 (n>=6) is 98 F[n] - 124 F[n-1] + 560, |
#D where F[n] is the n'th Fibonacci number. (F[0]=0, F[1]=1, and |
#D F[n] = F[n-1] + F[n-2] for n>=2.) |
#D Dean Hickerson, dean@ucdmath.ucdavis.edu 5/12/91 |
#N |
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