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

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