Shareware Overload Trio 2/Shareware Overload Trio Volume 2 (Chestnut CD-ROM).ISO/dir44/lifepnew.zip/IRRAT5.LIF

Text File | 1994-04-04 | 4KB | 409 lines

#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, [e-mail]  5/12/91
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