kolibrios/programs/demos/life2/lif/IRRAT5.lif
Yogev Ezra 2bf6bb3b5b Added sources of life2 demo to SVN.
git-svn-id: svn://kolibrios.org@1769 a494cfbc-eb01-0410-851d-a64ba20cac60
2011-01-28 13:00:06 +00:00

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#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
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