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352 lines
3.0 KiB
Plaintext
352 lines
3.0 KiB
Plaintext
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#Life 1.05
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#D Irrational 5
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#D Population growth is linear with an irrational multiplier.
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#D Each middleweight spaceship produced by the puffers either hits a
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#D boat or is deleted by a glider. Denoting the first possibility by
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#D 1 and the second by 0, we obtain a sequence beginning 101011011010...
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#D If we prepend 101, we obtain the Fibonacci string sequence, defined
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#D by starting with 1 and then repeatedly replacing each 0 by 1 and each
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#D 1 by 10: 1 -> 10 -> 101 -> 10110 -> 10110101 -> ... (See Knuth's
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#D "The art of computer programming, vol. 1", exercise 1.2.8.36 for
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#D another definition.) The density of 1's in this sequence is
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#D (sqrt(5)-1)/2, which implies that the population in gen t is
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#D asymptotic to (8 - 31 sqrt(5)/10) t. More specifically, the
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#D population in gen 20 F[n] - 92 (n>=6) is 98 F[n] - 124 F[n-1] + 560,
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#D where F[n] is the n'th Fibonacci number. (F[0]=0, F[1]=1, and
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#D F[n] = F[n-1] + F[n-2] for n>=2.)
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#D Dean Hickerson, dean@ucdmath.ucdavis.edu 5/12/91
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#N
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#P -67 -32
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#P -62 -25
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***
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#P -58 -31
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*...*
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.*..*
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#P -57 -26
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.*.*
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#P -49 -16
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#P -58 -8
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#P -53 -2
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#P -49 5
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#P -73 10
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#P -64 16
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#P -64 9
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#P -56 25
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#P -48 21
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#P -43 16
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#P -38 11
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#P -33 6
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#P -28 1
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#P -40 -10
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#P -26 -12
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#P -17 -3
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#P -8 -4
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#P -5 -16
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#P 1 12
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#P 5 1
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#P 13 -13
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#P 22 9
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#P 26 -3
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#P 31 -8
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#P 36 -13
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#P 41 -18
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#P 46 -23
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#P 52 -29
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#P 36 8
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#P 69 -26
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#P 60 -20
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#P 61 -12
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#P 54 -8
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#P 51 -3
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#P 46 -8
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#P 45 12
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#P 63 14
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#P 61 21
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#P 52 21
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.....*
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.*****
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..*
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#P 55 28
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**.**
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