Amiga Plus Extra 1996 #3/AmigaPlus_CD-ROM-EXTRA_Nr.3.bin/aminet-spiele/bunte mischung/axlife/patterns/irrational5.life

Text File | 1993-09-21 | 3KB | 411 lines

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