Home  |  About Us  |  Link To Us  |  FAQ  |  Contact

# Random Fibonacci Sequence 1.0

Date Added: May 03, 2013  |  Visits: 195

This routine shows the surprising behaviour of a random Fibonacci sequence.As reported by Divakar Viswanath - "RANDOM FIBONACCI SEQUENCES AND THE NUMBER 1:13198824..." - in MATHEMATICS OF COMPUTATION, 1999; 69(231): 1131-1155:"For the familiar Fibonacci sequence (defined by f1 = f2 = 1, and fn = fn1 + fn2 for n > 2), fn increases exponentially with n at a rate given by the golden ratio (1 + sqrt(5))/2 = 1:61803398.... But for a simple modification with both additions and subtractions - the random Fibonacci sequences defined by t1 = t2 = 1, and for n > 2, tn = dlT-tn-1 dlT-tn-2, where each dlT- sign is independent and either + or - with probability 1/2 - it is not even obvious if |tn| should increase with n. Our main result is that:|tn|^(1/n) -> 1:13198824... as n->Infwith probability 1."More details are available on http://www.advancedmcode.org/rndfibseq.html

 Requirements: No special requirements Platforms: Matlab Keyword: Additions,  Modification,  Ratio,  Sequences,  Sqrt,  Subtractions,  Tn1,  Tn2 Users rating: 0/10