Talk:Random Fibonacci sequence

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I removed the following text from the article:

the ratio of the absolute values of successive terms converges to the value of the constant

If this were true, then f(n-1) would be approximately Vf(n-2), where V denotes Viswanath's constant. Hence f(n) is either f(n-1) + f(n-2) = (V+1) f(n-1) or f(n-1) - f(n-2) = (V-1) f(n-1), so f(n) / f(n-1) is either (V+1)/V or (V-1)/V. These numbers differ, so the ratio f(n) / f(n-1) does not converge.

I replaced the above text with the definition from Viswanath's paper. -- Jitse Niesen 23:17, 28 Apr 2004 (UTC)

Is the definition correct?

Latest comment: 15 years ago3 comments3 people in discussion

Mathworld (see references) defines the random Fibonacci sequence as

${\displaystyle a_{n}=\pm a_{n-1}\pm a_{n-2}}$ 

with +/- sign in front of the two terms. The definition in the main article has only one +/-. TomyDuby (talk) 18:27, 28 August 2008 (UTC)Reply

Yep, you're right. I checked against Viswanath's article, and he does the same. A bit unfortunate, in my opinion, because it just complicates the definition without making much difference. But we better follow the source, so I changed the article. -- Jitse Niesen (talk) 19:13, 28 August 2008 (UTC)Reply

My problem with the latest "recursive" definition change, is that it implies that one should drop or change some of the true signs, since the formula of 4, is actually a reduced form of all 8 possible operations. For example when a negative number is subtracted, it can be reduced to merely addition ofcourse. However "recursively" that sequence will be different, if that negative number remains a reduced postive number upon recursion. Anyways, I think it was inappropriate and/or inacurate to change this wikipedia definition from 1/2 probability to 1/4, instead of a more precise 1/8. Primedivine (talk) 23:12, 19 February 2010 (UTC)Reply

Significance

Latest comment: 15 years ago2 comments1 person in discussion

The second paragraph of this section appears to be meaningless speculation (rabbits preying on each other?), whereas only the first 2 sentences of the first paragraph are relevant to the article, and need to be highlighted sooner, as they provide a theoretical underpinning for exponential growth of the sequence. Is there any reason why the section has been preserved virtually in its original form for so long? Arcfrk (talk) 02:23, 19 April 2010 (UTC)Reply

Fixed it. Arcfrk (talk) 05:12, 22 April 2010 (UTC)Reply