#macro Fibonacci(A)
   #local M = (pow(1.618033989,A)-pow(0.618033989,A))/2.236067977;
   #local R = int(M) + select( (mod(M,1) >= 0.01),1,0,1);
   (R)
#end

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this works? up to what index?


"Tim Attwood" <tim### [at] comcastnet> wrote in message
news:44fbb900$1@news.povray.org...
> #macro Fibonacci(A)
>    #local M = (pow(1.618033989,A)-pow(0.618033989,A))/2.236067977;
>    #local R = int(M) + select( (mod(M,1) >= 0.01),1,0,1);
>    (R)
> #end
>
>

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> this works? up to what index?

Up to *any* index, assuming there's no floating point rounding errors.

A quick trip to Wikipedia will probably demonstrate why - if not, 
Wolfram's MathWorld will have the derrivation.

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>> this works? up to what index?
Up to 34 or so in windows.
BTW I must have looked at too many of those
WTF coding examples...
#local R = int(M+0.56);

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>>> this works? up to what index?
> Up to 34 or so in windows.

And in O(1) time instead of O(n)...

> BTW I must have looked at too many of those
> WTF coding examples...
> #local R = int(M+0.56); 

;-)

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Is there something special about this beside that it's the non-recursive
form of the fibonacci sequence?

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Orchid XP v3 <voi### [at] devnull> wrote:
> >>> this works? up to what index?
> > Up to 34 or so in windows.

> And in O(1) time instead of O(n)...

  Up to index 34 you could just make a table which you index with the
number and that would also be O(1), and probably with a faster factor.

-- 
                                                          - Warp

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> Is there something special about this beside that it's the non-recursive
> form of the fibonacci sequence?

No not really.

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>>>>> this works? up to what index?
>>> Up to 34 or so in windows.
> 
>> And in O(1) time instead of O(n)...
> 
>   Up to index 34 you could just make a table which you index with the
> number and that would also be O(1), and probably with a faster factor.

That's also true...


I can't actually think of a *use* for Fibonacci numbers, come to think 
of it.

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Orchid XP v3 <voi### [at] devnull> wrote:
> I can't actually think of a *use* for Fibonacci numbers, come to think 
> of it.

http://en.wikipedia.org/wiki/Fibonacci_number#Applications

  One thing where I know it is also used is in predicting currency
market fluctuations.

-- 
                                                          - Warp

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>> I can't actually think of a *use* for Fibonacci numbers, come to think 
>> of it.
> 
> http://en.wikipedia.org/wiki/Fibonacci_number#Applications
> 
>   One thing where I know it is also used is in predicting currency
> market fluctuations.

Their appearence in Pascal's triangle might make them useful, 
possibly... The rest looks mainly like theoretical uses.

I know the *ratio* of consecutive numbers approaches the golden mean - 
but there are much easier ways to compute that.

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Orchid XP v3 <voi### [at] devnull> wrote:
> I know the *ratio* of consecutive numbers approaches the golden mean -
> but there are much easier ways to compute that.

You don't need to compute that, it's (1+sqrt(5))/2 ;-)

Regards Roman

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"Orchid XP v3" <voi### [at] devnull> schreef in bericht 
news:44ff13a2@news.povray.org...
>
> I can't actually think of a *use* for Fibonacci numbers, come to think of 
> it.

see:
news://news.povray.org/39B44A76.2ECBA98A%40online.no


Thomas

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Orchid XP v3 <voi### [at] devnull> wrote:


> I can't actually think of a *use* for Fibonacci numbers, come to think
> of it.

Someone posted this link recently, and I found it quite fascinating...

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#seeds

Ken W.

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