[PD] Data structures with $0?
João Pais
jmmmpais at googlemail.com
Fri Jun 18 22:01:17 CEST 2010
thanks, I'll try to put this in when I can. meanwhile dtmod wrote me
saying that he's doing a real external for this, so that would be a better
solution. anyway since I started, I'll try to finish my work.
>> [expr pow(1-$f1,3)*pow($f1,0)*$f2 +
>> pow(1-$f1,2)*pow($f1,1)*$f3 +
>> pow(1-$f1,1)*pow($f1,2)*$f4 +
>> pow(1-$f1,0)*pow($f1,3)*$f5]
>
> doh, I forgot some multipliers.
>
> [expr 1*pow(1-$f1,3)*pow($f1,0)*$f2 +
> 3*pow(1-$f1,2)*pow($f1,1)*$f3 +
> 3*pow(1-$f1,1)*pow($f1,2)*$f4 +
> 1*pow(1-$f1,0)*pow($f1,3)*$f5]
>
> when you vary the order, the 1 3 3 1 sequence goes like this :
>
> 1
> 1 1
> 1 2 1
> 1 3 3 1
> 1 4 6 4 1
> 1 5 10 10 5 1
> 1 6 15 20 15 6 1
>
> notice how the numbers for each order are made from the numbers for the
> previous order : each number is the one above plus the one to the left of
> the one above.
>
> you also get that same pattern of numbers doing various things such as
> the
> theory of coin-flipping, approximations of Gaussian blur, or if you
> expand
> pow(x+1,n), e.g. :
>
> pow(x+1,4) is the same as :
> 1*pow(x,0) +
> 4*pow(x,1) +
> 6*pow(x,2) +
> 4*pow(x,3) +
> 1*pow(x,4)
>
> Note that http://en.wikipedia.org/wiki/Pascal_triangle has some cool
> drawings and animations about it. (I especially like the fact that a
> fractal appears in that number pattern if you make many rows of it)
>
> _ _ __ ___ _____ ________ _____________ _____________________ ...
> | Mathieu Bouchard, Montréal, Québec. téléphone: +1.514.383.3801
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