# [PD] Data structures with \$0?

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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