[PD] Data structures with $0?

[Mathieu Bouchard]

On Thu, 17 Jun 2010, Mathieu Bouchard wrote:

>  [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)

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