Do you know where your variables are? PerlMonks

### Sierpinskij (Re: Binomial Expansion)

by larsen (Parson)
 on Mar 29, 2001 at 13:48 UTC ( #68067=note: print w/replies, xml ) Need Help??

A pattern? Yes, of course!
Here what you can obtain if you paint a Pascal Triangle.

Update I think this link could be amusing: Pascal's Triangle

```#!/usr/bin/perl

use strict;

my \$n = 10;

for my \$i (0 .. \$n) {

for my \$j (0 .. \$i) {
my \$coefficient = nCr(\$i, \$j);
if (\$coefficient % 2) {
print '#';
} else {
print ' ';
}
}

print "\n";
}

# returns n!/r!(n-r)!
sub nCr
{
my \$n=shift;
my \$r=shift;

return int nFactorial(\$n) / int nFactorial(\$r) * int nFactorial(\$n
+-\$r);
}

# like the name says, n!
sub nFactorial
{
my \$n=shift;
my \$product = 1;

while(\$n>0)
{
\$product *= \$n--;
}

return  \$product;
}

Replies are listed 'Best First'.
(tye)Re: Sierpinskij (Re: Binomial Expansion)
by tye (Sage) on Mar 29, 2001 at 21:13 UTC

I thought part of the point of Pascal's triangle was to show that you don't have to compute factorials:

```my @line= (1);
while( 1 ) {
print "@line\n";
push @line, 0;
for(  reverse 1..\$#line  ) {
\$line[\$_] += \$line[\$_-1];
}
}
Be sure to pipe the output to more.

- tye (but my friends call me "Tye")
Re: Sierpinskij (Re: Binomial Expansion)
by rpc (Monk) on Mar 29, 2001 at 23:10 UTC
Not only is it Pacal's triangle, it's also a Sirpinski Gasket if you associate one character/color to even numbers, and another to odd.

Math rox.

Update: Ugh i am not awake yet. Forgive my redundancy.

Re: Sierpinskij (Re: Binomial Expansion)
by oha (Friar) on Dec 19, 2003 at 20:05 UTC
i found that code some times ago, unfortunately i don't know the author. i post here, maybe someone don't know.
```#!/usr/bin/perl -l
s--@{[(gE^Ge)=~/[^g^e]/g]}[g^e]x((!!+~~g^e^g^e)<<pop).!gE-ge,
s-[^ge^ge]-s,,,,s,@{[(g^';').(e^'?')]},(G^'/').(E^'|')^Ge,ge,
print,s,(?<=/[^g^e])[^g^e][^g^e],\$&^(G^'/').(E^'|')^gE,ge-ge

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