in reply to Binomial Expansion

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; }

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(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