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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