Showing posts with label beautiful algebraic mandalaimage processing php gd library. Show all posts
Showing posts with label beautiful algebraic mandalaimage processing php gd library. Show all posts

Monday, September 15, 2008

Mandalas

I started using a new building block that imparts a circular quality that I find appealing:

$r=sqrt(pow($x,2)+pow($y,2));

When I am using this cosine function the details become amazing:

$cosXY=cos($x*$y);

So why not put them together?

$eq=round( log($r,$i) * $cosXY );


Next up we'll take the natural logarithm of $r*$i and multiply that by $r squared:

$eq=round( log($r,$i) * $r2 );

This next image illustrates some new features. First I have the molulos listed in the colors that they represent. And the -r after the 'modulo' indicates that the modulo color scheme is weighted high to low (mod 8 over mod 7 over mod 6, etc). When you see -n it is normal (mod 2 over mod 3, etc). Also notice that if a certain modulo is not used it's number will not print.

This one is amazing. I may have to post a series of this just because.

$eq=round( cos($r*$i)*sqrt($r)*$i );


This one uses the same logarithmic function and multiplies that by the inverse of the square root of a pair of common building block equations:

$cosYi=cos($y*$i); $cosXi=cos($x*$i);
$eq=round( log($r,$i) * (1/sqrt($cosYi*$cosXi)) );


My next post will have some chose mandalas to view!