More morph

This posts follows the last one with the concept of morphing our favorite formulas. Cool!

Today we are going to morph some stuff together. First I am going to take the ever popular arctangent variation which produced an amazing series and morph it with one of my all-time favorites.

So we will take the formula:
$eq1=round($i*(atan($x/$y))*cos(atan($x/$y))); //The Arctangent Variant

And this formula:
$eq2=round((cos($i*$y))*(sin($i*$x))*$i); // The Cosine/Sine Amazingness

And use this formula to 'join' them in a new an interesting way:
$eq=sqrt($eq1*$eq2);

We get a beautiful interplay between these two patterns in such a way that the whole is much greater than the su of its parts. Each individual pattern is present and yet the new emergin series is quite unique and on a level that is beyond its roots in Algorithmic Imagery. Behold!




Next we'll take same artTangen Series formula
$eq1=round($i*(atan($x/$y))*cos(atan($x/$y)));

And morph it with our Squares formula:
$eq2=round((M_PI*($x*$y)*$i));

Like this:
$eq=$eq1*$eq2;

And again we have furthered the craft:

Amazing, simply amazing.