Algorithmic Imagery Secrets Revealed!!!

In my studies I have discovered a few interesting functions and their related image counterparts. $i is the multiplier and I used 0.0285 and 2.8500 as examples. The multiplier is a control point that can push the image from a crystalline beauty to chaotic static. I always experiment with a sequence from 0.0025 to 2500 incrementing by 10X each step to see what the range of numbers has to offer. Then I dive in to the detailed sequences.

I digress. Here are some of the building blocks I have found:

$eq=round(atan($x/$y)*$i);
$i>1.00 or you get all points plotted

$eq=round(cos($x*$y)*$i);
Again, $i>1.00

$eq=round(sin($x*$y)*$i);
And again, $i>1.00

$eq=round(sqrt($x*$y)*$i);
The Squares engine

Now the rest of these build off from the squares formula to get some very interesting image effects:

$eq=round(sqrt($x*$y)*atan($x/$y)*$i);

$eq=round(sqrt($x*$y)*cos($x*$y)*$i);

$eq=round(sqrt($x*$y)*sin($x*$y)*$i);

$eq=round(sqrt($x*$y)*cos($x*$y)*sin($x*$y)*$i);