Friday, September 26, 2008


This one reminds me of the falls in between Lakes Erie and Ontario. Here is the equation:


Remembering that:

Sunday, September 21, 2008

More Simplicity Gone Awry

To add to the last two posts I have this equation:


The results show us some more of Sierpiński's triangle in a distorted form:

Simplicity Often Yeilds Complexity

Take this formula:


Or more simply:


And we get these amazing images:

Friday, September 19, 2008

Triangles, sort of

Today I put together this equation:


It outputs some interesting patterns when I ran a series from -25 t0 25. The patterns change interestingly when $i>=1. Pretty cool and quite different from what I have found so far.

As soon as $i>1 we find Sierpiński's triangle (wow!)

Circular log-ic


Monday, September 15, 2008

A Selection of Mandalas



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


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


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!