This is the coolest program. I've been fooling with it since it was just v. 1.24 - but the new 2.0 has good fixes for some of the annoying problems in v. 1.24.
The coolest images are found by using a Mandelbrot set and zooming in on different areas. I don't totally understand the math completely - but here is the best shot I can take at it:
We all worked with geometry in high school. In geometry you take an equasion and find a set of points that satisfy the equasion (for example: x2 + y2= 1). When you instead iterate an equasion instead of solving it, the equasion becomes a process instead of a description - dynamic instead of static. When a number goes into the equasion, a new number comes out; the new number goes in and on and on - points hop from place to place. A point is plotted not when it satisfies the equasion but when it produces a certain kind of behavior. One behavior might be a steady state, another might be a convergence to a periodic repetition of states, another might be an out-of-control race to infinity.
In the Mandelbrot set you simply take a number, multiply it by itself, and add the original number z = z2 + c
Pretty wild. A 2 element equasion with only 4 characters results in what is considered the most complex mathematecal object known today.
(the equasion for this image in the program looks like this: Z=Fn1(Z); Z=Z*Z + Fn2(C) - In the program it looks longer because you have to label the function of Z (Fn1) and function C (Fn2).)
This is what a Mandelbrot set looks like:

Anyway - here are some of the images I've created (click on the thumbnail for the full version) - all of these images except one come from zooming in on a Mandelbrot graph (by as much as 1,000,000x magnification):





These last images were created by altering the colors of the original set:


Or by using a different equasion - in this case a Newton attractor:

Now - go forth and create funky images.
The best images are found along the edges. If you focus on large blank areas (either black or with only one or two colors) - you get nothing.
Don't let the math fool you - creating these images involved no manipulation of the math - it is a graphics program first and foremost. If you understand the math you can do really cool stuff, but it isn't necessary.
Myself - I save the images I like into 1024 x 768 and use them as desktop graphics (all the large images that can be linked to are that size). If you're really into this type of stuff, you can get the 3-D generator as well and create fractal landscapes. That is pretty cool stuff - but I don't have quite the patience for it.