We all know what fractals are, even if we can't explain them very well (myself included). In simplest terms, fractals are geometric shapes that can be split into increasingly smaller, yet identical, fragments.
In 2002, Scott Draves created something called "fractal flares," which are a class of fractals that use nonlinear transformations and color in a way to create spectacular images. His work was put into a free, open-source fractal-flame called Apophysis.
I've been playing a bit with Apophysis this week, and be warned: once you get started, you may find yourself spending hours creating increasingly impressive artwork and tweaking your inventions. The learning curve for Apophysis is fairly steep, but there are plenty of tutorials online to get you started.
Once you get comfortable with two-dimensional creation using Apophysis (and your computer can handle a somewhat intense processing demand), you can take the fractal madness up a notch with the "experimental" 3D version of the software, one of several beta versions of Apophysis.
For lower-maintenance fractal flames on your desktop, Scott Draves also created an open-source screensaver called Electric Sheep. This most excellent software uses your computer's down cycles to generate fractal flames and share them with the community at large.
You can even vote for other users' creations, or "sheep," to increase their lifespan and ensure that they "mate" with other sheep to create beautiful children. You can also create sheep using scripts built into Apophysis and then submit them to the Electric Sheep Web site. A gallery of the user-generated fractal flames displays all sorts of images, as well as useful and trivial data about both living and dead sheep.
What other software do you use to create cool-looking fractals or any other digital art? Tell me about it in the comments.