Apophysis is a free package based on something called Fractal Flames. Apophysis runs on Windows and generates some of the most breathtaking fractal images. Most of them are based on dynamical systems, and hence some of concentric spirals and loops. For such a little program, there are quite a few parameters you can toy with.

I came across the package in early 2005, when I was doing some fractal research for what was then preparation for entering a Master’s degree. I didn’t continue, for various reasons, but I did fiddle around with Apophysis. It took me a year to really figure out how to play with the parameters, and tiny little changes could have such profound effects in the displayed fractal. (I make it a habit to save intermediate steps regularly because if I go too far in parameter changes, I’m not always able to undo exactly to the stage I was at.)

A few examples are shown on this page (click to enlarge), which you are free to use in any way you want. I will post better ones from time to time. Each successive image is created from slight changes to the previous one.

There is another feature that gives automatic “mutation” images of your fractal, as well as animation window that rotates the current fractal through minute parameter changes. It’s almost like watching a galaxy expand.