This is a Mandelbrot set. I animated it by incrementing the real part of Z(0) in each frame. Changing the imaginary part produces different but equally interesting results.
This image was created with Fractint.
You can get a copy of Fractint at http://spanky.triumf.ca/www/fractint/fractint.html.
The animation was strung together with GIFMake.
You once could get a copy of GIFMake at http://www.fastlane.net/~samiel/, but the link is now dead.