The UI controls are functional while an image is drawn; you don't have to wait until it's done. Clicking on the "Approximation: On/Off" label toggles approximation mode, which shows an increasingly finegrained approximation of the final image. This is useful to get a first idea of what an image looks like, and zoom/pan without having to wait for the whole image to be finished.
The source code can be found here.
If you're interested in experimenting with Mandelbrot images some more,
you might want to check out my Expression plugin for ImageJ.