Buddhabrot is a fractal explorer in the form of a free filter for Photoshop, and anything else - like Paint.NET - that supports 8bf files (it won't run stand-alone).
This isn't yet another Mandelbrot clone. Instead it uses Melinda Green's own custom rendering technique where pixels are coloured according to their density - how many times a sample hits the same spot. (Check out the grab and the developer's site for some gorgeous example images.)
As usual with this kind of application, there are a vast number of parameters to tweak. It can produce Buddhabrot and Nebulabrot versions of the Mandelbrot, Tricorn, Burning Ship and Diamond fractals, using alternate 4D projection planes, and with complete colour control.
Alternatively, if the math seems too complicated you can just keep clicking the RND button to randomise the parameters and produce a different image each time.
However you use the package, the developer says Buddhabrot is capable of "extremely high resolution fractals, in excess of 900 megapixels". It's probably best to start with something smaller, as super-sized images would take an age to generate, but Buddhabrot can at least use all your CPU cores to maximise performance.