Gnofract 4D supports a variety of fractal formulae apart from the vanilla mandelbrot set. These have been pillaged from a variety of sources, notably Fractint. I've tried to keep the names consistent.
The Cubic Mandelbrot function calculates z^3 + c, rather than the standard z^2 +c. The Quadratic function calculates z^2 - z + c.
The Lambda function calculates lambda * z * ( 1 - z). Because lambda is zero in the default view, all you'll see is a blank screen when you first switch to this fractal. Simply change z or w to get a more interesting image.
The Barnsley fractals originally come from Michael Barnsley's book Fractals Everywhere, though I haven't seen the book and have copied the implementation from Fractint.
The Burning Ship and Buffalo fractals are described on the web page http://www.theory.org/. They are closely related functions.