Gnofract 4D: For when 2D fractals just aren't weird enough
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# Fractal Types

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 a family of functions of the form A*z^2 - B*z + C*c.

The Lambda function calculates lambda * z * ( 1 - z). The complex parameter lambda is set by the z and w parameters, so if lambda is zero, all you'll see is a blank screen.

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/fracdyn/. The Burning Ship is essentially a Mandelbrot variant where the real and imaginary parts of the current point are set to their absolute values after each iteration, ie z <- (|x| + i |y|)^2 + c. The Buffalo fractal uses the same method with the function z <- z^2 - z + c, making it equivalent to the Quadratic type with the "absolute value" modification.

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