Gnofract 4D: For when 2D fractals just aren't weird enough | ||
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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 Quadratic function calculates a family of functions of the form A*z^2 - B*z + C*c. The Cubic Mandelbrot function calculates z^3 + c, rather than the standard z^2 +c. MandelZPower calculates z^A + c, where A is a complex parameter. Setting this to 2.0 produces the standard Mandelbrot set, and 3.0 produces the cubic mandelbrot. The more specialized functions are naturally much faster.
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 Mandelbar fractal is the same as the Mandelbrot, except that the complex conjugate of the number is used at each iteratin step, eg z <- (x + i |y|)^2 + c. 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.
Nova is Paul Derbyshire's Nova fractal.Newton Newton's method applied to a polynomial.
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