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Hypercomplex numbers are similar to the usual 2D complex numbers, except they can be extended to 3 dimensions or more. When you use hypercomplex numbers to generate fractals, you can create some interesting looking 3D fractals. Quadratic 3D Mandelbulb Set - C++, 7/3/09
3D Power Mandelbulb Set - C++, 8/20/09
Positive Z-Component Variation of the 3D Mandelbulb Set - C++, 10/3/09
Cosine Variation of the 3D Mandelbulb Set - C++, 11/25/09
3D Juliabulb Set - C++, 7/28/09
Lambdabulb 3D Juliabulb Set - C++, 11/25/09
3D Mandelbrot / Mandelbar Set - C++, 7/5/09
Here are some higher order variations of this fractal.LinksMandelbrot / Mandelbar Set - includes explanation, by Eric Baird RockBrot - by David Makin 3D Mandelbrot Set Pickover Stalks - C++, 8/18/09
4D Quaternion Mandelbrot ("Mandelquat") Set - C++, 7/7/09
4D Quaternion Julia Set - Mathematica 4.2: 7/9/04, POV-Ray 3.1: 8/5/04
Inverse 4D Quaternion Julia Set - C++ version: 9/15/09; POV-Ray, version: 7/4/06; Mathematica version: 7/18/04
Mandelbox - 2/22/11
Inverse 3D Juliabulb Set - C++, 9/21/09
3D Glynn Juliabulb Set - C++, 11/17/09
4D Bicomplex Mandelbrot Set ("Tetrabrot") - C++, 7/30/09
4D Bicomplex Julia Set - C++, 7/29/09
Inverse 4D Bicomplex Julia Set - C++, 9/21/09
4D Julibrot Set - C++, 7/6/09
4D Hopfbrot Set - C++, 12/2/09
3D Exponential Mandelbrot Set - C++, 7/6/09
4D Mandelbulb Set - C++, 7/7/09
3D Nebulabrot - C++, 9/9/09
3D Mandelbrot Set Orbit Traps - C++, 8/18/09
3D Mandelbrot Set, based on Rudy Rucker's formula for squaring a 3D hypercomplex number - C++, 9/6/09
3D Christmas Tree Mandelbrot Set - C++, 12/2/09
3D Mandelbrot Set based on my attempt to combine the forward method with a reversed method - C++, 11/20/09
4D "Roundy" Mandelbrot Set - C++, 7/24/09
4D "Roundy" Julia Set - C++, 7/28/09
Bristorbrot Set - C++, 12/4/09
3D Mandelbrot Set, based on David Makin's formula for squaring a 3D hypercomplex number - C++, 10/14/09
3D Mandelbulb / Juliabulb Sets, based on Roger Bagula's parameters - C++, 12/15/09
3D Mandelbrot Set - C++, 12/9/09
3D Mandelbulb Orbits - POV-Ray 3.1, 1/5/10
4D "Squarry" Mandelbrot Set - C++, 7/30/09
4D "Squarry" Julia Set - C++, 7/29/09
4D "Mandy Cousin" Mandelbrot Set - C++, 7/30/09
4D "Mandy Cousin" Julia Set - C++, 7/29/09
4D Mandelbrot Set Variation - C++, 7/30/09
4D Julia Set Variation - C++, 7/29/09
Quadray Quaternion Julia Set - C++, 10/15/09
BoneYard - C++
Other Hypercomplex Fractal Links 3D Fractals - created by Richard Rosenman using Terry Gintz' QuaSZ software, includes "quaternion, hypercomplex, cubic Mandelbrot, complexified quaternion and octonion" |