Art by Computer What is a Mandelbox - Mandelbox A Mandelbox is a box-like fractal object that shares several properties with the well known Mandelbrot set; it is a map of continuous, locally shape preserving Julia sets. This means the object varies at different locations, since each area uses a Julia set fractal with a unique formula. Like the Mandelbrot set a Mandelbox is calculated by applying a formula repeatedly to every point in space. That point v is part of a Mandelbox if it does not escape to infinity. In fact it replaces the Mandelbrot equation z = z2 + c with: v = s*ballFold(r, f*boxFold(v)) + c where boxFold(v) means for each axis a: if v[a]>1 v[a] = 2-v[a] else if v[a]<-1 v[a] =-2-v[a] and ballFold(r, v) means for v's magnitude m: if m<r m = m/r^2 else if m<1 m = 1/m The standard Mandelbox uses this formula with s=2, r=0.5 and f=1. Unlike the Mandelbrot set a Mandelbox can exist in any number of dimensions. Properties It is probably a multi-fractal, which means it doesn't have a single fractal dimension measure, however:
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XenoDream Software 3D graphics - index Software 3D graphics - index Ultra Fractal Fergus Ray Murray's Homepage - Science, Sculpture, Photography, Animation, etc Hypercomplex Fractals Here is a 4th order inverse Juliabulb set with 600 million spheres. The triplex raised to the 4th power has 16 unique valid roots. Garth Thornton was the first person to point out that, in general, the triplex raised to the nth power has n2 unique valid roots. I posted a formula for all integer powers here.
Mandelbulber Most people have heard something about fractals. There are many natural fractal shapes like clouds, trees, broccoli, etc. The most famous mathematical fractal is the Mandelbrot set. This fractal is two-dimensional. By the end of 2007, a small group of people from www.fractalforums.com decided to develop algorithms and software for rendering 3D fractals. Rendering of first images took a lot of time, and was very difficult because the first programs didn't have any user interface. New types of 3D formulas were also discovered. These fractals can be zoomed infinitely like two-dimensional fractals.
FLAM3 Mystery of the Real 3D Mandelbrot Fractal They're all very nice, but imagine such pictures in three dimensions, with all the advantages that 3D can allow such as parallax, perspective, and richer detail along with subtle light sourcing, shadows, and reflections. And actually, it turns out there are quite a few '3D' Mandelbot pics out there if you look..... Mandelbrot Flavours .....But are they the real McCoy, or just pale imitations? Existence of 3D Mandelbrot set? No, the thing I've been looking for has the essential characteristics of the traditional 2D Mandelbrot, but extended to 3 dimensions. We can try and guess the overall shape's outline too. Below is a third visualization using a formula I created based on pseudo 3 dimensional complex numbers (and nicely rendered by Thomas Ludwig). Also see Thomas' amazing metallic render of the same design. But even more than the overall shape, like the 2D Mandelbrot, the most incredible visuals would be witnessed once you've zoomed in to the hypothetical 3D Mandelbrot. External links:
Structure Synth the electric sheep screen-saver