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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Mandelbulber ::: 3D fractal explorer ::: open source / 64-bit / ray marcher XenoDream Software 3D graphics - index Software 3D graphics - index Ultra Fractal fleur fractal symétrique, illustrations numériques pour la création graphique — Photographie fbatista72 © #39331309 Résolutions Taille Taille: Pouces | Cm Prix: Prix Crédits | Souscription S 500 × 500, JPG Lic. 500 × 500 17.6 × 17.6 (72 dpi) 6.9" × 6.9" (72 dpi) 1 1 téléchargement Re-télécharger M 1000 × 1000, JPG Lic. 1000 × 1000 8.5 × 8.5 (300 dpi) 3.3" × 3.3" (300 dpi) 4 1 téléchargement Re-télécharger L 2000 × 2000, JPG Lic. 2000 × 2000 16.9 × 16.9 (300 dpi) 6.7" × 6.7" (300 dpi) 8 1 téléchargement Re-télécharger XL 6000 × 6000, JPG Lic. 6000 × 6000 50.8 × 50.8 (300 dpi) 20.0" × 20.0" (300 dpi) 12 1 téléchargement Re-télécharger EL 6000 × 6000, JPG Lic. 80 Uniquement par crédits Re-télécharger
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.
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