Top Document: Fractal Frequently Asked Questions and Answers Previous Document: How can I take photos of fractals? Next Document: Fractint See reader questions & answers on this topic!  Help others by sharing your knowledge Q20: How can 3D fractals be generated? A20: A common source for 3D fractals is to compute Julia sets with quaternions instead of complex numbers. The resulting Julia set is four dimensional. By taking a slice through the 4D Julia set (e.g. by fixing one of the coordinates), a 3D object is obtained. This object can then be displayed using computer graphics techniques such as ray tracing. View Frank Rousells hyperindex of clickable/retrievable 3D images: ftp://ftp.cnam.fr/pub/Fractals/3D/Index.gif The papers to read on this are: 1. J. Hart, D. Sandin and L. Kauffman, Ray Tracing Deterministic 3D Fractals, _SIGGRAPH_, 1989, pp. 289296. 2. A. Norton, Generation and Display of Geometric Fractals in 3D, _SIGGRAPH_, 1982, pp. 6167. 3. A. Norton, Julia Sets in the Quaternions, _Computers and Graphics,_ 13, 2 (1989), pp. 267278. Two papers on cubic polynomials, which can be used to generate 4D fractals: 1. B. Branner and J. Hubbard, The iteration of cubic polynomials, part I., _Acta Math_ 66 (1988), pp. 143206. 2. J. Milnor, Remarks on iterated cubic maps, This paper is available from anonymous ftp: math.sunysb.edu:/preprints/ims906.ps.Z . Published in 1991 SIGGRAPH Course Notes #14: Fractal Modeling in 3D Computer Graphics and Imaging. Instead of quaternions, you can of course use other functions. For instance, you could use a map with more than one parameter, which would generate a higherdimensional fractal. Another way of generating 3D fractals is to use 3D iterated function systems (IFS). These are analogous to 2D IFS, except they generate points in a 3D space. A third way of generating 3D fractals is to take a 2D fractal such as the Mandelbrot set, and convert the pixel values to heights to generate a 3D "Mandelbrot mountain". This 3D object can then be rendered with normal computer graphics techniques. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: Fractal Frequently Asked Questions and Answers Previous Document: How can I take photos of fractals? Next Document: Fractint Single Page [ Usenet FAQs  Web FAQs  Documents  RFC Index ] Send corrections/additions to the FAQ Maintainer: stepp@marshall.edu
Last Update March 27 2014 @ 02:11 PM
