The Mandelbulb: First ‘True’ 3D Image of Famous Fractal

New Scientist (11/18/09) Aron, Jacob

mandelbrotDaniel White has created an image, the Mandelbulb, that he says is the most accurate three-dimensional (3D) representation to date of the Mandelbrot set, a fractal equation named after Yale University mathematician Benoit Mandelbrot, who coined the term “fractal.” Previous attempts at a 3D Mandelbrot image do not display real fractal behavior, White says.

“I was trying to see how the original [two-dimensional] Mandelbrot worked and translate that to the third dimension,” he says. “You can use complex maths but you can also look at things geometrically.”

White’s approach works due to the properties of the “complex plane,” a mathematical landscape in which ordinary numbers run from east to west while imaginary numbers run from south to north. Multiplying numbers on the complex plane is the same as rotating it, while addition is like shifting the plane in a particular direction. Creating the Mandelbrot set requires repeating these geometrical actions for every point in the plane.

In 2007, White published a formula for a shape that was close to a 3D Mandelbrot, but still lacked true fractal detail. White then began a collaboration with Paul Nylander, who realized that raising White’s formula to a higher power would create the desired effect. White acknowledges that the Mandelbulb is still not quite a “real” 3D Mandelbrot, as there are still areas without enough detail.

“If the real thing does exist–and I’m not saying 100 percent that it does–one would expect even more variety than we are currently seeing,” he says.

No More Geeky Glasses to Watch 3D

ICT Results (06/10/09)

European researchers are working on technology that may make it unnecessary to wear special eyewear in order to watch three-dimensional (3D) video. The breakthrough was accomplished through the HOLOVISION project, which ended in April 2008, and the OSIRIS project, which will be completed at the end of 2009.

The chief goal of the HOLOVISION effort was to develop technologies that could generate a very high-resolution 3D image.

“We basically organized projection engines in a special way and used holographic imaging film for the display screen,” says Akos Demeter of Holografika. “The combination of these, with the projection engines being driven by a cluster of nine high-end PCs, and new sophisticated software, allowed us to achieve our aims.”

HOLOVISION yielded a prototype system with about 10 times the resolution of high-definition TV at 25 frames per second in six colors, rather than the standard three. One of OSIRIS’ key objectives is the development of high-resolution, big screen, reflective projection 3D cinema, and the prototype being worked on has a wall-mounted screen and a ceiling-mounted projector.

The OSIRIS technology employs an array of mirrors and light sources to provide the re-projected images and give the screen a depth of between 15 and 20 inches. Holografika’s Zsuzsa Dobranyi envisions military combat training and gaming as potential applications for the technology, while computer-aided design and other industrial and professional applications could be rolled out in a matter of months.

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I just love it when science fiction becomes reality, don’t you?  I immediately thought of the odd 3-D hair buns of  Princess Leia while she was saying, “Help me, Obi Wan Kenobe! Help Me!”