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

Daniel 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.