The quest by a group of math geeks to create a three-dimensional analogue for the mesmerizing Mandelbrot fractal has ended in success.
They call it the Mandelbulb. The 3-D renderings were generated by applying an iterative algorithm to a sphere. The same calculation is applied over and over to the sphere’s points in three dimensions. In spirit, that’s similar to how the original 2-D Mandelbrot set generates its infinite and self-repeating complexity.
The following images are worth a look. Each photo is a zoom on one of these Mandelbulbs. Daniel White, the amateur fractal image maker who coordinated the Mandelbulb effort, admits this creation isn’t exactly the Mandelbrot in 3-D. It’s mesmerizing and beautiful, but as he notes, only some versions of their original formula generate the kind of detail and complexity they are looking for. Their original equation doesn’t work very well unless you take it beyond the 2nd power. The picture above, White says, doesn’t have the level of detail that should be there.
“That means the biggest secret is still under wraps, open to anyone who has the inclination, and appreciation for how cool this thing would look,” White wrote on his website.
Via Dr. Stefan Gruenwald