In November 2002, I saw Benoît Mandelbrot’s presentation, “The Fractal Revolution”, in Portland Oregon. It was a short overview and introductory presentation about fractals. I’m an enthusiast, so the content was familiar. The great pleasure was seeing the man himself – Benoît Mandelbrot, the Father of Fractal Geometry – talk about how he revolutionized science, math, and our entire view of the world. Fractal dimensionality explains something truly fundamental about the forms and patterns we see daily. However, fractal dimensionality was unknown before Benoît Mandelbrot’s work, which from the late 60s on illuminated this deep truth about the geometry of the world. During Mandelbrot’s 2002 talk, it struck me how much intuition informed his discovery of fractal geometry. Mandelbrot described looking at the ‘drunkard’s walk’— a kind of ‘random walk’ equation—and “seeing” what its fractal dimension was, intuitively. Such amazing intuitive leaps are familiar in science. The formal steps of providing solid proof soon follow this “eureka” moment, during which the answer is revealed. Mandelbrot’s sudden deciphering of the ‘drunken walk’ is no different from, nor any less significant than, Einstein’s discovery of relativity, Isaac Newton’s apple-inspired understanding of gravity, and the original “eureka” moment, when Archimedes’ bodily volume displaced the water in his tub. Like those intellectual explorers before him, Mandelbrot looked at the world and saw a previously unseen truth. He built on what came before, and in so doing, revolutionized it. Mandelbrot intuited the world’s fractal nature. …
Enter the Mandelbulb
3D fractal environments both beg and dare you to enter them
Welcome to Mandelbulb.com
Mandelbulb.com is about raising awareness of 3D fractal forms—the Mandelbulb and its relatives—with striking images and thought-provoking information. We hope to add to the larger conversation about 3D fractals, bring it to new audiences, and to engender a greater appreciation of math, art, science, and their interrelationships. About the Mandelbulb In 2009 fractalforum.com members set out to find a three dimensional analogue of the Mandelbrot set. They discovered instead a three dimensional manifestation of the set—a way to project the set into three-space using a spherical coordinate system. It was a team effort. Daniel White and Paul Nylander spearheaded the discovery of the Mandelbulb, with Rudy Rucker, Krzysztof Marczak and many others working to develop the maths and create applications to view these newly-discovered fractal objects. More about 3D fractals.