Benoit Mandelbrot, Father of Fractal Geometry

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.

Benoît Mandelbrot speaking in 2007, image from Wikimedia

Benoît Mandelbrot speaking in 2007, image from Wikimedia

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.

The Mandelbrot set, named for Benoit Mandelbrot. Image from Wikimedia.

The Mandelbrot set, named for Benoit Mandelbrot. Image from Wikimedia.

Mandelbrot intuited the world’s fractal nature. He saw the laws that apply to stock markets and clouds, population trends and eddies in a stream; the basic organizational principles of all systems. Fractals and deterministic chaos have always surrounded us, but had never before been identified. Mandelbrot’s insights revolutionized thousands of years of scientific thought.

As you look at the Mandelbulb’s strange organic forms, you are looking at the legacy of Benoît Mandelbrot, one of the most influential scientific thinkers of the last hundred years.

Reference: Benoît Mandelbrot “The Fractal Revolution” Nov, 2002, Portland OR.

From Wikipedia’s entry on Benoît Mandelbrot:


Benoît B. Mandelbrot (20 November 1924 – 14 October 2010) was a French American mathematician. Born in Poland, he moved to France with his family when he was a child. Mandelbrot spent much of his life living and working in the United States, and he acquired dual French and American citizenship.

Mandelbrot worked on a wide range of mathematical problems, including mathematical physics and quantitative finance, but is best known as the popularizer of fractal geometry. He coined the term fractal and described the Mandelbrot set. Mandelbrot also wrote books and gave lectures aimed at the general public.

Mandelbrot spent most of his career at IBM’s Thomas J. Watson Research Center, and was appointed as an IBM Fellow. He later became a Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale’s history to receive tenure.[6] Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique. Continue reading (Wiki)


Welcome to 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 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. Continue reading