From 2D Mandelbrot to 3D Mandelbulb: A Tour of Mystery and Intrigue

The co-discoverer of the Mandelbulb, a three-dimensional version of the Mandelbrot set, talks about the mathematics and art of fractals

The word "fractal" may be an unfamiliar word for something which is actually all around us. It embodies the way large scale shapes are repeated at smaller scales. Examples found in nature include a lightning strike, snowflake, or a broccoli floret. But the discovery of one of the most beautiful fractals has only been made possible since the advent of computers, due to the millions of calculations that are needed. It is known as the "Mandelbrot set", and was found by Benoit Mandelbrot about 30 years ago. No matter how far you zoom in, or how tiny the detail, there will always be further exquisite detail to be found. With its colourful and hypnotic patterns, it quickly
found its way into the public imagination.

Elaborate and beautiful though the Mandelbrot may be, it has always remained flat and two-dimensional. But not anymore, as for the first time, the "Mandelbulb" is a successful attempt to bring all that detail into glorious 3D, so that shadows, light sourcing and real depth become possible. The Mandelbulb is a relatively simple extension of the same simple formula, and one which yields intricate, strange, but somehow compelling detail, forever.

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