Father of fractals

The mathematician Benoit Mandelbrot died today of pancreatic cancer at the age of 85. Most people probably have no idea who he was. Which is unfortunate, because he spent a good part of his life showing us that mathematics can be spectacularly, almost indecently beautiful.

Mandelbrot is often called the father of fractals, one of the most well-known pioneers into this abstract field of mathematics. Fractals is one of those wonderfully strange corners of mathematics where the deeper you look, the more complicated things become. Zoom in and you find another world. Zoom in again and there’s another one waiting underneath. Keep going and, theoretically at least, you never reach the bottom.

Getting lost inside the Mandelbrot set.

He built on the work of mathematicians such as Gaston Julia and eventually coined the term fractal for geometric forms displaying these peculiar properties. The underlying ideas weren’t entirely new, as Leibniz had poked around similar territory centuries earlier, but Mandelbrot dragged fractal geometry out of mathematics’ dusty back room and into the light.

In 1980 he saw the first computer visualization of what would become known as the Mandelbrot set. And what a magnificent little monster it is.

At first glance it resembles some mutant black beetle floating in psychedelic space. Start zooming, however, and things get interesting. Spirals emerge from spirals. Tiny copies of the original shape appear in unexpected places. Elaborate landscapes unfold from what looks like mathematical chaos, revealing more detail the further down the rabbit hole you go. The infinitely complex patterns of a fractal geometry become apparent as more intricate details appear during recursive zooming.

The colors aren’t really there, of course. They’re visual representations of numbers in the complex plane, added so that our poor human brains have something attractive to look at. Think of those spectacular telescope photographs of distant nebulae: the science is real, but somebody has sensibly turned up the colors.

Fractals are mathematics behaving weirdly, and looking magnificent while doing it. Mandelbrot gave us a way to see them.