Benoît Mandelbrot – Rest In Peace

Benoît Mandelbrot has passed away.

Mandelbrot is one of the few mathematicians whose contributions – at least some of them – can be immediately recognised and appreciated by a number of non-mathematicians. His name is attached to the now famous Mandelbrot set, beautiful pictures of which are immediately recognizable, and stunningly beautiful.

An unusual 3-D rendering of the Mandelbrot Set
An unusual 3-D rendering of the Mandelbrot Set

As well as discovering the Mandelbrot set, Benoît Mandelbrot is also known for inventing the word “fractal” – and pointing out to mathematicians that fractals are not just odd, curious mathematical exceptions. A fractal is any shape which, no matter how closely you look at it, is not made up of neat smooth curves and lines. Some examples from nature :-

  • The shape of a tree, with branches dividing into smaller branches, and the smaller branches dividing into still smaller branches and so forth.
  • The path of a butterfly’s flight
  • The curve of a coastline

He emphasized this with these lines from his most famous book, “The Fractal Geometry of Nature” :

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

It was Benoît Mandelbrot who encouraged mathematicians to try to understand this kind of “fractal” shape. He was influential in opening up the field of mathematics called “chaos theory”. The results of chaos theory can be applied to understanding some heart conditions, pest control and many other fields. Breakthroughs in chaos theory may one day help physicists make a clean fusion-powered reactor, providing humanity with unlimited clean green energy. He also did work in probability theory – trying to understand the likelihood of catastrophic events such as the Global Financial Crisis.

Can you find the Mandelbrot set? Jenny Hen using her new pen in "First Phonics", ISBN 1-74124-874-4
Can you find the Mandelbrot set? Jenny Hen using her new pen in "First Phonics", ISBN 1-74124-874-4

The Mandelbrot set is one of the most instantly recognizable pictures to come from mathematics. It’s filtered down into common consciousness. I’ve even seen Mandelbrot sets used to illustrate children’s phonics books! Can you spot it in the picure on the right? (Hint – look at the tin)

It has achieved this level of recognition for a few reasons. First of all, it’s a strikingly complicated structure, whose details become ever more intricate the closer you examine it. Secondly, it lends itself easily to beautifully coloured pictures that expose this complexity. Thirdly, the mathematical algorithm for creating these pictures is very simple, which means there is a huge array of software available allowing anyone with a computer to create these amazing fractal images. Fourthly, it’s a mathematically important shape. This might not seem like an important reason, but if it were not important mathematically, Benoît Mandelbrot would never have brought it to the world’s attention. It’s mathematically important because it turns up in very unexpected situations. In the video below, for example, I create a fractal with a very different formula from Benoît Mandelbrot’s – and yet, images of the Mandelbrot set appear as one zooms in on the fine details.

Benoît Mandelbrot will be long remembered by mathematicians for his contributions to the mathematics of chaos theory. Images of the Mandelbrot set will continue to inspire digital artists for many years to come. He was born in Poland in November 1924, and died on the 14th of October 2010, aged 85, in Cambridge, Massachusetts, of pancreatic cancer.