Thursday, 21 October 2010

In memory of Benoit Mandelbrot

The mathematician Benoit Mandelbrot has died, aged 85.

Although hardly a household name, he is known amongst mathematicians and computer scientists as the father of the fractal. Fractals are mathematical constructs that states that something can be split into small parts that are similar to the larger object.

Fractals would probably have remained a mathematical curiosity except for the fact that fractal geometry can explain many of the things we observe in nature - a classic example is a fern frond, where the entire frond consists of small parts that resemble the whole. Ice crystals and clouds exhibit fractal characteristics, as can some financial systems.

This means that a fairly complex system such as the shape of a leaf can be controlled by very simple rules; understand the rules and you can recreate the shape.

Fractals can be used to generate images of startling beauty, for instance the Mandelbrot or Julia sets. These can be zoomed into, each level of zoom producing images of startling beauty. They are the best of maths: relatively simple in theory, with vast implications for the real world, that can also produce startling beauty.

There is one other reason why Mandelbrot appeals to me: one of his first papers on fractals was called "How long is the coast of Britain?", published in 1967. In this, he details how finding a 'correct' length for the coastline of Britain is next to impossible, as it depends on the scale you measure it at. The closer you look, the more detailed and longer the coastline becomes.

I first wrote Mandelbrot and Julia set creation programs a couple of decades ago, when the computer power required meant that the zooming was exceptionally slow. I loved both the maths and the resultant images. So, courtesy of Wikipedia, here is a Mandelbrot set:

And why not discover the beauty for yourself: have a play at Yale's website.

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