Clouds are not spheres, mountains are not cones, coastlines are not circles”
During the 1980s, people became familiar with fractals through those weird, colourful patterns made by computers.
But few realise how the idea of fractals has revolutionised our understanding of the world, and how many fractal-based systems we depend upon.
On 14 October 2010, the genius who coined the word - Polish-born mathematician Benoit Mandelbrot - died, aged 85, from cancer.
The best way to get a feeling for what fractals are is to consider some examples. Clouds, mountains, coastlines, cauliflowers and ferns are all natural fractals. These shapes have something in common - something intuitive, accessible and aesthetic.
They are all complicated and irregular: the sort of shape that mathematicians used to shy away from in favour of regular ones, like spheres, which they could tame with equations.
Mandelbrot famously wrote: "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."
The chaos and irregularity of the world - Mandelbrot referred to it as "roughness" - is something to be celebrated. It would be a shame if clouds really were spheres, and mountains cones.
Look closely at a fractal, and you will find that the complexity is still present at a smaller scale. A small cloud is strikingly similar to the whole thing. A pine tree is composed of branches that are composed of branches - which in turn are composed of branches.
The fractal mathematics Mandelbrot pioneered, together with the related field of chaos theory, lifts the veil on the hidden beauty of the world. It inspired scientists in many disciplines - including cosmology, medicine, engineering and genetics - and artists and musicians, too.
Read more at www.bbc.co.uk
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