Beauty by numbers

What do spiders' webs, snowflakes and snail shells have in common? They all contain fractals: Nature's exquisite, endlessly repeating mathematical pattern. Deborah Nicholls-Lee unpicks their complex geometry

- Deborah Nicholls-Lee

A FRACTAL, according to Franco-Polish mathematician Benoît Mandelbrot, is 'a way of seeing infinity'. Simply put, it is a pattern that appears to self-replicate indefinitely, constantly reproducing an imitation of the previous shape. The term dates back to 1975, when Mandelbrot-to whom it is credited-applied the mathematics of theoretical fractional dimensions to the geometric patterning found in the natural world. Fractals are everywhere, even within the human body: our nervous system, blood vessels and the structure of our brain and lungs are all examples.

The archetypal fractal takes a form that is a blueprint for the smaller elements within it. The trunk and boughs of a tree, for example, echo the forked forms within the tree as the branches split into twigs, which, in turn, throw off shiny new shoots. The flat-planed geometry that we often use to describe forms is inadequate when it comes to conceptualising them: 'Clouds are not spheres, mountains are not cones, coastlines are not circles and bark is not smooth,' Mandelbrot asserted.

Fractals are all around us throughout the year, but, as the cold starts to bite, they become that much more obvious. Acorns in lacy caps litter the ground, pine cones are stuffed in children's pockets and the most flamboyant edible fractal, Romanesco broccoli, is ready to be harvested as autumn arrives. With the first frosts come intricate ice fractals, impossibly delicate and robustly infinite in equal measure.