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Above: Mandelbrot Set by Nick Mee
Left: Satellite photograph of south-west Ireland. NM23-762-192 Bantry Bay, Macgillicuddy’s Reeks, Ireland Winter/Spring 1997

The study of surfaces that enclose a particular volume of space by an anomalously large surface area has become very fashionable among mathematicians and computer-graphics aficionados. Such surfaces are examples of what the French-American mathematician Benoit Mandelbrot has called 'fractals'. Fractals can be constructed by copying a basic design over and over again on a larger or smaller scale. We see that Nature uses fractals everywhere: in the branching of trees, the shaping of leaves, flowers, and vegetables. Take a look at the head of a cauliflower, or broccoli, and you can see how the same branching pattern is repeated over and over again on different scales. Another reason for the ubiquity of fractal designs in Nature is that they offer a general recipe for escaping the strait-jacket on design that is imposed by the simple relation between volume and surface area that we find in regular objects, like a perfect sphere, where volume is proportional to the two-thirds power of the surface area. By allowing the surface of a ball to become intricately crenellated, its exposed surface can be greatly increased over that needed to enclose the same volume by a smooth ball. Examples of fractal surface enlargement abound. Our lungs display a branching fractal network of tubes that maximize the absorption of oxygen through their surfaces.  When we step out of the shower, we dry ourselves with a towel that has a complicated knotted surface. This increases the area of towel that makes contact with your body, and so increase the uptake of moisture by the towel.

Wherever there is a need to expose as large an exposed surface as possible, but there is a restriction on the total volume of material available, or a penalty to be incurred by increasing weight, then fractals seem to be selected by the evolutionary process. Fractal structures are also good at damping dozen vibrations. For example, if one were to make a drum with a fractal-shaped edge, then a beat of this drum would be quickly dulled. Fractal shapes may therefore be extremely robust in situations, like those of trees in the wind, panting lungs, or pounding hearts, where it is necessary to withstand a large amount of vibration.

The more we scrutinise the structure of Nature, the more fractals we find. Indeed, their ubiquity in the natural world of which we are a part may be one reason why we find them so comfortingly attractive. They are a form of computer art that has captured one of Nature's essential programs -- self-similar reproduction of the same pattern with different sizes -- for building living things.   

Text from ‘The Artful Universe’ by John Barrow