The Powerful Equations That Explain the Patterns We See in Nature

Where do a zebra's stripes, a leopard's spots and our fingers come from? The key was found years ago by the man who cracked the Enigma code.

In 1952 a mathematician published a set of equations that tried to explain the patterns we see in nature, from the dappled stripes adorning the back of a zebra to the whorled leaves on a plant stem, or even the complex tucking and folding that turns a ball of cells into an organism. His name was Alan Turing.

More famous for cracking the wartime Enigma code and his contributions to mathematics, computer science and artificial intelligence, it may come as a surprise that Turing harboured such an interest. In fact, it was an extension of his fascination with the workings of the mind and the underlying nature of life.

The secret glory of Turing's wartime success had faded by the 1950s, and he was holed up in the grimly industrial confines of the University of Manchester. In theory he was there to develop programs for one of the world's first electronic computers a motley collection of valves, wires and tubes but he found himself increasingly side-lined by greasy-fingered engineers who were more focused on nuts and bolts than numbers. This disconnection was probably intentional on Turing's part, rather than deliberate exclusion on theirs, as his attention was drifting away from computing towards bigger questions about life.

It was a good time to be excited about biology. Researchers around the world were busy getting to grips with the nature of genes, and James Watson and Francis Crick would soon reveal the structure of DNA in 1953. There was also a growing interest in cybernetics the idea of living beings as biological computers that could be deconstructed, hacked and rebuilt. Turing was quickly adopted into a gang of pioneering scientists and mathematicians known as the Ratio Club, where his ideas about artificial intelligence and machine learning were welcomed and encouraged.

Against this backdrop Turing took up a subject that had fascinated him since before the war. Embryology the science of building a baby from a single fertilised egg cell had been a hot topic in the early part of the 20th century, but progress sputtered to a halt as scientists realised they lacked the technical tools and scientific framework to figure it out. Perhaps, some thinkers concluded, the inner workings of life were fundamentally unknowable.

Turing viewed this as a cop-out. If a computer could be programmed to calculate, then a biological organism must also have some kind of underlying logic too.

He set to work collecting flowers in the Cheshire countryside, scrutinising the patterns in nature. Then came the equations complex, unruly beasts that couldn't be solved by human hands and brains. Luckily the very latest computer, a Ferranti Mark I, had just arrived in Manchester, and Turing soon put it to work crunching the numbers. Gradually, his "mathematical theory of embryology", as he referred to it, began to take shape.

Like all the best scientific ideas, Turing's theory was elegant and simple: any repeating natural pattern could be created by the interaction of two things molecules, cells, whatever with particular characteristics. Through a mathematical principle he called 'reactiondiffusion', these two components would spontaneously self-organise into spots, stripes, rings, swirls or dappled blobs.

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The Powerful Equations That Explain the Patterns We See in Nature