Alan Turing is famed as the mathematician who helped cut short World War Two by two years, with his work cracking Germany's Enigma codeThe Enigma was a type of machine used by the Germans to send secret messages during the war. Turing helped to build a machine called the Bombe to make it quicker to crack a code that the Germans changed every day..

But he made another remarkable, lesser-known contribution to science: a mathematical theory - now proved correct - that explains all of nature's patterns.

In the natural world, some shapes and patterns recur time and time again - from the immense, cosmic spirals of galaxies right down to the circles of dividing cells in an embryoA fertilised egg that is developing into a foetus..

Turing published his paper, "The chemical basis of morphogenesis" in 1952The same year that Turing was convicted of "gross indecency" for homosexual acts. As a punishment, he was chemically castrated and died by suicide two years later. In 2013, he was given a royal pardon.. In it, he theorised that these seemingly random designs are actually controlled by the interaction of two chemicals, which he called "morphogens". Different reactions between these chemicals produce a range of patterns, like spots, stripes and spirals.

Turing even worked out that the patterns produced can be predicted by two mathematical equations.

Today, modern computers can use Turing's equations to make patterns that mimic everything - from human fingerprints to the way that pools of water gather on the shore.

"There's an elegant simplicity and beauty in nature revealed by mathematical patterns and shapes," says physicist Max Tegmark, author of Our Mathematical Universe. The beauty of the natural world, it appears, is ordered by the laws of maths.

For thousands of years, humans have been trying to understand how mathematics shapes the world around us. The golden ratioIf a line is divided into two unequal parts, the larger part will be bigger than the smaller part by a particular proportion, or ratio. If the ratio of the larger part to the smaller part is the same as the ratio of the total line to the larger part, that ratio is then known as 'golden'. The golden ratio is about 1.618 to 1. (first described by the Greek mathematician Euclid, in the 4th century BC) has been regarded by artists throughout history as the perfect, most beautiful proportion.

The ratio is based on the Fibonacci sequence, where each step is equal to the sum of the previous two steps. This exact sequence appears in the flowering of an artichoke and the spirals of seashell. Even the proportions of the human body can be divided into the golden ratio.

We now believe that the ratio was replicated by architects in the design of Egypt's Great Pyramid and the ParthenonAn ancient Greek temple in Athens that was once dedicated to the goddess Athena. It was built around 440 BC. It is regarded as the highest example of ancient Greek architecture. in ancient Greece. By the Renaissance, artists were using it to construct their paintings.

Is beauty really down to maths? Isn't beauty about looking at something and being overwhelmed by an ineffable wonder? It can't be explained by rules or laws. There aren't any right or wrong answers: it's just something that strikes you. Surely, real beauty is the opposite of maths.

But is beauty ever random? Doesn't all art obey rules? The paintings of Jackson PollockModern abstract, American artist (1912-1956), famed for pouring or splashing paint onto canvases to create his art. may look like chaos, but there is order and decades of learning behind them. Why else, for thousands of years, have artists and architects studied the golden ratio if they could just make it up for themselves? Beauty depends on patterns of order beneath the surface.