*The Imitation Game*, a big-budget biopic of British mathematician and computer science pioneer Alan Turing, hits Canadian theatres in December. The film profiles Turing’s work as a top-secret British code breaker during the Second World War, portraying the man who cracked Nazi Germany’s Enigma code, only to be later prosecuted for his homosexuality. While best known for his work in math and computer science, the British scientist also made fundamental contributions to mathematical biology. UBC mathematician Leah Edelstein-Keshet talks about some of Turing’s lesser-known work on pattern formation and cell development.

## What were some of Turing’s most significant contributions to mathematics?

Turing is perhaps best known as one of the pioneers of computer science (before computers even existed) and for forging some of the basis of the theory of computation. One of his fundamental contributions to mathematics was to demonstrate that patterns can form inside systems in which both diffusion and chemical reactions take place. Before his work, it was thought that diffusion would always wipe out any kind of chemical concentration pattern.

## How are Turing’s findings applied today?

Turing Instability, which is the term mathematicians use to describe the tendency to form patterns in reaction-diffusion systems, is now a fundamental hallmark of pattern formation theories. The work provided standard tests that can be applied to ask whether a specific system (with known interactions) could result in interesting spatial patterns.

## How do Turing’s findings apply to animal prints?

Originally, Turing was thinking of chemicals that signal cells, telling them how to differentiate into specialized cell types. So he was thinking of the development of an embryo or parts of the embryo. In the 1980′s, Jim Murray—then an Oxford professor—suggested that Turing patterns can account for the stripes and spots on animals like zebras and leopards. Later research extended that idea to the colourful patterns on fish, the arrangement of branches on plants and the physical manifestations of many other living things. Today we recognize that cell development is much more complex, but in some instances, there are chemical signals that govern cellular development that have some relationship to Turing’s original concepts.