Researcher studies shark patterns in Maldives for documentary celebrating Alan Turing’s legacy

A researcher at the University of Sheffield helps explain the mathematics behind patterns found in nature in a new documentary.

Kriss Ceuca and Natasha Ellison
Filmmaker Kriss Ceuca and University of Sheffield PhD student Natasha Ellison with a statue of Alan Turing.

Natasha Ellison came up with the concept for A Natural Code, which is based on an area of mathematics first explored by Natasha’s scientific hero, Alan Turing.

The project was brought to life by filmmaker and professional diver Kriss Ceuca, while Natasha played a key role in its production as scientific consultant and narrator.

Although best known as a Second World War codebreaker and pioneering computer scientist, Turing was also a foundational figure in Natasha’s field, mathematical biology.

Natasha, who is in the final year of her PhD in the School of Mathematics and Statistics, said: "Turing thought very deeply about the relationship between mathematics and nature. In his final paper, he proposed the idea that two chemicals within an embryo might react with each other in a way that produces patterns. He used mathematics to show how these chemicals behave and form familiar visual patterns.

"Since then, scientists have developed his idea to explain the formation of many parts of nature from a zebra’s stripes to the way our fingers grow. More recently, studies at an embryonic level have allowed scientists to find two chemicals driving the patterns, giving strong evidence towards his theory."

Natasha's research aims to use mathematics to understand movement patterns of animal’s and Alan Turing’s work has a huge influence.

A Natural Code takes the viewer from the equations first developed by Turing to the Maldives, where Natasha and Kriss saw how conservationists are using an animal’s pigment patterns to protect an endangered species.

They searched the reefs for whale sharks with researchers from the Maldives Whale Shark Research Programme, who are using software to create a digital record of each whale shark’s pattern – similar to a human fingerprint database. They can then use a mathematical algorithm to scan photos and footage of any whale sharks via their app, and identify the individual shark, its location and its migration pattern.

Natasha said: "Whale sharks are so elusive, we have no estimate for their population and nobody has studied how their patterns from an embryo, though we can create their beautiful patterns using the mathematics in Turing’s theory. The researchers in the Maldives were very excited to hear about Turing’s theory of how the sharks may obtain these patterns."As well as Natasha, A Natural Code features on-screen contributions from Dr Philip Ball, author of 'Patterns in Nature: Why the Natural World Looks the Way It Does', and Professor Philip Maini, head of the University of Oxford’s Centre for Mathematical Biology.

Natasha met Kriss at a screening of To Find A Harpy, a documentary by University of Sheffield graduate Daniel O'Neill in which Natasha travels to Guyana in search of a rare harpy eagle.

Natasha said: "Kriss really wanted to create a wildlife film with a true scientific element and when we met she instantly loved the idea of communicating Turing’s theory. Kriss is an excellent diver so we decided to make the film a combination of Turing’s theory and understanding the use of whale shark’s patterns in conservation. Swimming together with the whale sharks and taking part in the data collection first hand was very special."

Kriss produced A Natural Code as part of the same MA Wildlife Filmmaking course that Daniel completed at the University of the West of England in Bristol. His film has since won a number of awards in competitions stretching from Italy to California.

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