The Turing Pattern Project

The Turing Pattern Project has launched! Register here to take part

The year of 2021 will see the great mathematician Alan Turing appear on the Bank of England’s £50 note. To celebrate this, the Turing Pattern Project provides a collaborative nationwide activity for primary schools to learn about Turing and use his mathematical ideas to understand more about patterns in nature.

Watch our launch video here

Turing is famously known as being the father of modern computing and decoding messages that helped Britain win the war. However, one aspect of his story is conspicuous in its absence. Alan Turing used mathematics to formulate a theory of biology which describes many of the beautiful patterns which we see throughout the natural world. See here for a popular science article about these patterns.

Below I show a particular example, the pigment pattern seen on the fur of a cheetah. Using Turing’s theory we can build mathematical equations to describe the chemicals residing inside a cheetah, that define that colour of fur, as the cheetah it develops in the womb!

How can primary school children calculate these seemingly complicated patterns? Some equations are too difficult to solve by hand and instead we can approximate them using a computer. For the cheetah, the computer describes the equations as a grid of numbers and algorithmically creates a different grid for each minute (each frame in the video) of a cheetahs life. Each school will be given a grid that corresponds to a time in an animal’s life. The school will then perform calculations on the grid and subsequently pass it on to the next school to perform the next set of calculations, eventually producing the pattern.

A video showing the output of the mathematics used to describe the developing pattern of a cheetah. The first frame shows a random pattern where each part of square is allocated with a random number representing the amount of dark chemical. Calculations are performed algorithmically between frames and the pattern begins to emerge.
An example of how students will follow an algorithm

The algorithms used to create the patterns require undergraduate level mathematical training and I have adapted them to become calculations suitable for primary school children of mixed attainment levels. The calculations involve adding, subtracting and multiplying small whole numbers and they have been tested with year 5 classes.

The project will use Turing’s ideas to show primary school students that mathematics can be used to understand the world. Turing’s description of patterns in nature is such a visually striking subject that engages children’s mathematical drive and desire for science.

A hypothetical example of the schools taking part in the project.

Two 50 minute lessons are currently reiteratively and carefully developed to be suitable to be taught by ordinary class teachers. Lessons are currently being trialled with increasing success. The first lesson introduces patterns in nature and Alan Turing. Children will take part in activities about patterns, colours, scientific vocabulary and the history of Alan Turing. The second lesson is where the mathematical calculations occur; after some careful examples from the teacher the students will work together in small groups to determine the answers to the problems which will lead to their contribution to the pattern. In addition to these teacher led lessons, videos to accompany a home learning version of the project will be available.

After the launch of the project, class teachers or parents will be able to create a log in to a website, download resources and input the answers to their calculations online. Each school will have a different point in time and will calculate the pattern at that point. As more schools take part and more calculations are input the end pattern will start to emerge.


This project is a collaborative endeavour from the School of Mathematics and Statistics at the University of Sheffield and is supported by the Bank of England. The team consists of the following people.

Natasha Ellison is a final year PhD student working on the mathematical modelling of ecological processes, such as the interactions between animals and plants. Natasha is a trained secondary school maths teacher and devotes a lot of time to engaging the public and schools with using mathematics to understand nature.

Dr Fionntan Roukema brings an unparalleled and infectious enthusiasm for learning to the project and has fantastic connections with the primary school network in Sheffield. Fionntan dedicates a lot of his time visiting primary schools and enthusing the students to engage and be excited. about learning mathematics.

Aidan Hughes is currently enrolled in a General Engineering Masters course specialising in Mechanical Engineering at the University of Sheffield. He has over 5 years of experience working in software development and 3 years experience as a full-stack web developer. He has helped develop websites in collaboration with Plus Group, University of Sheffield and Bank of England. Aidan is currently undertaking his final year project where he is developing a mechanical exoskeleton controlled by the brain for the purpose of post-stroke rehabilitation

Dr Alex Fletcher in an expert in using mathematical modelling, including the equations used by Alan Turing, to understand biological processes. Alex uses mathematics to understand more about embryogenesis, tissue renewal and wound healing with an aim to impact on tissue engineering and cancer treatment strategies.

Project updates

October 2019 – The project has been trialled by the wonderful year 5 children at Springfield School and the fantastic year 5 and 6 classes at Meersbrook School in Sheffield. We’ve had great feedback from both staff and students.

March 2020 – The project is ready to be teacher led by two more schools in Sheffield, however we are postponing our trials until October due to Covid 19.

April 2020 – The project will be available for both home learning and schools to accommodate safe education throughout the Covid 19 pandemic.

July 2020 – Exciting news, the main website begins! Sheffield own engineering student Aidan Hughes joins the team to apply his excellent talents to building our website.

October 2020 – I’m starting work on the project full time now. I’m working on creating the lesson resources and they will be trialled in schools throughout November and December 2020. Thanks to all the fantastic teachers who are offering their help with this!

October 2020 – Follow us on twitter from today! @TuringPrimary

March 2021 – The Turing Pattern Project has launched. Register on our website, watch our launch video or read these articles (Yorkshire Post, BBC Bitesize, TES)

Get in touch

Are you a primary school teacher or parent and interested in being involved? Register on our website or if you have further questions, send me an email on