The year of 2021 has seen the great mathematician Alan Turing appear on the Bank of
England’s £50 note. To celebrate this, the School of the Mathematics and Statistics at The
University of Sheffield has created The Turing Pattern Project. The project is a collaborative
nationwide activity for upper Key Stage 2 (KS2) and lower Key Stage 3 (KS3) school students
to learn about Turing and use his mathematical ideas to understand more about patterns in
nature.

We provide options for teaching the project in the classroom or online. Alternatively, the project can be ran entirely by students working from home using our premade videos.

To read more about the project see this TES article, BBC bitesize article or follow us on Twitter!

We provide options for teaching the project in the classroom or online. Alternatively, the project can be ran entirely by students working from home using our premade videos.

To read more about the project see this TES article, BBC bitesize article or follow us on Twitter!

Turing is famously known as a brilliant mathematician, the father of modern computing and
a codebreaker in World War II. However, one aspect of his story is conspicuous in its
absence. Turing used mathematics to formulate a theory of biology which describes many of
the beautiful patterns which we see throughout the natural world. See
a popular science article
for more about these patterns.

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

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

Portrait of Alan Turing

Patterns on animals can be described using mathematics. By zooming in on a picture of an
animal, the colours of the pixels can be represented by numbers. In the picture below, darker
shades of fur are indicated by higher numbers.

Turing imagined that there are two chemicals inside an animals body and that the concentrations of these chemicals can be represented as a grid of numbers. Performing certain calculations on the grid of numbers causes visual patterns to form.

This mathematics can be broken down into an algorithm that uses just adding, subtracting, multiplying and dividing, suitable for KS2 and KS3 level arithmetic.

Turing imagined that there are two chemicals inside an animals body and that the concentrations of these chemicals can be represented as a grid of numbers. Performing certain calculations on the grid of numbers causes visual patterns to form.

This mathematics can be broken down into an algorithm that uses just adding, subtracting, multiplying and dividing, suitable for KS2 and KS3 level arithmetic.

Each school that takes part in the Turing Pattern Project will be given worksheets that correspond to a time in an animal’s life. Students follow Turing's algorithm and send their answers back to us. Those answers will instruct us to reveal the next part of an exciting pattern. The pattern of the giant puffer fish!

The trajectory of schools taking part in the project will be visible on the map further down this page, alongside the evolving pattern. The more schools that take part, the further the pattern evolves.

Our project provides class teachers with resources to follow Turing's story and his mathematical algorithm using a combination of teacher led demonstrations, videos and worksheets.

The trajectory of schools taking part in the project will be visible on the map further down this page, alongside the evolving pattern. The more schools that take part, the further the pattern evolves.

Our project provides class teachers with resources to follow Turing's story and his mathematical algorithm using a combination of teacher led demonstrations, videos and worksheets.

The first lesson introduces patterns in nature and Alan Turing. Students will take part in activities about patterns, colours, scientific vocabulary and the history of Alan Turing.

The second lesson is where the calculations are done to be sent back to us! Students can 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.

Each school is given their own grid of numbers that correspond to a point in time in the
puffer fish’s pattern development. The animation shows the pattern evolving as more
schools take part.

The animation shows the pattern evolving as more schools take part.

The animation shows the pattern evolving as more schools take part.

- To inspire primary school children into STEM subjects using Turing’s mathematics.
- To connect with widening participation schools to breakdown social barriers and enable students to have the very highest educational and career aspirations.

- To give primary school children more confidence in their mathematical ability and show them that mathematics has a wealth of interesting uses and isn’t just about arithmetic.
- To promote and disseminate Turing’s life and work through his theory of pattern formation.

Why can’t a cheetah change its spots?
A question Alan Turing thought about a lot

We looked at the cheetah’s fur,
Until it turned into a pixelated blur,
We looked at the cheetah’s spots,
Until we could barely see any dots

We looked at numbers in animal cells,
To figure out what they could tell,
Fire cells! Water cells!
What a challenge for our brain cells

What do the numbers in animal cells tell us about a cheetah’s skin?
Oh we need help from Alan Turing!
Before we can even begin,
This mathematical thing

We looked at Alan Turing’s Algorithm,
Until we found our mathematical rhythm,
Addition, Subtraction, Multiplication and Division,
How did Alan make such mathematical decisions?

Hip Hip Horray, Hip Hip Horray,
Alan Turing found a way!
Turing’s algorithm must perform,
To see the cheetah’s black spots form

Fire cells, water cells,
The chemicals react,
Releasing mathematical facts,
That turned the cheetah’s spots black

Hip Hip Horray, Hip Hip Horray
Thank you very much Natasha Ellison,
And Sheffield University for sharing the work you’ve done,
We had so much fun,
Each and every one!

By Marta O’ Sullivan, fourth class primary teacher