If you're an artist with an interest in mathematical ideas and patterns then here's a competition for you. The Anomalous mathematical patterns sci-art competition invites you to submit your art works on a mathematical theme (see below for more) to win a prize of up to £750.
The competition is held in connection to the Stochastic systems for anomalous diffusion research programme (SSD) that is currently taking place at the Isaac Newton Institute for Mathematical Sciences in Cambridge.
The goals of the contest are to:
- showcase the interplay of mathematics (in particular of probability theory) and art in the modern world;
- explore the different ways in which artists and mathematicians approach mathematical concepts;
- find ways to communicate research in mathematics to as wide an audience as possible;
- inspire new generations towards mathematical education and training;
- potentially spark collaborations among and between mathematicians and artists.
What to enter
There are three competition categories:
- Photograph, painting, film, print, animation;
- Textile, sculpture or other medium (such as 3D printing, laser cutting, CNC routing);
- AI and computer-generated art, which maybe also contains digitally or otherwise enhanced or altered photos.
Closing date is March 31, 2025. See the competition website for details on how to enter.
The prizes
There'll be a £750 award for the best entry in each category. Runners up will receive £300 and there will be one £150 honourable mention award in each category. A public vote on the contest website will select from all submissions an additional £750 award for the People' Choice Prize artwork. Finally, there will be a £500 Programme Participants' Choice Award, voted by the participants at the Stochastic systems for anomalous diffusion (SSD) research programme from a choice of all the 30 finalists.
The inspiration
Underlying the SSD research programme is the phenomenon of diffusion: the fact that particles moving at random under the influence of thermal energy spread themselves around. You can witness diffusion everytime you make a cup of tea. It's this process that wafts tea particles towards your nose and allows the tea to spread around the water. Diffusion underlies a huge number of processes — from food digestion to generating the patterns in animal coats.
The first to make progress in understanding diffusion was the mathematician Joseph Fourier in the early nineteenth century, when he became interested in the way heat propagates in solid bodies. If you heat up one end of a metal rod, what will the temperature be at any point along the rod at some time in the future?
Maths in a Minute: Diffusion — Fourier realised that a relatively simple equation describes the way temperature changes at a given point on the rod at any instant of time. See this brief article to discover the equation.
The maths describing diffusion is extremely useful, not only to model what's going on in physical and chemical systems, but also in biology, for example to understand the motion of microbes, and in ecology, for example to understand the foraging and migration behaviour of animals.
Anomalous diffusion does what it says on the tin: it describes processes whose behaviour deviates fundamentally from what you would expect from ordinary diffusion. Anomalous diffusion can occur, for example, when the past of the system influences its future (eg roaming animals might not want to retrace their steps) or when physical barriers stop ordinary diffusion from happening.
The Stochastic systems for anomalous diffusion research programme brings together experts from different areas to join forces in understanding and developing the maths needed to describe anomalous diffusion. The following mathematical ideas and concepts are central to the programme and might help to inspire your artwork.
Turing patterns
The idea of diffusion inspired the mathematician Alan Turing, also known as a WWII code breaker, to come up with a mathematical model that can explain how patterns form in the skins and coats of animals. It involves two chemical substances that diffuse through the skin of an animal embryo and interact.
How the leopard got its spots — Such a reaction-diffusion system can give rise to amazing patterns. It can also explain why there are animals with spots on their bodies and stripes on their tail, but not the other way around. Find out more in this article.
Randomness
Processes that exhibit diffusion, or anomalous diffusion, involve motion that is random (eg tea particles moving through water) or at least appear to be random. Nature provides many other examples of randomness — the way leaves scattered by the wind on the ground, the path of a dog sniffing out its local park, or the outline of a cloud.
Pure randomness in art — Randomness has also been used to interesting effects in art. Read this article, written by master of randomness David Spiegelhalter, for some examples.
Fractal expressionism — You might also be interested in this article about the seemingly random patterns created by Jackson Pollock in his famous drip paintings
In maths random motion can be modelled by random walks.
Maths in a Minute: Random walks — Random walks are extremely useful for understanding real-life processes, but are also fun to think about, and they can create some interesting visual patterns. Read this brief introduction to find out more.
To know how it works, see how it moves — Living things don't usually move completely randomly, but random walks are still useful in understanding their behaviour — from migrating whales to foraging lions. Find out more in this article.
Another concept that's extremely useful when it comes to systems made up of many components is that of random networks.
Maths in a Minute: Random networks — A random network is made up of nodes connected by links which are randomly chosen. See this brief article to find out more and create some beautiful random networks using our interactivity.
Probability theory
Randomness is intimately connected to chance (at least on the face of it, there are some serious philosophical debates about whether it really is). In maths, chance is quantified by probabilities.
Maths in a Minute: The axioms of probability theory — Calculating with probabilities is commonplace in maths and many areas of sciences, but to do this right we need some rules. Find out more in this short article.
Maths in a Minute: Probability distributions — When a process has lots of possible outcomes that occur by chance, then the probability distribution tells you which probability each outcome has of occurring. Find out more in this short introduction and learn about some common probability distributions too.
Struggling with chance — Finally, it's worth noting that, despite the ubiquity of probability theory in maths and science, chance is still a slippery concept. What exactly does it mean to say an event has a probability x of occurring? Find out more in this article.
Systems of many, many components
Many of the system we observe in nature consist of lots of interacting components. Think of the molecules sloshing around and colliding in your cup of tea, or people in a large crowd. One way of simulating such systems mathematically is provided by agent based models, in which the motion and interactions of components are dictated by clearly defined mathematical rules.
The dynamics of crowds — Find out in this article how agent based models can help simulate the behaviour of crowds of people and flocks of birds, and what the simulations can tell us.
When it comes to molecular systems though, the number of particles involved is usually too large — keeping track of individual particles is simply impossible.
Maths in a minute: Statistical mechanics — In this case, it makes more sense to only look at the average statistical behaviour of individual components. Statistical mechanics does just that. For example, it explains temperature of a cup of tea in terms of the average kinetic energy of all the particles within it, providing a beautiful bridge between the microscopic and the macroscopic. Find out more in this short introduction.
If your cup of tea is really hot, then you'll become a witness to a common, but nevertheless amazing, phenomenon of nature: some of the liquid inside the cup will spontaneously change its nature and turn into steam. If you put the tea in the freezer, it'll eventually turn into ice, which has completely different properties again.
Maths in a minute: Phase transitions — Such dramatic changes in the nature of a material are known as phase transitions and can be explained in terms of the behaviour of its microscopic constituents. Find out more in this brief article.
Finally we'd like to draw your attention to one of the most amazing set of equations in mathematics. If you treat a fluid as a macroscopic entity, rather than a system of gazillions of particles, then its behaviour is described by the Navier-Stokes equations.
Maths in a minute: The Navier-Stokes equations — These equations are extremely useful, but also extremely difficult to solve. In fact, nobody knows if a general solution even exists. This is intimately linked to the complexity of one of the most striking, beautiful, dramatic, and even dangerous phenomena in nature: turbulence.
Whatever you decide to create, whether it's inspired directly by nature, the beautiful mathematics that describes nature, or both, be sure to submit your entry. The world, and mathematics, are your oyster!
This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.
The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.
