The worlds of maths and art rarely collide, but when they do, the results can be intriguing. The artist and printmaker Gemma Anderson has recently begun one such collaboration with mathematicians at London’s Imperial College who are working on a ‘periodic table of shapes’.
Gemma Anderson’s model of a rhombic dodecahedron
Just as with the famous periodic table in chemistry, the mathematicians are searching for the building blocks, or ‘elements’, of the shape world. These are shapes that cannot be divided any further, named ‘Fano varieties’ after the Italian mathematician Gino Fano. They’re the prime numbers of geometry – the purest of shapes.
As well as the standard three-dimensional forms, the researchers are looking for shapes in four and five dimensions – shapes which can only be represented by algebraic equations. There are estimated to be around 500 million four-dimensional shapes, made from thousands of different building blocks!
And although this research may sound very abstract, the Fano shapes have potential applications in a wide range of areas. Tom Coates, one of the mathematicians working on the project, gives a couple examples:
“If you are working in robotics, you might need to work out the equation for a five-dimensional shape in order to figure out how to instruct a robot to look at an object and then move its arm to pick that object up,” says Coates, speaking to Cosmos magazine.
“If you are a physicist, you might need to analyse the shapes of hidden dimensions in the Universe in order to understand how subatomic particles work. We think that the work we’re doing in our new project will ultimately help our colleagues in many different branches of science.”
A cube model by Gemma Anderson
Gemma Anderson, a London-based artist who graduated from the Royal College of Art in 2007, is also part of the Fano team. Gemma’s artwork has a very distinctive style – her beautifully intricate drawings are etched directly onto copper, an uncommon technique, and then painted with Japanese inks. Here are a couple of her previous artworks:
Malachite (left) and Ezo Owl (right) by Gemma Anderson
Gemma has now begun to make etchings and models inspired by some of the weird and wonderful Fano shapes. My interest piqued, I got in touch with Gemma to ask her a few questions.
Gemma, how did your collaboration with the Fano team come about?
I was in Imperial College last March for a meeting with someone in Material Sciences and, while I was waiting, I started reading the Imperial College newsletter. One of the articles was titled ‘Periodic Table of Shapes’ with an image of a Fano (now one of my favourites), and I was struck by both the image and the description. As an artist, I was very excited by the Fano form – I hadn’t seen anything like it before and I wanted to know more about the research. I emailed Dr Tom Coates the same day, we met the following week (by then I had drawn many of the Fanos I found on the team’s blog) and the rest is history!
Gemma Anderson’s 3-D sliceform model
What artwork are you working on for the project?
Since the initial meeting and drawings, we have been developing a few different strands of work based on the Fano varieties. One is drawings and etchings, working with Fanos and their related symmetry groups. We have also been developing a method (and a computer program!) to make some Fano varieties into 3-D models. There are lots of details in each area and it is all still work in progress – we’re developing new ways of imagining the Fanos all the time.
Some of Gemma’s work in progress
Intricate shapes often feature in your etchings – is geometry something you’re interested in?
Yes, I am very interested in geometry, and love drawing geometric forms. I am especially interested in where geometry occurs in natural forms, so crystallography and mathematical biology are subjects I work with.
Your previous work focuses on organic subjects – people, plants, animals, and landscapes. Is this project a departure for you in that it deals with more rigid, static objects?
I see this work as an interesting departure, but more and more it is linking to my previous work and current interests in my PhD research. The Fanos are very interesting to work with as in lots of ways they are quite alien, but when compared to things like radiolarians, they suddenly feel more earthly. I don’t see the Fanos as rigid or static and I suppose part of the aim of this collaboration is to move them away from those associations.
Gemma’s copper etchings of some of the shapes
Do you have any plans to exhibit this work?
Yes, we are thinking of a few places as we would like to site the work within the science context and also the contemporary art world. So we’re applying to the Royal Society Summer Exhibition and planning on exhibiting at Imperial College, as well as including the works in a solo show I will have next year at a gallery in London.
See more of Gemma’s work here and keep up-to-date with Imperial College’s Fano research team on their blog.
There are just so many ways to learn math! Appreciate the post.