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Mathematician turns chaos into crochet

Lorenz manifold

This crocheted representation of a mathematical equation may one day allow researchers to make better weather predictions (Image: University of Bristol)

Crochet is helping researchers to better understand mathematical equations designed to make sense of chaotic weather patterns.

Dr Hinke Osinga, a mathematician from the University of Bristol, will discuss her work at the Australian and New Zealand Industrial and Applied Mathematics meeting in Fremantle this week.

Osinga is working on the Lorenz equations, which are used to model the difficult-to-predict system we know as the weather.

In these equations, small changes in initial conditions have a big effect on the long-term behaviour of the system.

This is the maths behind the idea that a butterfly flapping its wings in one part of the world affects the weather in another.

What makes weather prediction difficult is being precise enough when defining these initial conditions.

Osinga and colleague Professor Bernd Krauskopf have been working on visualising the Lorenz equations, which is how Osinga ended up with a crochet model.

Part of modelling the weather is predicting how air particles behave. And the researchers liken air particles in turbulent weather to leaves dropped upstream of a rock in a turbulent river.

It's difficult to predict where the leaves will flow in relation to the rock, says Osinga.

The Lorenz equations simplify such a system to predict the path of these leaves.

But the equations are limited because they are dynamic. You have to wait and see what happens over time to see what path the leaves take, says Osinga.

She and Krauskopf decided to try and get a static picture of what happens in such a system.

They took a particular set of solutions to the equations that modelled, in the river analogy, the 'middle path' in which leaves head straight for the rock and stick to it.

They modelled this on a computer and found it gave a unique complex curved shape, they called the 'Lorenz manifold', that centred on one point.

"On the top part, the geometry is incredibly complex where you have a helical rotation going up and you have a spiralling rotation going in one of the opposite directions," Osinga says.

While staring at the Lorenz manifold on computer, Osinga had a brainwave.

"I realised the way that we computed the surface naturally translated into crochet instructions," she says.

"When I saw that, I just had to try. It was too good for words really that you could actually make one."

Osinga, the daughter of a handicrafts teacher, spent 85 hours crocheting a 3D model that she says really put things in perspective.

For a start, she says the model gave her an idea of the size of chaotic systems in real life.

And reducing a system of chaotic behaviour into a unique shape also gave Osinga a better understanding of the Lorenz equations themselves.

"Here we have an instant image and it tells us quite a lot," she says.

She says the crocheted 3D model could tells us what kind of weather patterns the Lorenz equations are best at predicting.

Apart from that, though, the crocheted Lorenz manifold is a fascinating thing in itself, says Osinga.

"It has absolute artistic value. I get lots of comments from artists who've found out about this that are totally smitten by the shape," she says.
