Today’s post by Haggis the Sheep demonstrates how crochet can help understand some topologically-interesting surfaces, so I felt I should mention a similar piece of fibre art I encountered this weekend. The object on the left is a Lorenz Manifold made out of over 25,000 stitches (plus three wires), and took Bristol mathematician Hinke Osinga 85 hours to assemble. Osinga (along with Bernd Krauskopf) had been experimenting with computer visualisation of the manifold, and developed an algorithm which ‘grew’ the image from a small disc, adding layers with additional or fewer points at each step to specify the local features of the surface. This approach conveniently works just as well for wool as pixels – each row of a crochet pattern differs from the last by increasing or decreasing the number of stitches to alter the shape.
But what does it actually represent? Lorenz was one of the founders of chaos theory, discovering the ‘butterfly effect’, the way in which seemingly small changes to a system such as the weather could escalate into major differences in behaviour. The Lorenz oscillator is a set of rules for evolving the position of a point in 3-dimensional space which exhibits this chaotic nature: starting points generally find their way to the Lorentz attractor, a complex pattern that never repeats itself. However, points on the Lorenz manifold manage to avoid this trap, and instead settle at the origin, the ‘central’ point of space.
Some of Hinke and Krauskopf’s computer visualisations, their crochet of the manifold, and a rendition in steel by Benjamin Storch can be viewed for the rest of the month at The Bristol gallery, which can found down by the harbourside. They’re there as part of one of the Changing Perspectives exhibitions, which also includes work from my department’s invaluable Chrystal Cherniwchan: the photographic project Exploring the Valley, and the Mathematical Ethnographies films. As well as maths, there are exhibits inspired by scientific topics from shifting glaciers to high voltage electricity, so if you’re local, why not take a look in person? If not, well, you can get a taste from the links above, or if you’re feeling brave, grab the instructions to crochet your own Lorenz manifold!