March 2009

It is not often that a serious mathematics journal contains a crochet pattern, Dr Osinga and Prof Krauskopf have provided the pattern in the journal Mathematical Intelligencer. (link to the pdf document of the paper and the pattern is here.) They are challenging anyone to make their own crochet chaos model (theres a bottle of champers in it for you). info frombbc news

Extract from the paper:

The Lorenz attractor is the best known image of a chaotic or strange attractor. We are concerned here with its close cousin, the two-dimensional stable manifold of the origin of the Lorenz system, which we call the Lorenz manifold for short. This surface organizes the dynamics in the three-dimensional phase space of the Lorenz system. … We have been working for quite a while on the development of algorithms to compute global manifolds in vector fields and have computed the Lorenz manifold up to considerable size. Its geometry is very intriguing and we explored different ways of visualizing it on the computer. However, a real model of this surface was still lacking. … We start from a small disc in the stable eigenspace of the origin and add at each step a band of a fixed width. In other words, at any time of the calculation the computed part of the Lorenz manifold is a topological disc whose outer rim is (approximately) a level set of the geodesic distance from the origin. What we realized then and there is that the mesh generated by our algorithm can directly be interpreted as chrochet instructions!

About the authors:
Hinke Osinga learnt crocheting, and other handcraft techniques, from her mother around the age of seven. A bit later she got a Ph.D. in Mathematics … The Lorenz manifold is her first project that combines handcraft with mathematics. Bernd Krauskopf works in the general area of dynamical systems theory, the basic idea of how to grow a global manifold emerged over a bagel with Hinke at a bagel store on Nicolette Mall.

This is not the only combination of craft and maths out there. In 1997 Cornell University mathematician Daina Taimina finally worked out how to make a physical model of hyperbolic space that allows us to feel the tactile properties of this unique geometry. The method she used was crochet. Read more about why crochet works so well here, gallery of the various models here, interview with Daina Taimina here.

resources:
interweave
new york times
bbc news
chaotic crochet at plus maths
university of bristol
crochet fantasy
instructions on crocheting the hyperbolic plane
mathematical knitting

{ 1 comment }