the Lorenz manifold sits between the wings and represents the collection of paths by which the leaf collides with the obstacle.

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Modeling Multiple Dimensions: The Lorenz Manifold

 

http://blog.thinkwell.com/2011/07/the-lorenz-manifold.html

By Lauren on July 6, 2011 11:00 AM | No TrackBacks

When you think of non-linear mathematics, your mind may not jump immediately to crocheting, but Thinkwell's summer intern Gregory Becker found a really cool way to combine the two. For his high-school senior thesis, he crocheted a Lorenz manifold. What exactly is a Lorenz manifold? I'll let him explain in his own words:

"The Lorenz system is a chaotic system of dimension 2.06 (+ or - 0.01, empirically discovered). The most famous image of the Lorenz system is the Lorenz attractor. You can picture the two 'wings' of the Lorenz attractor as the collection of possible paths that a leaf floating downstream could take around an obstacle.

The less famous image of the system is the Lorenz manifold. Impossible to represent accurately in a stable two-dimensional medium, the Lorenz manifold sits between the wings and represents the collection of paths by which the leaf collides with the obstacle.

Because of the challenge in representing the Lorenz manifold, a small niche of the mathematical community has taken to crocheting it. Crocheting works well for representing the manifold for two reasons: It can warp, and it can represent a lattice."
 

Here's a close-up of Gregory's Lorenz manifold, which has 25,511 stitches (!) and took just over 150 hours (!!) to crochet and mount.


Gregory is interning at Thinkwell as an advanced mathematics adviser for our Trigonometry and Calculus titles. He graduated from the Austin Waldorf School and will be attending Williams College in the fall as a mathematics major. We can't wait to see what his senior thesis at Williams will look like!