The first real workshop of last year was a material technology workshop. Our group (Julian Jones, Shipra Narang, and me (we did have another member, but he was never there so I’ll just pretend it was just the 3 of us) work with Yusuke Obuchi (with whom we’ve been working since).

His brief was pretty confusing at first. He talked about finding a material system that works in an “iterative” way and formed “attractors,” giving us the even more obscure example of the Lorenz Attractor. Now if you can figure what that means from the start, then you should be here and I should be getting you coffee.

We had no idea, so some Googling and Wikipedia searches later we were still confused, but at least had something to start with. Here’s what we found:

*Iteration* means repeating a process over and over. Countless examples of iteration can be found in the real-world:

- To walk, you simply iterate the process of taking a step.
- To eat french fries, you iterate the process of putting a fry in your mouth.
- To pump up a flat bicycle tire, you iterate the process of pushing the pump down and up.

http://library.thinkquest.org/2647/chaos/concepts.htm

** attractor** An attractor of a map is a set of points which “attracts” orbits, from some set of initial points of nonzero probability of being selected

http://www.cecm.sfu.ca/organics/papers/corless/confrac/html/node20.html

An **attractor** is a set to which a dynamical system evolves after a long enough time. That is, points that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure known as a *strange attractor.* Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.

A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor. The trajectory may be periodic or chaotic or of any other type.

http://en.wikipedia.org/wiki/Strange_attractor#Strange_attractor

Lorenz’s Attractor:

Got all that. Good. So what would you do?