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Strange Attractors

Taking the V-day bait, let's ask, "How are geeks spending their supposedly solitary Valentine's Days?" If they are into all that sweet mathematical physics action, they may be envisioning attractors. Like a mathematical pin-up, just seeing a snapshot of the fractal spirals of a strange attractor can keep a physicist up late at night.

strange_attractors_two.jpg

There are two types of patterns inherent to the strange attractor. The first is what is called fractal. When you zoom in on a fractal, it has smaller and smaller patterns that look just like the larger pattern. As far in as you go, a fractal never looks like a smooth line, but always like a pattern of shapes that are the same as the big shape.

mandelbrot.jpg
Mandelbrot fractal. Each circle branching off to the left is a complete recreation of the larger one to its right

Spirals require somewhat less description: they are simply patterns that start from some point and circle around that point, constantly moving further away.

Where are these strange patterns found to exist? The answer is, literally, everywhere. You just have to look through some strange glasses; these patterns occur when you look at the world from a different perspective.

When you walk your dog, you worry about where the dog is in terms of "how far in front of me, how far to the left and right, and how high off the ground." ("And is there a car at that spot?") These patterns occur when you look at something like how fast the dog is walking compared to how far it is away from you.

What do they actually mean? To the mathematically minded, strange attractors are "a type of pattern in the geometry of manifolds in the phase space of chaotic dynamical systems."

For the rest of us, a fractal pattern arises from situations that are chaotic. Chaos, to a physicist, is when models of reality are forced to be unable to accurately predict what happens. This happens because the outcome of an experiment is wildly different based on minuscule changes in the conditions that cannot be seen.

This is known popularly as the "butterfly effect," the idea that the flapping of a butterfly's wings on one side of the earth may noticeably effect the wind patterns on the other side. Another example might be the behavior of the stock market. The buying or selling of one share at one moment can trigger completely unpredictable swings, booms and crashes that do not happen if the trade is made a second later. Two plumes of smoke never form anything close to an identical pattern regardless of how similar the stuff burning is.


Tom Hartsfield
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