Chaos = Order

April 5, 2006

Yuuuppp…. I've known that for years ever since I realized that patterns can be found in seemingly random series of numbers, behaviors, thoughts, decisions…. But today I came across an article in which a group of physicists came to some interesting and amazing conclusions based on some work they were doing on oscillations.

http://news-info.wustl.edu/tips/page/normal/6845.html

While working on their model — a network of interconnected pendulums, or "oscillators" — the researchers noticed that when driven by ordered forces the various pendulums behaved chaotically and swung out of sync like a group of intoxicated synchronized swimmers. This was unexpected — shouldn't synchronized forces yield synchronized pendulums?

But then came the real surprise: When they introduced disorder — forces were applied at random to each oscillator — the system became ordered and synchronized.

Chaos Theory, Catastrophy theory, game theory, and other mathematically applied sociological models (or is that socially applied mathematical models?) are generally "new", mostly theoretical, fields. The conclusions found in the article could affect conclusions and studies being made in everything from neurobiology and neural systems to politics and economics.

Personally, my favorite example of ordered systems through chaos (or maybe perceived chaos, or absurdism) is the fractal art of Jackson Pollock. It's truly inspiring stuff. In Pollock's paintings you can occaisionally see thick round blotches of paint, or sometimes thin fijords (only word that I can think of to describe it). This is a sign of the speed (or rather velocity) of Pollock's brush. The Australian Physicist Richard Taylor, as far as I know, was the first to analyize Pollock's painting mathematically. "[Drip painting] produced trajectories of paint on the canvas that were like a [two-dimensional] map or fingerprint of his [three-dimensional] motions around the canvas."

Taylor and a small team of researchers took pictures of Pollock's work to analyize the trajectories. They concluded that Pollock's paintings reflect fractals – an aesthetic mode typically sanctioned only in the computer realm – because there were several repeating forms within the same object at different scales. They also concluded, through some mathematical models, that Pollock's drip technique was refined over the years and with that refinement his style came closer to larger fractal dimensions. His earlier work has a fractal dimension of about 1.2 whereas his work in the 1950s is closer to a fractal dimension of 2.0 Basically, they became more complex.

http://www.maa.org/mathland/mathtrek_9_20_99.html

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