Friday, February 10, 2006

Small Things

Fractal geometry is a branch of mathematics that deals with finding recurring patterns on large and small scales. Fractals are based on formulae repeated many times to create patterns. One example of a fractal in nature is a mountain. From far away, the mountain has a jagged appearance. Up close, the pieces of the mountain resemble the general rocky appearance — each rock looks like a small mountain — but also have different qualities.

Fractals make incredible designs that yield discoveries with every magnification.

Richard P. Taylor is an associate professor at the University of Oregon. He teaches what is an apparently very popular course called Physics of Light and Color. He also uses fractal geometry to study the work of Jackson Pollack — examining the paint splatters in high magnification — and has questioned the authenticity of some newly discovered Pollack paintings. He located very precise patterns in 14 genuine Pollacks that did not appear in these new works. That doesn’t make them fakes, it just puts a question mark on the table.

This reminded me criminal tremors, which are method of spotting a forged signature by looking for vibrations at the start of a letter caused by a split second of doubt. Patricia Highsmith wrote a book called “The Tremor of Forgery” (the main character of the book also wrote a book by the same title, I think).

This idea is also similar to micro-expressions — small facial ticks we make while lying. This appeared in “Blink” and also in a New York Times Magazine article last week.

Charles and Ray Eames touched on this with “Powers of Ten.” Nature doesn’t provide a steady stream of content. There are always periods of high activity surrounded or followed by periods of high inactivity. All the fractal drawings have large empty middles and intricate borders, and that pattern is always related regardless of the magnification.

This plays out everywhere from city planning, to the construction of atoms, and from outer space to personal workload.

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