Last week NOVA aired a three-part series, Hunting the Hidden Dimension, in which yours truly made a brief cameo appearance. I thought the producers did an excellent job exploring the fascinating hidden world of fractal patterns, and PBS has an excellent affiliated Website set up, wherein you can design your very own fractal.
What exactly are fractals? They arise from chaos theory.
To scientists, "chaos" denotes systems that are so sensitive to initial
conditions that their output appears random, obscuring their underlying
internal rules of order: the stock market, rioting crowds, brain waves
during an epilectic seizure, or the weather. In a chaotic system, tiny
effects are amplified through repetition until the system goes critical.
The mathematical offspring of chaos theory is fractal geometry. Fractals may appear haphazard at first glance, yet each one is composed of a single geometric pattern repeated thousands of times at different magnifications, like Russian dolls nested within one another. A fractal pattern is what is left behind by chaotic activity. If a hurricane is a chaotic system, then the wreckage strewn in its path is its fractal pattern.
Some fractal patterns exist only in mathematical theory, but others provide useful models for the irregular yet patterned shapes found in nature – the branchings of rivers and trees, for instance. Mathematicians tend to rank fractal dimensions on a series of scales between 0 and 3. One-dimensional fractals (such as a segmented line) typically rank between 0.1 and 0.9; two-dimensional fractals (such as a shadow cast by a cloud) between 1.1 and 1.9; and three-dimensional fractals (such as a mountain) between 2.1 and 2.9. Most natural objects, when analyzed in two dimensions, rank between 1.2 and 1.6.
There is even a chance that all the matter in our universe is arranged in a fractal pattern, at least according to a study released last year by Italian physicists. Here's what New Scientist had to say about the work:
"Nearly all physicists agree that on relatively small scales the distribution is fractal-like: hundreds of billions of stars group together to form galaxies, galaxies clump together to form clusters, and clusters amass into superclusters. The point of contention, however, is what happens at even larger scales. According to most physicists, this Russian doll-style clustering comes to an end and the universe, on large scales, becomes homogenous."
Francesco Sylas Labini and Luciano Pietronero beg to differ. Their analysis of data from the Sloan Digital Sky Survey shows that instead of the fractal pattern smoothing out at scales of over 200 million light years, if the distribution does smooth out -- and they maintain this is still an "if" -- it would have to be at scales larger than 300 million light years across.
I expect they'll be debating this for years to come. The point is, fractals are cool, so check out Hunting the Hidden Dimension this weekend if you're looking to chill, and learn more about these amazing patterns.
Image: The most famous fractal, the Mandelbrot Set.
Tags:
comments ( )