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From surface scum to fractal swirls.

Flecks of soapy scum floating on the surface of water draining out of a bathtub sometimes gather into intricate patterns. The geometry of the resulting patterns provides a snapshot of currents within the draining water. These convoluted flows cause local upwelling in some locations and downwelling --where floating particles tend to collect - in others.

Two physicists have now applied this phenomenon to demonstrate a direct link between the complicated motion of a fluid and the resulting fractal pattern displayed by an aggregate of floating particles. Fractals are complex shapes that look roughly the same whether greatly magnified or viewed from a distance.

Researchers have noted fractal patterns in the shapes of clouds, the branching of blood vessels, the jaggedness of coastlines, and the roughness of fractured rocks. But there has been no obvious connection between such patterns and the physical processes responsible for creating them.

"[Our] research may be a first step on the road to understanding why fractals exist in nature,' says John C. Sommerer of the Johns Hopkins University Applied Physics Laboratory in Laurel, Md. Sommerer and Edward Ott of the University of Maryland in College Park report their findings in the Jan. 15 SCIENCE.

The researchers' apparatus - their scum machine - consists of a cylindrical tub sitting inside a larger, taller cylindrical tub. Both are filled with a thick syrup. A pump forces the syrup upward between the inner and outer cylinders. The flowing syrup crosses over the inner cylinder's lip, then moves downward to drain out of a central spout. Tiny plastic spheres that fluoresce in ultraviolet light float on the liquid's surface.

With steady pumping and under perfectly symmetrical conditions, these tracer particles would simply converge on the exit. But a sequence of pumping pulses produces a complicated, unstable flow, and the particles gather wherever the flow is downward.

By photographing the tracer particles under ultraviolet light, the researchers obtain images from which they can derive the Lyapunov exponent, which indicates how rapidly the paths of nearby particles spread apart. They can also measure the fractal dimension - the intricacy - of the resulting pattern.

The results show that the fractal characteristics of the patterned surface quantitatively mirror the physical process that created the pattern, as characterized by its Lyapunov exponent.

"This establishes that a fractal's dimension is related in some way to the set of forces that produce it," Sommerer says. "In our experiment, we have a fractal, and we know where it comes from."
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Title Annotation:research indicates that fractal size and shape related to the forces that created it
Author:Peterson, Ivars
Publication:Science News
Article Type:Brief Article
Date:Jan 23, 1993
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