Maryland physicists find consistency amid chaos Study sheds light on fractal forms

January 17, 1993|By Douglas Birch | Douglas Birch,Staff Writer

Two Maryland scientists have demonstrated for the first time the physics behind some of nature's most intriguing forms: complex geometric shapes called fractals.

The researchers hope their work, published in this week's edition of Science magazine, may one day help explain why everything from cracks to galaxy clusters, from clouds to coastlines, from bronchial tubes to blood vessels assume fractal shapes.

"They are everywhere we look and are obviously an important organizing principle in the universe," said one of the scientists, John C. Sommerer of the Applied Physics Laboratory in Laurel. "When you see something that ubiquitous, it says there's fundamental physics going on that we need to comprehend."

William Ditto, a fractal researcher at the College of Wooster in Ohio, said Dr. Sommerer and his colleague, Edward Ott of the University of Maryland at College Park, are on to something.

"It's one of the first experiments to show why fractals come about -- because of the underlying physics," he said.

L "It's like a hard-core proof that fractals exist in nature."

Although fractals may seem totally random, they are actually made up of the same pattern repeated at smaller and smaller scales -- the way a satellite photograph of the Mississippi resembles an airplane photo of one of its tributaries, which resembles a ground-level snapshot of a rivulet.

The geometry of fractals has been studied for a century. But in terest in natural fractals has emerged only in the past couple of decades, as computer scientists created a new field called chaos theory -- which, stated simply, is the study of very complex processes.

The discovery by Dr. Sommerer and Dr. Ott is basic science, with no immediate application.

Eventually, though, their findings could help provide the tools tobetter understand chaotic processes, from the beating of the heart to the flow of nutrients in Chesapeake Bay to the mixing of fuel and air in engines.

Before that can happen, scientists need to predict what kind of chaotic process will create what type of fractal shape.

So Dr. Sommerer and Dr. Ott set out to study a basic chaotic system

to see if they could predict something about the type of fractal it produced.

In a series of experiments last year, the researchers circulated a solution of sugar water sprinkled with tiny particles of fluorescent plastic in a 6-inch bowl. The sugar made the water viscous so the liquid could be swirled more slowly.

Dr. Sommerer swirled what he calls his "high-tech scum," let the liquid settle, and photographed the resulting pattern under ultraviolet light.

He and Dr. Ott kept swirling, stopping and taking photographs until they produced a fractal shape.

"It's like stirring cream up in your coffee," Dr. Sommerer said, "but the real experiment goes much more slowly."

They measured the liquid's volume and viscosity and the time spent pumping.

When they plugged the resulting numbers into formulas derived from chaos theory, they found they could predict the dimension of the resulting shape.

In our simple three-dimensional world, that may seem like no big deal. But in fractal geometry, the concept of dimensions is much more complicated.

In standard geometry, of course, shapes can have dimensions defined only in whole numbers. A point has zero dimensions: no length, width or height. A line has one dimension: length but nothing else. A circle or square has two dimensions: length and width, which create area, but no depth. And a sphere or cube has three dimensions.

In fractal geometry, objects usually have fractional dimensions -- 1.46 for the Eastern Shore of the Chesapeake Bay, for example. The human bronchial system has a dimension of 2.9. One of the fractal patterns made by Dr. Sommerer and Dr. Ott, which appeared on the cover of the recent Science, has a dimension of 1.7.

This is grounded in mathematics, of course, and tough to visualize.

The researchers found that, given the right temperature, volume and mixing, they could always produce a fractal pattern with a given dimension.

They discovered a form of consistency in chaos.

"It wasn't just, 'Here's another fractal,' " Dr. Sommerer said. "The point is we can make some additional measurements of the properties of this moving fluid and, using the theory of chaos, we can predict what the dimension of the fractal pattern will be."

"There are mathematical theories that say that [simple natural processes] can result in a fractal distribution," said Dr. Ott, who has been working in the field of fractal research for a decade.

"And so this experiment is for the first time seeing a real-life realization of these theories. "It's sort of a very mundane situation that results in something more exotic than you might assume," he said.

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