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Tetrahedron of Silver Balls Models Chaos of Light Beams

Photonics Spectra
Sep 1999
Robert C. Pini

Get your laser pointer ready to create some (legal) chaos. Using a set of four silvered balls, each 12 inches in diameter, put three of the balls in a triangular pattern and add the fourth to the top to build a pyramid-shaped stack. Voila! You have a model for chaotic scattering of light beams.

Shine the laser pointer into the empty center of the pyramid. As the light enters, it will reflect repeatedly off the balls and form a dazzling fractal image.

Chaotic light beams

Scientists at the University of Maryland used the simple model to demonstrate the effect of chaos on light beams.

When light enters the interior space -- defined as a tetrahedron by imaginary lines among the four balls -- its path is predictable. However, as the beam continues to reflect among the balls, its path becomes unpredictable and it enters into a state of chaos.

Laser light launched into a tetrahedron of silver balls forms a colorful fractal image. The image teaches scientists about chaos. Courtesy of David Sweet.

The researchers, Edward Ott, James A. Yorke and a graduate student, David Sweet, constructed the model to demonstrate the Wada property of chaotic scattering.

Wada sight

The Wada property suggests that, for a set of initial conditions with several possible outcomes, the final result is unpredictable.

To add spectral beauty to their model, the scientists used sheets of colored paper.

With white underneath and sheets of blue and red stacked against the different sides of the pyramid, the researchers switched off the lab lights.

They used a camera flash to reflect light off the colored paper. Red, white, blue and black cascaded within the tetrahedron, and they soon saw that they had created a fractal image that was clearly visible from the remaining side of the pyramid.

"The lesson from this is that the Wada property can manifest itself in physical systems," Sweet said. The colors in the image seem to create clear boundaries, but the Wada property requires that no matter how small a circle you draw across the boundary among the colors, it will always contain all four of them.

"Any visible light source will do," Sweet said. "The fundamental thing is the geometry." By measuring the dimensions of the fractal light with a high-resolution camera and a standard plot measurement technique, the researchers can compare computer simulations of light paths with lab results.

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