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MatheMUSEments
Glitter Trap
By Ivars Peterson
Muse, December 1999, p. 37.
You've probably looked at your distorted reflection in one of
the shiny ornaments that decorate shops and homes during the
holiday season. But you may be surprised to learn what the
reflections in a pyramid of silvery balls are like.
You can try this at home with four round Christmas tree
ornaments and a small flashlight. Large, silver balls work best.
Place three of the balls on a table so they touch one another
and form a triangle. Position the fourth ball on top of the other
three to create a pyramid. In a darkened room, shine the
flashlight through the opening in between the ornaments and into
the center of the pile. You'll see an intricate pattern of light
and dark patches among the balls.
University of Maryland student David Sweet has taken this
procedure one step further. He's photographed the patterns that
appear when the four-ball pyramid is lit from below and has blue
and red poster boards placed outside two of the faces. The
reflections of the colors bounce back and forth among the mirror-like
balls and create striking patterns of blue, red, white, and black.
It turns out that the boundary between the colored patches is
very complicated. If you magnify a part of the boundary, you see
a patchy pattern that looks like the original, unmagnified image.
Zooming in further, you see even more of the same patchy pattern.
A pattern that looks similar at different magnifications is known
as a fractal.
But this "glitter trap" is more than a toy for
creating colorful patterns. Among other things, the behavior of
light in a stack of mirrored balls can help mathematicians and
physicists picture how electrons wander through the materials
used to make transistors, computer chips, and other electronic
devices.
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