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Hunting the Hidden Dimension
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Program Overview
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NOVA explores the fascinating world of fractals and looks at how
they can be used to better understand everything from coastlines and
rainforests to weather systems and human physiology.
The program:
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reports on one of the first applications of fractal
geometry—when a Boeing computer scientist in 1978 applied
principles of fractal geometry to create a mountain background
for a plane for publicity photos.
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introduces Benoît Mandelbrot's realization that many forms
in nature can be described mathematically as "fractals," a word
he invented to describe shapes that look jagged, or broken, or
that do not conform to traditional geometry.
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explains that fractals are produced by taking a smooth-looking
shape and dividing it repeatedly in a process known as
iteration.
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describes one of the defining characteristics of a
fractal—self-similarity—a state in which an object
looks the same regardless of the distance from which it is
viewed, or in which an object's parts look similar to the whole
object.
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notes that prior to Mandelbrot's discovery of fractal geometry
in the 1970s, mathematicians relied on classical mathematics to
describe geometric shapes but had no mechanism for
characterizing the erratic patterns that existed in nature.
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recounts that while he was working at IBM, Mandelbrot noticed
patterns in phone-line transmissions that reminded him of a
hundred-year-old mystery known as mathematical "monsters."
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illustrates some of the monsters, including the Cantor set,
Koch's snowflake, and the Julia set.
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shows how Mandelbrot used the Julia set to create his own
equation, which, when iterated and graphed on a computer,
generated the well-known Mandelbrot set.
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notes that many pure mathematicians turned against Mandelbrot
when his work first appeared, and that even today some
mathematicians maintain that his work has done little to advance
math theory.
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presents some of the many ways fractals are used and applied to
everyday life, including measuring coastlines, creating special
effects in film, downsizing wire antennas, better understanding
human physiology, and investigating why large animals use energy
more efficiently than small ones.
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follows researchers to a Costa Rican rainforest, where they try
to determine whether applying fractal geometry to data from a
single tree can reveal information about how much carbon dioxide
the entire rainforest can absorb.
Taping Rights: Can be used up to one year after program is
recorded off the air.
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