Essay, Research Paper: Fractals

Mathematics

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The videotape "Fractals" was narrated by a writer of science fiction,
R.C. Clark, who is the creator of 2001 Space Odessy. Individuals interviewed,
experts on the subject included professor Stuart, Dr. Michael Barnsley, Steven
Hawkins, author of A Brief History in Time, and creator of the Mandelbrot set,
Dr. Benoit Mandlebrot. These men introduced us to their insight of fractals,
provided people with much new and fascinating information on this obscure topic,
and left the audience with questioning minds. The scientists and experts
reporting on fractals gave detailed descriptions of these images. They explained
that a fractal is based on simple principles, rather than complicated
components, and it was not discovered until the era of modern computers. A
fractal is an image comprised of the equation Z z +c, which was formulated by
Dr. Mandlebrot. This equation is defined by coordinates and positions on a plane
that locate a spot. Fractals are images that are the same all over and their
changing patterns can be magnified unlimited times. The patterns and bright
colors change regularly and are very consistent. With continuous magnification,
a baby Mandlebrot set can be found in every image. Fractals are fragmented; they
are fractional images that we are surprisingly accustomed to. These images can
be observed in objects we see every day, specifically in nature. From the edges
and appearances of clouds, trees, rocks, ferns, and flowers, the fine structure
and resemblence of fractals is obvious. Certain objects are examples of the
entire fractal, including the Mandela, a religious symbol, stained glass designs
in many church windows, the sculpture of Buddha, paintings and the design of
blood vessels. It is understood that the fractal can be perceived, but what
purpose does it serve? And this is what the scientists are still researching,
the actual application of fractals. Fractal dimensions are applied primarily
through data, making them a major tool in descriptive science and engineering.
The military and NASA also have a use for fractals, which compress data for less
difficult transmission to satellites in space. Fractals make pictures of leaves
in collages and can reconstruct colorful and precise details of a magnified
image. Other than these examples, fractals are presently useless to the common
person. However, experts will soon be developing new devices to utilize, but it
is practically certain that it will take some time for them to really figure out
the fractal.
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