An Introduction to Fractals

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An Introduction toFractals

• By Brian Feuer

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What is a Fractal?

• A word coined by Benoit Mandelbrot in 1975 to
  describe shapes that are self-similar and are
  generated by a repeating pattern, typically a
  recursive or iterative process.

• Fractals are independent of scale.

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Components of a Fractal

• Self Similarity
• Two or more objects having the same
  characteristics. In fractals, the shapes of lines
  at different iterations look like smaller
  versions of the earlier shapes.
• Otherwise put, the shapes look the same at
  different magnifications.

• Iteration
• Repeating a set or rules or steps over and over.
• One single step is called an iterate.

• Recursion
• . Given some starting information and a
  rule for how
• to use it to get new information, the
  rule is then
• repeated using the new information.

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Fractals in Nature

• Can you think of any fractals found in nature?

Snowflakes are fractals.
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More Fractals in Nature
Seashells are fractals.
Ferns are fractals.
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Complex Fractals
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References

• http//www.dcet.k12.de.us/teach/quest/shari.htm
  by Shari Galgano
• http//math.rice.edu/lanius/frac/ by Cynthia
  Lanius
• http//astronomy.swin.edu.au/pbourke/fractals/fuz
  zylogic/ by Roger Bagula
• http//occawlonline.pearsoned.com/bookbind/pubbook
  s/billstein_awl/medialib/shodor_site/lessons/frac1
  .html by The Shodor Education Foundation, Inc.