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A fractal is a geometric pattern that repeats itself at smaller and smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry......think about the spirals in some seashells. That irregular pattern can be considered to be a fractal.
Fractals often exhibit the property of self-similarity and represent the many irregularly shaped objects in nature. A self-similar object is one whose component parts resemble the whole. Any of its smallest parts are similar in shape to its larger structure---like a broccoli flower or a fern leaf.
Sample some of the following activities to learn more about fractals.
Places To GoThe following are places to go (some real and some virtual) to find out about fractals.
Visit the Museum of Science in Boston and check out their exhibit on fractals and patterns in nature.
Fractals: eternal chaos and eternal order. This page contains colorful, decorative and very unusual images.
People To SeeMeet Benoit Mandelbrot. He is a French mathematician who helped develop chaos theory. He also developed fractal geometry which is used to find order in apparently erratic shapes and processes. Mandelbrot invented the term fractal. He based the term on fractus, a Latin word meaning a broken stone with an irregular surface.
Things To DoThis is a great site. It will lead you to fractal information and activities that you can actually understand.
Apparently the Fibonacci sequence can be found in the Mandelbrot set. Check it out.
Overload on fractals---fractal clouds, fractal music, fractal software, fractal pancakes, and more.
After you knock yourself out making Mandelbrot sets, make some Julia sets.
Create your own Mandelbrot sets. In case you've forgotten, a Mandelbrot set is the set of all complex c such that iterating z -> z^2+c does not go to infinity (starting with z=0). See the creations that other Mandelbrot aficionados have made.
Fractal music! Listen to fractal music while you view the Fractal of the Day. The inventor of fractals, Benoit Mandelbrot, also is a proponent of chaos theory. From this site, you can view a chaos demonstration and experience "strange attractors".
See how this site calls fractals "worlds within worlds".
Teacher Resources
Bibliography- Crownover, Richard M. Introduction to Fractals and Chaos. Boston: Jones and Bartlett, c1995.
- Dixon, Robert. Mathographics. New York: Dover Publications, 1991.
- Laplante, Phillip A. Fractal Mania. Blue Ridge Summit, PA: Tab Books, 1993.
- Peitgen, Heinz-Otto. Chaos and Fractals:New Frontiers of Science. New York: Springer-Verlag, c1992.
- Pickover, Clifford A.Chaos in Wonderland: Visual Adventures in a Fractal World. New York: St. Martin's Press, c1994.
- Turcotte, Donald Lawson. Fractals and Chaos in Geology and Geophysics. Cambridge, U.K.; New York: Cambridge University Press, c1997.