After Mandelbrot published his seminal work in 1975 on fractals, one of the first practical uses came about in 1978 when Loren Carpenter wanted to make some computer-generated mountains. Using fractals that began with triangles, he created an amazingly realistic mountain range [source: NOVA].
In the 1990s Nathan Cohen became inspired by the Koch Snowflake to create a more compact radio antenna using nothing more than wire and a pair of pliers. Today, antennae in cell phones use such fractals as the Menger Sponge, the box fractal and space-filling fractals as a way to maximize receptive power in a minimum amount of space [source: Cohen].
While we don't have time to go into all the uses fractals have for us today, a few other examples include biology, medicine, modeling watersheds, geophysics, and meterology with cloud formation and air flows [source: NOVA].
This article is intended to get you started in the mind-blowing world of fractal geometry. If you have a mathematical bent you might want to explore this world a lot more using the sources listed below. Less mathematically inclined readers might want to explore the infinite potential of the art and beauty of this incredible and complex source of inspiration.
- Bales, Judy. "Thinking Inside the Box: Infinity Within the Finite." Surface Design Journal. Pages 50-53. Fall 2010.
- Cohen, Nathan. "Fractal Antennas, Part 1." Communications Quarterly. Summer 1995.
- Eglash, Ron. "African Fractals: Modern Computing and Indigenous Design." Rutgers Univ. Press. 1999.
- Falconer, K. J. "The Geometry of Fractal Sets." Cambridge Tracts in Mathematics, 85. Cambridge, 1985.
- Fractal Foundation. "Online Fractal Course." (April 17, 2011)http://fractalfoundation.org/resources/lessons/
- Mandelbrot, Benoit. "The Fractal Geometry of Nature." Freeman. 1982.
- Mandelbrot, Benoit. "Fractals: Form, Chance, and Dimension" Freeman. 1977.
- Mandelbrot, Benoit. "How Long is the Coastline of England?: Statistical Self-Similarity and Fractional Dimension" Science, New Series. Vol.156, no.3775. May 5, 1967.
- NOVA. "Hunting the Hidden Dimension." PBS, 2008. Originally aired on Oct 28, 2008. (April 17, 2011)http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html
- Turcotte, Donald. "Fractals and Chaos in Geology and Geophysics." Cambridge, 1997.
- Weisstein, Eric W. "Dragon Curve." MathWorld. (April 22, 2011)http://mathworld.wolfram.com/DragonCurve.html
- Weisstein, Eric W. "Koch Snowflake." MathWorld. (April 22, 2011)http://mathworld.wolfram.com/KochSnowflake.html
- Weisstein, Eric W. "Menger Sponge." MathWorld. (April 22, 2011)http://mathworld.wolfram.com/MengerSponge.html
- Weisstein, Eric W. "Sierpiński Sieve." MathWorld. (April 22, 2011)http://mathworld.wolfram.com/SierpinskiSieve.html
- Weisstein, Eric W. "Strange Attractor." MathWorld. (April 22, 2011)http://mathworld.wolfram.com/StrangeAttractor.html