Fractal

Pronunciation: /ˈfræk tl/ ?

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Manipulative 1: Sierpinski Triangle. Created with GeoGebra.

A fractal is a geometric object that has an complicated boundary and is self-similar at all scales. One property of fractals is that, as the complexity of the shape increases, the area or volume approaches a finite value and the length of the boundary approaches infinity.

Manipulative 1 is a representation of a Sierpinski triangle. A Sierpinski triangle starts as a equilateral triangle. At each iteration, an area in the shape of an upside-down equilateral triangle 1/4 the size of the triangle is removed from each triangle. At each iteration, the area decreases by 1/4 and the length of the boundary increases by 1/3.

References

  1. fractal. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=fractal&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Kenneth Falconer. Fractal Geometry: Mathematical Foundations and Applications, 2nd ed.. Wiley, November 14, 2003.
  3. Manfred Schroeder. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. Dover Publications, August 21, 2009.
  4. Benoit B. Mandelbrot. The Fractal Geometry of Nature, 2nd ed.. Wiley, November 14, 2003.
  5. Heinz-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe. Chaos and Fractals: New Frontiers of Science, 2nd ed.. Springer, February 3, 2004.

More Information

  • McAdams, David. Interactive Math Art. lifeisastoryproblem.com. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.com/art/index.html.

Printed Resources

Cite this article as:


Fractal. 2010-02-05. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/fractal.html.

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2010-02-05: Added "References" (McAdams, David.)
2009-01-13: Initial version (McAdams, David.)

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