Pronunciation: /ˈfræk tl/ Explain

Click on the blue point on the slider and drag it to advance through the first levels of the Sierpinski triangle.

At level 100, what would the triangle look like?
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.


  1. Kenneth Falconer. Fractal Geometry: Mathematical Foundations and Applications. 2nd edition. Wiley. November 14, 2003. Buy the book
  2. Manfred Schroeder. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. Dover Publications. August 21, 2009. Buy the book
  3. Benoit B. Mandelbrot. The Fractal Geometry of Nature. 2nd edition. Wiley. November 14, 2003. Buy the book
  4. Heinz-Otto Peitgen, Hartmut Jürgens, and Dietmar Saupe. Chaos and Fractals: New Frontiers of Science. 2nd edition. Springer. February 3, 2004. Buy the book

More Information

  • McAdams, David E.. Interactive Math Art. Life is a Story Problem LLC. 3/12/2009.

Cite this article as:

McAdams, David E. Fractal. 7/11/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/5/2010: Added "References". (McAdams, David E.)
1/13/2009: Initial version. (McAdams, David E.)

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