Fractals - Research Article from Macmillan Science Library: Mathematics

This encyclopedia article consists of approximately 7 pages of information about Fractals.
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Constructing Geometric Fractals

Any mathematically created fractal can be made by the iteration, or repetition, of a certain rule. There are three basic types of iteration:

  • generator iteration, which is repeatedly substituting certain geometric shapes with other shapes;
  • IFS (Iterated Function System) iteration, which is repeatedly applying geometric transformations (such as rotation and reflection) to points; and
  • formula iteration, which is repeating a certain mathematical formula or several formulas.

The property of self-similarity holds true for the majority of mathematically created fractals.

The figure below illustrates the geometric construction of the Koch Curve, named after Helge von Koch, a Swedish mathematician who introduced this curve in a 1904 paper. First, begin with a straight line, as shown in (a). This initial object can be called the initiator. Partition this into three equal parts, then replace the middle third by an equilateral triangle and take away its base, as shown in...

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This section contains 1,994 words
(approx. 7 pages at 300 words per page)
Buy the Fractals Encyclopedia Article
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Macmillan Science Library: Mathematics
Fractals from Macmillan Science Library: Mathematics. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.
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