*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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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...

This section contains 1,994 words(approx. 7 pages at 300 words per page) |