The Basics of Fractals

For our upcoming Math Club meeting on Mathy Holidy Ornaments, we'll be learning about the structure of fractals.  These animations found through Wikipedia give a visual representation of the interations involved in creating a fractal.

The famous Sierpinski triangle deletes the triangle formed by connecting the midpoints of each triangle.

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A fractal is made up of copies of itself, as shown by zooming in on a "completed" Sierpinksi Triangle.


As described on the Wikepedia entry for Fractals, the above image shows the Koch Snowflake, "a fractal that begins with an equilateral triangle and then replaces the middle third of every line segment with a pair of line segments that form an equilateral 'bump'."

The animation above shows how fractals can be used to simulate moutainous terrain in addition to other natural structures.