Koch Snowflake

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Instructions

Set the Level slider to zero. Click on the green flag. A triangle will be drawn in the center of the screen. This is the 'initiator'.
Set the Level slider to one, click on the green flag, and the generator for the Koch curve (see http://scratch.mit.edu/projects/10992186/) will be constructed on the three sides of the triangle. Set the Level slider to 2, 3, 4, and 5 for more iterations of the curve.
Even though the perimeter increases, without limit, as Level increases without limit, the area of the Snowflake never exceeds eight-thirds the area of the originating triangle. Compare this fratal to the Squareflake fractal at http://scratch.mit.edu/projects/11100698/

Notes and Credits

This is the famous Koch curve named for its inventor, Helge von Koch (1870 – 1924), a Swedish mathematician. It is one of the mathematical 'curves' that forced mathematicians to rethink the definition of 'curve'.
The Koch curve is often the first fractal a student studies as it is perhaps the simplest of the class of fractals called 'similarity fractals'.
The script is easily adapted to many other similarity fractals by changing the define [curve][length] script to draw the 'generator' of the fractal.

Shared: 27 Jun 2013 Modified: 21 Oct 2017
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