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mgf1107lecture30

mgf1107lecture30 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 30 The Koch Antisnowflake In the previous lecture we looked at how to construct the Koch snowflake starting with an equilateral triangle. A variation on this is the Koch antisnowflake , where instead of the middle third of each side being replaced by two sides of an equilateral triangle whose vertex points away from the center of the triangle (thereby increasing the area), we replace the middle third of each side and delete an area formed by two sides of an equilateral triangle whose vertex points towards the center of the triangle (thus decreasing the area). Ex. Assume that the Koch antisnowflake starts with sides of length 1. Let M denotes the number of sides, l the length of each side, and P the perimeter. Then we can construct the following table: Iteration M l P

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The Sierpinski Triangle Another famous fractal is the Sierpinski triangle, created by Wac ł aw Sierpi ń ski (1882-1969). We start with an equilateral triangle and split it
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