Wednesday, 26 January 2011

Koch Snowflake

The is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a continuous curve without tangents, constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire") by the Swedish mathematician Koch.

The Koch curve can be constructed by starting with an equilateral triangle, then recursively altering each line segment as follows:

  1. divide the line segment into three segments of equal length.
  2. draw an equilateral triangle that has the middle segment from step 1 as its base and points outward.
  3. remove the line segment that is the base of the triangle from step 2.

After one iteration of this process, the result is a shape similar to the Star of David.

The Koch curve is the limit approached as the above steps are followed over and over again.



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