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Koch snowflake

Koch Snowflake

Koch snowflake is also called as Koch star or Koch island. It is the mathematical curve which can be modeled by using the fractal. Fractal is the mathematical object that shows self similar pattern at all levels.

Koch snowflake are constructed with the equilateral triangle using the following methods,

  1. Divide the line segment into three equal segments with equal length.
  2. Draw an equilateral triangle that has middle segment from step 1 as its base and points upwards.
  3. Remove the line segment that forms the base of the triangle from base 2.

After the first iteration, you will get the shape of Hexagram.

If the process is repeated, the curve will never intersect and at a limit you will get a shape of Koch Snowflake. Koch Each process creates four times as many line segment in the previous process, length at each process grows 4/3 times. So the length of the curve after n iterations will be (4/3)n times.

Snowflake is the snow of infinite length. It will have an infinite boundary but finite area. The fractal dimension fo the Koch curve 4/log 3 = 1.26186.

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