Koch's Snowflake is another geometric iterative fractal, based this time on an equilateral triangle. It was first published in 1906 by the Swede

The iterative step, like Cantor's Set, is applied to any remaining line segments. This step consists of splitting a line in 3, removing the middle third and replacing it with two copies of itself angled 60 degrees apart, to make a kink in the line similar to the equilateral triangle.

An interesting feature of this curve is how quickly it grows in complexity - the numer of edges increases by 4 with every iteration, with the length of the perimeter increasing by 4/3. This means that the actual Koch Snowflake has an infinite perimeter.