The Snowflake Curve is based on the Koch curve which appeared in the 1904 paper entitled, "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" by Helge von Koch, a Swedish mathematician.  I first saw approximations of the Snowflack Curve at a museum (maybe in Chicago) when I was maybe ten years old.  Use the right and left arrows to adjust the complexity.

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Consider the limit of these curves.  What is the perimeter?  What is the area?