The Koch Snowflake
First developed in 1904, this is one of the first and most well known fractal images. It was developed by the Swedish mathematician Helge von Koch and appeared in the snappily named paper "On a continuous curve without tangents, constructible from elementary geometry".
To create a Koch snowflake, start with an equilateral triangle and replace the middle third of every line segment with a pair of line segments that form an equilateral "bump." Then perform the same replacement on every line segment of the resulting shape, ad infinitum. With every iteration, the perimeter of this shape grows by 4/3rds. The Koch snowflake is the result of an infinite number of these iterations, and has an infinite length, while its area remains finite.
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