Snowflake Peano (Fifth Step)

This shows the first five steps in the generation of a Peano curve that fills the Koch snowflake. The generator is a seven-segment polygonal curve; at each step, each segment is replaced by a scaled copy of the original. The resulting figure consists of a single open, simply connected polygonal curve. In principle the entire curve can be traced on paper without lifting one’s pencil or crossing a line, beginning at the lower left-hand point of the star and ending at the lower right-hand point. This curve was designed by Benoit Mandelbrot and described in his Fractal Geometry of Nature.

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