Koch Doodles

One of the most famous fractals was invented long before the concept of a fractal was well-understood, or even understood at all. It was invented by a Swedish mathematician called Helge von Koch (1870-1924) and is usually called the Koch snowflake. To see how to construct it, take a line, divide it into thirds, and erect a triangle on the middle third. Next, take the four new lines and do the same to each of them.

Et cetera ad infinitum. Play with these images to follow the process:

And if the line one begins with is one side of triangle, and the other two sides are treated in the same way, you get the Koch snowflake. Though it doesn’t end there, of course. One can use squares or rectangles instead of triangles, or both, and one can vary where one erects them and how high one erects them. The possibilities are endless, but you can get some flavor of them from the following:

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