African Fractals Background 1: Self-similarity

 

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Fractals have the property of self-similarity: a small part looks like the whole. We can see that in the Koch curve above, a fractal named for Swedish mathematician Helge von Koch. At top we see three big clusters, like the arms and head of a lumpy snowman. But each is made of simlar clusters, and so on down to infinity. How did Koch construct such an infinitely wiggly curve?

       

         
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