This is the Von Koch curve. Its construction is almost as easy as the Sierpinski Triangle. You start with a triangle (equilaterality is really more important in this case than for the Sierpinski Triangle), and, on each side, tack on little equilateral triangles, so you end up with a shape very much like a Star of David.

The Star of David has six little triangles sticking out. For each triangle, repeat the previous process. Iterate infinitely.

Under construction.

This page is very much under construction. When it is finished, there will be more on fractal dimension, more about coastlines, and a complete explanation of why the Von Koch curve has a infinite perimeter surrounding a finite area.

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