Beginning with a single triangle, replace that triangle with three half-size copies arranged so that their outer border form a new triangle of the same size as the original. Then, replace each of those three triangles with three triangles half that size, and so forth. (Turns out of course, that the fractal pattern is due to the algorithm of shrinking and positioning the shapes, not due to the fact that the initial shape that we began with was a triangle– any plane figure can be used.) This algorithm is easy enough to implement directly and physically, using a flexible medium like polymer clay.

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