Self-similarity and recursion

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

Benoît MandelbrotThe Fractal Geometry of Nature (1983)

Though this be madness, yet there is method in’t.

William ShakespeareHamlet (Act II, Scene II)

HAVE you ever noticed, while laying on your back under a tree, that each branch of the tree resembles the tree itself? If you could take any branch, from the smallest to the largest, and place it upright in the ground, it could probably be mistaken for a smaller tree. This phenomenon, called self-similarity, is widespread in nature. There are also computational problems that, in a more abstract way, exhibit ...

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