Barnsley’s central insight was this: Julia sets and other fractal shapes, though properly viewed as the outcome of a deterministic process, had a second, equally valid existence as the limit of a random process. By analogy, he suggested, one could imagine a map of Great Britain drawn in chalk on the floor of a room. A surveyor with standard tools would find it complicated to measure the area of these awkward shapes, with fractal coastlines, after all. But suppose you throw grains of rice into the air one by one, allowing them to fall randomly to the floor and counting the grains that land
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