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And in fact, if a coastline were some Euclidean shape, such as a circle, this method of summing finer and finer straight-line distances would indeed converge. But Mandelbrot found that as the scale of measurement becomes smaller, the measured length of a coastline rises without limit, bays and peninsulas revealing ever-smaller subbays and subpeninsulas—at least down to atomic scales, where the process does finally come to an end. Perhaps.
