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Actually I think it may be possible with calculus.
Graph the first iteration of Koch's Curve, then find the function that makes up that curve. Then integrate to find the area underneath that curve. Repeat this with the second iteration of the curve, and, after finding say 10 or so of these areas (I know, too much work, I wouldn't want to do it either), you can estimate the average area underneath a Koch Curve, then, you can predict a best fit graph line and find a probability that, in some iteration n number of iterations in the future, that point will be beneath the best fit graph line. No to well versed in calc, but it seems it would work in theory.
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