@graveolens This isn't what you're asking, but I wonder if fractals can have a concept of "area" extended to fractional dimension.
idle wondered interpolation problem (the world is arrgh these days, so rainbows.)pic.twitter.com/p2d1gyj2l6
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@tshellstudio most of the papers about that are by Xavier Buff and Arnaud Cheritat. http://annals.math.princeton.edu/2012/176-2/p01 is probably what you want...
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