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Everytime I see people talking about the length of their coastlines ...

Look at how long this edge of my fractal is, Ma!

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I understand the infinite coastline concept in theory but in practice would you even want to measure a coastline that way? Even if your goal was “perfect” precision, coastlines are variable. You’d have to take an average across tides and that would require zooming out enough to get a normal sounding answer.
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It is obvious when you think that 3d volumes scale cubicly and 1d lengths scale linearly. Adding another 1 meter to a cube of said filaments would increase the total length by a power of 3!
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How would this compare with packing the volume with DNA ?
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