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I mean I just made up the ratio but the 2 quantities are well-known things… a fractal would end up at like 0.7 or something for eg. Legible things would be 1
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Graph shortest path is very unlikely to honor the triangle inequality. Trying to apply spatial metaphors to graphs seems ill-fated, at best you can try to have edges represent orientational metaphors a la Lakoff and Johnson.
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I don’t understand what you’re talking about An illegible environment will have wiggly paths that will on average be longer than Euclidean shortest path, You’re not applying the triangle inequality on the graph. You’re applying it in the embedding space where it will work fine
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i'm thinking maximum legibility corresponds to a closed set of closed proper subsets that are all either disjoint or proper subsets of subsets, which is isomorphic to a tree
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