just occurred to me that there is probably a topological metric for legibility
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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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Why would you expect them to be if the intent is to model legibility
Another metric: straight line distance/graph shortest path
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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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Ie denominator will always be equal or bigger. An open plaza will give you 1. A 1E+1N path on a Manhattan grid will give you sqrt(2)/2 ~ 0.7. A complicated maze will give you very low ratios. The average ratio for all pairs of points will measure legibility decently well.


