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For question borderline with, or having application to, computer science. Consider also posting http://cs.stackexchange.com/ or http://cstheory.stackexchange.com/ instead of here, if appropriate.

6 votes

Estimating the fractal dimension of a point cloud

You might look at Robert MacPherson and Benjamin Schweinhart's recent preprint "Measuring Shape with Topology", where they use topological methods (i.e. persistent homology) to estimate fractal dimens …
Matthew Kahle's user avatar