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Questions about dimensions of possibly highly irregular or "rough" sets, Hausdorff–Besicovitch dimension and related concepts such as box-counting or Minkowski–Bouligand dimension.

8 votes

Fractals of dimension zero

If by a fractal you mean a self-similar set and if the corresponding iterated function system (IFS) satisfies the Open Set Condition (OSC), then the answer is no. The Moran-Hutchinson formula gives …
Nikita Sidorov's user avatar