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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.
4
votes
Can Hausdorff dimension make sets into a Tropical Semiring?
Hatano gives on page 19 of this article "Notes on Hausdorff Dimensions of Cartesian
Product Sets" HIROSHIMA MATH. J.1 (1971), 17-25 as class of generalized symmetric Cantor sets whose products have Ha …
6
votes
Fractal questions: Weierstraß-Mandelbrot
A quick, partial answer to your second question about the definition of fractals. If a fractal is generated by an iterated function system with a scaling ratio less than one then you do get a Hausdorf …