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It's a generalization of the everyday concept in an analogous way to how the reals generalize the integers. Obviously fractals exist in ordinary integer-dimensi
by dreamcompiler 7y ago
It's a generalization of the everyday concept in an analogous way to how the reals generalize the integers. Obviously fractals exist in ordinary integer-dimensional space, but the Hausdorff (or fractal) dimension provides additional descriptive mathematical insight.
https://en.m.wikipedia.org/wiki/Hausdorff_dimension https://en.m.wikipedia.org/wiki/Hausdorff_dimension
- westoncb 7y agoI think that's a misleading characterization. It's actually a particularization not a generalization: the ordinary notion only deals with topological properties, fractal/Hausdorff dimension deals with metric properties as well. That's the main distinction: the old notion doesn't care about roughness or changes in measurement at varied scales since it has nothing to do with metric properties. The generalization from integers to reals in the actual values is not indicative of the relationship between the two concepts.