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after reading something about fractals, I was wondering if it is possible to find invariants on fractal entities. For example in 3D Euclidean space we know that curvature and torsion uniquely define a regular curve: they are invariant to rigid motions.

In fractal geometry and in several papers dealing with fractal quantities, it seems to me that the only quantity that is invoked to "describe" a fractal, is its dimension (for example its http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension" [Broken]).

Is that really the only way to "distinguish" a fractal curve from another fractal curve?

Thanks.

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# Invariants in fractal geometry

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