Hello, 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.