There has been "some" debate on the notion of fractal (as an illustration, see for example the discussion in this link). One of the possible notions includes relating Hausdorff dimension and packing dimension. While I really don't care about what could be any reasonable definition of fractal, I find it peculiar that people might have introduced such a notion without apparently understanding whether packing measure and packing dimension occur "naturally" say in dynamical systems.
To my best understanding, packing dimension occurs naturally on the boundary of some Kleinian groups, but I know no other "natural" occurrence. So my question is:
Are there any other "natural" occurrences of packing dimension and/or packing "measure"? My personal preference would be in dynamical systems but it can be in other fields.
Quoting from here: "If not, then why should we have a definition involving such a notion? A notion should be somewhat motivated, say in the context of dynamics or of some other area. Let me note that Hausdorff measure and Hausdorff dimension seem to occur "naturally" much more."
Added December 21: Let me point out that Patterson-Sullivan measures should relate to the question, and the same goes for the study of the behavior at the critical exponent.