Hausdorff Dimension
Let 
be a Subset of a Metric Space 
. Then the Hausdorff dimension 
of is the Infimum of
such that the 
-dimensional Hausdorff Measure of is 0. Note that this need not be anInteger.
In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with FractalLorentz's conjecture. 
However, in general, the properdimension to use turns out to be the Minkowski-Bouligand Dimension (Schroeder 1991).
References
Federer, H. Geometric Measure Theory. New York: Springer-Verlag, 1969. Hausdorff, F. ``Dimension und äußeres Maß.'' Math. Ann. 79, 157-179, 1919. Ott, E. ``Appendix: Hausdorff Dimension.'' Chaos in Dynamical Systems. New York: Cambridge University Press, pp. 100-103, 1993. Schroeder, M. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, pp. 41-45, 1991.
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