Minkowski-Bouligand Dimension
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).
Let 
be the Area traced out by a small Circle with Radius 
following a fractal curve. Then,providing the Limit exists,
(Schroeder 1991). It is conjectured that for all strictly self-similar fractals, the Minkowski-Bouliganddimension is equal to the Hausdorff Dimension
; otherwise 
.See also Hausdorff Dimension
References
Berry, M. V. ``Diffractals.'' J. Phys. A12, 781-797, 1979. Hunt, F. V.; Beranek, L. L.; and Maa, D. Y. ``Analysis of Sound Decay in Rectangular Rooms.'' J. Acoust. Soc. Amer. 11, 80-94, 1939. Lapidus, M. L. and Fleckinger-Pellé, J. ``Tambour fractal: vers une résolution de la conjecture de Weyl-Berry pour les valeurs propres du laplacien.'' Compt. Rend. Acad. Sci. Paris Math. Sér 1 306, 171-175, 1988. Schroeder, M. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, pp. 41-45, 1991.
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