In many cases, the Hausdorff dimension correctly describes the correction term for a resonator with fractal perimeter in Lorentz's conjecture. However, in general, the proper dimension to use turns out to be the Minkowski-Bouligand dimension. Let F(r) be the area traced out by a small circle with radius r following a fractal curve. Then, providing the limit exists, D_M congruent lim_(r->0) (ln F(r))/(-ln r) + 2 (Schroeder 1991). It is conjectured that for all strictly self-similar fractals, the Minkowski-Bouligand dimension is equal to the Hausdorff dimension D; otherwise D_M>D.
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