Hausdorff Dimension

Robert P. Munafo, 1999 Oct 20.

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For a shape F embedded in D-dimensional Euclidean space S_D, define the measure M_e to be

M_e = e^D N_e

where e is an arbitrary small quantity (an "epsilon" value) and N_e is the minimum number of points in the space S_D such that every point in F lies within a neighborhood of radius e of at least one point. Then the Hausdorff dimension of F is

lim_e->0 [ ln(N_e) / ln(e) ]

See also Delta Hausdorff Dimension.

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From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo.     Mu-ency index

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