# Hausdorff Dimension

Robert P. Munafo, 1999 Oct 20.

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.

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2023.

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