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Hausdorff Dimension  

Robert P. Munafo, 1999 Oct 20.

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

Me = eD Ne

where e is an arbitrary small quantity (an "epsilon" value) and Ne is the minimum number of points in the space SD 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

lime->0 [ ln(Ne) / ln(e) ]

See also Delta Hausdorff Dimension.

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2022.     Mu-ency index

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