Hausdorff dimension

The Hausdorff dimension of the real line is equal to one.

The Hausdorff dimension of these paths is 5/4 almost surely.

The upper and lower box dimensions are strongly related to the more popular Hausdorff dimension.

A consequence of the above is that these all have Hausdorff dimension .

That article also discusses another useful characterization of the Hausdorff dimension.

The Hausdorff dimension of this set is 0.

Its similarity dimension and Hausdorff dimension are both the same.

This suggests that the scaling limit should have Hausdorff dimension between and 5/3 almost surely.

There are, however, many irregular sets that have noninteger Hausdorff dimension.

However, the Hausdorff dimension is always less than two but no less than one.

Hausdorff dimension of L under other dimension functions has also been investigated.

The Hausdorff dimension of such a construction is which agrees with the finite area of the figure.

The Apollonian gasket has a Hausdorff dimension of about 1.3057.

This number is the Hausdorff Dimension of the fractal.

For a quasi-Fuchsian group and showed that the Hausdorff dimension "d" of the limit set is always greater than 1.

The resultant three-dimensional H tree has Hausdorff dimension equal to 3.

However, there is no metric space quasisymmetric to K with a 0 Hausdorff dimension.

The discovery of fractals and other "rough" geometric objects (see Hausdorff dimension).

The effective Hausdorff dimension of a set of natural numbers X is .

Because the Moore curve is plane-filling, its Hausdorff dimension is 2.

Its boundary is fractal, and the Hausdorff dimension of this boundary equals 1.0933.

The circle S has Hausdorff dimension 1.

Their Hausdorff dimensions are slightly more difficult to calculate than lower n-flakes because their scale factor is less obvious.

Its Hausdorff dimension is equal to , which is exactly equal to 2.

The Hausdorff measure is not to be confused with the notion of Hausdorff dimension.