Minkowski-Bouligand dimension

The Hausdorff dimension is a successor to the less sophisticated but in practice very similar box-counting dimension or Minkowski-Bouligand dimension.

These notions (packing dimension, Hausdorff dimension, Minkowski-Bouligand dimension) all give the same value for many shapes, but there are well documented exceptions.

In fractal geometry, the Minkowski-Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a set S in a Euclidean space R, or more generally in a metric space (X, d).