The Box-counting dimension reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Box-counting dimension

In fractal geometry, the box-counting dimension is a way of determining the fractal dimension of a set S.

To calculate this dimension imagine the fractal lying an an evenly-spaced grid, and count how many boxes are required to cover the set. The box-counting dimension is calculated by seeing how this number changes as we make the grid finer.

Suppose that N(ε) is the number of boxes of side length ε required to cover the set. Then the box-counting dimension is defined as:

This number is not necessarily an integer. It is also important to note that the various methods of calculating fractal dimension are not equivalent. Hence the box-counting dimension will not necessarilly give the same result in all cases as the Hausdorff dimension or correlation dimension.

This is the "Box-counting dimension" reference article from the English Wikipedia. All text is available under the terms of the GNU Free Documentation License. See also our Disclaimer.