Introduction - If you have any usage issues, please Google them yourself
A set (e.g. an image) is called "fractal" if it displays self-similarity: it can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.
A possible characterisation of a fractal set is provided by the "box-counting" method: The number N of boxes of size R needed to cover a fractal set follows a power-law, N = N0 * R^(-DF), with DF<=D (D is the dimension of the space, usually D=1, 2, 3).
DF is known as the Minkowski-Bouligand dimension, or Kolmogorov capacity, or Kolmogorov dimension, or simply box-counting dimension.