**3. Fractal dimension**

In fractal geometry, the fractal dimension *D* is a real number that generalizes the concept of ordinary dimension for geometric objects that do not admit tangential space and is an exponent, which accounts for the wholeness, that seems to fill a fractal in space as it moves toward finer and finer scales. The problem here is that there exists a series for its calculation which frequently but not always is equivalent. Among the ones mostly used are: Hausdorff-Besicovitch dimension, packing dimension, homothetic dimension, and Rényi dimensions. None of these is universally used, and one of the reasons for this is that the discrepancy among them is related to differences in the structure of the fractal. Although for a great number of classical fractals the values of the various definitions of fractal dimension and all those dimensions coincide, they are not equivalent. The positive aspect of this is that some definitions of fractal dimension are easy to calculate and are probably more used. However, they do not always have the most desirable mathematical properties.
