A study of the different methods usually employed to compute the fractal dimension

The fractal dimension (FD) is a widely used magnitude having a basic formulation in terms of the Hausdorff measure. However, there are a lot of practical definitions mostly used to compute the FD of a given system not yet having a mathematically rigorous approach. In this paper, we analyze these alternative FDs and present a mathematical formalism for all of them obtaining practical expressions that can be used to compute each FD so far described. The conditions for applying these expressions are also analyzed. Finally, we have applied all the definitions to compute the FD of fractal aggregates formed at the air–liquid interface.