Experimental results from Geotail and Galileo, as well as results from large-scale kinetic modeling, demonstrate the characteristic structuring of ion distribution functions, especially in the distant and middle parts of the magnetotail. This structuring of the distributions is associated with nonadiabatic acceleration processes in the magnetotail. This paper suggests that the complexity of ion distributions can be quantified by using the analog of the fractal dimension D of the isodensity contours of the ion velocity distributions. It is found that D is usually larger than 1 for various locations within the tail and that as a result of the smearing of the structuring, the value gradually approaches the topological dimension D=1 as the Earth is approached. The use of the parameter D may be helpful in comparing the degree of granularity of the distribution functions obtained in different regions of the magnetotail, as well as in comparing experimental and theoretical results. ¿ American Geophysical Union 1996