The physical appearance of a great number of granular media shows, together with the heterogeneity of grain sizes, suggests the existence of geometrical scale invariance. This note focuses its attention on discussing how such physicoempirical property, visually perceived, can be mathematically formulated and used in the modeling of particle size distribution (PSD). Two ways of encoding that property by means of respective equations of different natures are analyzed. They lead to respective fractal particle size distribution (PSD) models coming from sources from the literature. The nature and features of the two different models are analyzed and the simulation of the PSD by means of both models are compared. In addition, the parameters that both models provide and their role in characterizing PSD are discussed. This note aims mainly to contribute to the clarification of some conceptual, methodological, and historical aspects within the frame of the fractal modeling of PSD of granular media.

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