Fig. 5. Schematic representation of the three domains of the present era, (quantum microscopic, classical and cosmological) in the case of special scale-relativistic (Lorentzian) laws.The variation of the effective fractal dimension is given in terms of the logarithm of resolution. It is constant and equal to the topological dimension in the classical, scale-independent domain. It jumps fastly to towards small and large scales (Galilean regime), then it increases continuously in the Lorentzian regime (Eq. (A.2.2). The (relative) transitions are given by the Compton length at small scale and (presumably) by the Emden radius at large scale.