Variation of the fractal dimension of space-time geodesics (trajectories), according to the resolution, in the framework of special scale relativity. The scale symmetry is broken in two transitioning scales λ and Λ (non-absolute), which divide the scale space in three domains: (1) a classical domain, intermediary, where space-time doesn’t depend on resolutions because the laws of movement dominate over scale laws; and two asymptotical domains towards (2) very small and (3) very large scales where scale laws dominate over the laws of movement, which makes explicit the fractal structure of space-time.