On a “holographic implementation” in the dynamics of physical systems

A review on some fundaments and applications of Scale Relativity Theory is presented. The mathematical model started from the hypothesis that any entity of any physical system moves on continuous and non-differentiable curves (fractal curves). In such a context, equations of dynamics in their geodesic representations on various stationary cases were obtained, corresponding to several special physical effects (fractal tunneling type effect with or without spontaneous breaking symmetry, fractal type radioactive law, etc.). Once the motion curves exhibit the property of self-similarity in each of its points (every part reflecting the whole and vice-versa), this dynamics can be viewed as a “holographic implementation” of the description of the said dynamics.