Motivated by the need to understand the movement of microbes in natural porous systems and the evolution of their genetic information, a renormalization procedure for motile particles in media with fractal functionality between upper and lower cutoffs is developed and applied to L¿vy particles. On the micro scale, particle trajectories are the solution to an integrated stochastic ordinary differential equation (SODE) with Markov, stationary, ergodic drift subject to L¿vy diffusion. The L¿vy diffusion allows for self-motile particles. On the meso scale, the trajectory is the solution to an integrated SODE with L¿vy drift and diffusion arising from the microscale asymptotics. L¿vy drift is associated with the fractal character of the Lagrangian velocity. On the macro scale, the process is driven by the asymptotics of the mesoscale drift without additional diffusion. Renormalized dispersion equations are presented on the meso and macro scales.