Figure 1. Random walk on a sphere.

Trajectory (blue) of the extremity of a unit vector n (in red) describing a rotational Brownian motion. Initially the vector is aligned with the z direction (θ = 0). Each blue segment represents the angle variation of this unit vector where D_r = 0.16 rad²/s (the rotational diffusion coefficient for a sphere of radius 1 µm in a liquid of viscosity η = 1 mPa.s at ambient temperature T is [17]). The time step is dt = 30 ms (total of 100 steps).