Since ⋆ ⋆ -composition of functions is thoroughly nonlocal (the "quantum probability fluid" diffuses, as observed by Moyal), vestiges of local trajectories in quantum systems are barely discernible in the evolution of the Wigner distribution function. In the integral representation of ⋆ ⋆ -products, successive operations by them have been adapted to a phase-space path integral, to solve the evolution equation for the Wigner function (see also ). This non-local feature of Moyal time evolution is illustrated in the gallery below, for Hamiltonians more complex than the harmonic oscillator. In the classical limit, the trajectory nature of the time evolution of Wigner functions becomes more and more distinct. At ħ = 0, the characteristics' trajectories reduce to the classical trajectories of particles in phase space.