We study the dynamics of phasons in a nonlinear photonic quasicrystal. The photonic quasicrystal is formed by optical induction, and its dynamics is initiated by allowing the light waves inducing the quasicrystal to nonlinearly interact with one another. We show quantitatively that, when phason strain is introduced in a controlled manner, it relaxes through the nonlinear interactions within the photonic quasicrystal. We establish experimentally that the relaxation rate of phason strain in the quasicrystal is substantially lower than the relaxation rate of phonon strain, as predicted for atomic quasicrystals. Finally, we monitor and identify individual 'atomicscale' phason flips occurring in the photonic quasicrystal as its phason strain relaxes, as well as noise-induced phason fluctuations.