We report a systematic study of colloidal diffusion over a substrate with quasicrystalline-patterned holes. Silica spheres of diameter comparable to the hole diameter diffuse over the patterned substrate and experience a gravitational potential U(x, y). Using optical microscopy, we track the particle trajectories and find two distinct states: a trapped state when the particles are inside the holes and a free-diffusion state when they are on the flat surface outside the holes. The potential U(x, y) and dynamic properties of the diffusing particle, such as its mean dwell time, mean square displacement, and long-time diffusion coefficient DL, are measured simultaneously. The measured DL is in good agreement with the prediction of two theoretical models proposed for diffusion over a quasicrystal lattice. The experiment demonstrates the applications of this newly constructed potential landscape.