Recently we reported the formation of a quasiperiodic Cu thin film on the fivefold icosahedral Al-Pd-Mn quasicrystal using scanning tunneling microscopy, low energy electron diffraction, and Auger electron spectroscopy. Here we provide details pertaining to the growth, stability, and structure of this film. Structural information has been gained by LEED measurements carried out at 85 K. Cu atoms are organized periodically with a nearest-neighbor distance of 2.5±0.1 Å along the aperiodically spaced rows. Above 8 ML spontaneous mass transport resulting in island formation has been observed by STM. These observations point to ascending adatoms being responsible for the formation of 3D features. Finally, flashing the multilayer film to 570 K results in the desorption or diffusion of Cu into the bulk and the formation of five domains of a periodic structure.