We performed computer simulation of the film growth process on the two
-dimensional (2D) Penrose pattern, which is considered a typical struc
tural model of quasicrystal. The atomistic structure of the deposited
atoms was calculated as a function of time under various conditions of
atomic binding energy, temperature and deposition rate. The Monte Car
lo method based upon the solid-on-solid model was utilized for the pre
sent calculation. We found a geometrical restriction on the growth fro
nt of grains in the 2D Penrose pattern, which is also expected for the
growth of an actual quasicrystal.