We performed Monte Carlo simulation of the aggregation process of a tw
o-component Lennard-Jones system on the two-dimensional (2D) Penrose l
attice for the purpose of studying the details of the creation and gro
wth process of quasi crystals. We adopted the potential parameter valu
es proposed by Widom et al. [Phys. Rev. Lett. 58 (1987) 706]. The pres
ent simulation clarified that the stability of the formed quasi crysta
ls depends on temperature and the strength of the potential and that t
he transition from solid state to liquid state occurs when the value o
f the inverse of the dimensionless temperature is approximately 4.0.