  The growth of quasicrystals, i.e., aperiodic structures with long-range
order, seeded from the melt is investigated using a dynamical phase field
crystal model. Depending on the thermodynamic conditions, two different growth
modes are detected, namely defect-free growth of the stable quasicrystal and a
mode dominated by phasonic flips which are incorporated as local defects into
the grown structure such that random tiling-like ordering emerges. The latter
growth mode is unique to quasicrystals and can be verified in experiments on
one-component mesoscopic systems.
