  Using molecular simulations, we show that the aperiodic growth of
quasicrystals is controlled by the ability of the growing quasicrystal
`nucleus' to incorporate kinetically trapped atoms into the solid phase with
minimal rearrangement. In the system under investigation, which forms a
dodecagonal quasicrystal, we show that this process occurs through the
assimilation of stable icosahedral clusters by the growing quasicrystal. Our
results demonstrate how local atomic interactions give rise to the long-range
aperiodicity of quasicrystals.
