As far as I understand a new pattern of crystal growth has been found experimentally. How does it relate to the known 2D and 3D nucleation and growth of crystals? The dominating theory of crystal growth nowadays is that initiated by Cabrera and Frank. How is the new finding related to what we know so far or is it at odds with what we know and how?
The Cabrera-Frank theory is strictly speaking valid for crystals only. Quasicrystals – which were awarded by the Nobel prize – are strictly speaking not crystals. Crystals, by definition, have to be periodic while quasicrystals are not. So details of the theory for crystals of course don't have to hold for quasicrystals. But there are still many similarities in their growth and structure.
Indeed, Shechtman's 1982 discovery falsified some assumptions that people used to believe, e.g. that non-periodic quasicrystals with five-fold symmetries (otherwise behaving just like crystals for which five-fold symmetries are forbidden) were impossible. He was being humiliated by many people before he was admitted to be clearly right.