MDMD(1): Forbidden Symmetries

[Matthew P Wiener]

>While fivefold symmetry is naturally "forbidden" in crystal formation, as
>Penrose points out, certain quasicrystalline structures, have been
>discovered  which are based on fivefold symmetry. Penrose states: "...a
>remarkable feature of the quasicyrstalline tiling patterns...is that their
>assembly is necessarily *non-local*" Meaning that there has to be some way
>in which the evolving pattern (which is aperiodic!) is "known" many atoms
>ahead of where the structure has already formed.

Actually, Penrose is flat out wrong, although a way of doing so was not
known at the time.
--
-Matthew P Wiener (weemba at sagi.wistar.upenn.edu)