Rose-engine rosette — Cartonnage

Paper width

Paper height

Margin Seed Rosette lobes Rosette swell Rosette passes Border depth Border width Border lobes Border swell Border passes

12×12 mat — 8.50″ × 11.00″ — 28 strokes, 2 pens

r = R + A·cos(nθ), the banknote curve: a stack of closed rosettes at rising radii, each turned a fraction of a lobe from the one inside it so the passes braid. One pen-down per rosette, which is the exception the section makes — ramping R with θ collapses a whole family into a single unbroken line, but the line has to arrive back where it started a spacing further out, and that step is a seam in plain sight on an otherwise closed figure. The rosette and the border a note carries round it are two families with nothing in common but a centre, so each takes its own lobes, swell and passes. Depth is how far in from the rim the border reserves and width is how much of that it fills, so the white between the two figures is the difference and is set rather than assumed: depth at zero gives the rosette the whole disc, and width short of depth opens the gap without moving either figure. They take a pen each, so the border can be inked apart from what it surrounds — which is most of why a note carries one. The seed sets where the figures sit and how far each pass turns from the last, which is what the braid is.