whatA Victorian parlour machine: a pen hangs from two pendulums, one swinging it side to side, one fore and aft, each the sum of two sinusoids, and every swing decays a fraction of a percent per cycle the way real brass loses its energy. Set it going and the machine draws. The seed sets the frequency ratio, its tiny detuning, the phases, and the decay: the whole studio in one integer.

whyThe claim: the beauty lives at NEAR-rational ratios. Tuned exactly to three against two the pen retraces one dead figure; detuned by a few thousandths, each pass lands beside the last and the decay walks the family of curves inward, so the drawing breathes, a ribbon of near-misses tightening to the centre. Measured here: the envelope halves exactly on its printed half-life, and successive passes miss by the detune's prediction. Every seed a signature, reproducible forever.

howTwo sinusoids per axis, exponential decay, the path traced live onto persistent paper. The print computes the machine's complete output analytically, so it is the finished figure even when the pen is mid-stroke. Click for the next figure in this seed's line; the volume closes with the piece that is a machine for making its own prints.