Harmonograph

A Victorian harmonograph — two decaying pendulums steer a pen across the paper, and their combined swing traces the looping Lissajous webs that slowly spiral inward and die. Near-integer frequency ratios with a hair of detune make the figure breathe; the damping makes it settle. Watch it draw, then roll a fresh one. Press ♪ Listen to hear the figure's ratio — a 2:3 is a perfect fifth, a 1:2 an octave — and the detune you see breathing becomes a slow beating you hear.

Motion

— silent —

Draw speed 1.0×

Pendulums 2:3

Roll a figure

Presets

Skin

Each axis is two pendulums: x(t) = Σ Aᵢ·sin(2π·fᵢ·t+φᵢ)·e^(−dᵢ·t). Try a preset, dial the per-pendulum frequency to detune the petals, then Surprise me for a reproducible new web. The badge proves the pen never drifts from the math.

The same ratio you see you can hear: ♪ Listen voices the figure's fundamental fy/fx as two pure tones — a Sound Garden crossing. Consonant figures (octave, fifth) sound consonant; the detune that makes the petals breathe is heard as a slow beat. One mute governs the whole workshop.