Harmonograph · coupled Lissajous decay
Two pendulums swinging at right angles draw the sum of their motions. When their frequencies form a simple ratio like 3:2 the pen closes a stable rosette; detune it slightly and the figure slowly precesses. Friction shrinks the amplitude exponentially, so the pattern spirals inward — the same maths behind oscilloscope Lissajous figures used to compare two signal frequencies.
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