x = A sin(aωt + δ), y = B sin(bωt) — closed when a/b is rational
3
2
0.50π
1.00
1.5
Lissajous figures arise from perpendicular harmonic oscillations. The pattern closes after LCM(a,b)/ω time.
Lissajous (1857) used optical interference of tuning forks. Used today in oscilloscope calibration.