The graph of a system of parametric equations which describe complex harmonic motion. This family of curves was investigated by American mathematician Nathaniel Bowditch in 1815, and later detailed in 1857 by French physicist Jules Antoine Lissajous, hence its name.
A Lissajous curve is used in experimental tests to determine if a device may be properly categorised as a memristor. It is also used to compare two different electrical signals, a known reference signal and a signal to be tested. The curves could be generated mechanically by means of a harmonograph or using an oscilloscope.
In the 1960s and 1970s, Lissajous figures were sometimes displayed on oscilloscopes meant to simulate high-tech equipment in science-fiction TV shows and movies.
In popular culture, the title sequence by John Whitney for Alfred Hitchcock’s 1958 feature film Vertigo is based on Lissajous figures. The German Dadaist artist Max Ernst also painted Lissajous figures directly by swinging a punctured bucket of paint over a canvas in the early 20th century.