In the classical oscilloscopic representation, a physical quantity is represented in time reference. It is different with the Lissajous figures. Here the X-axis of the oscilloscope is deflected by a sinusoidal voltage.
In Lissajous figures, the vertical and horizontal deflections are controlled by synchronous sinusoidal signals. The resulting plots show convoluted figures from which phase shifts and harmonic relationships can be determined.
If both deflections, the horizontal and the vertical, occur with the same frequency and phase, a diagonal line appears on the screen as a Lissajous figure. As the phase between the two frequencies changes, the line opens and an ellipse appears, which becomes a circle at 90° phase difference.
The Lissajous figures are named after their discoverer, the French mathematician Jules Antoine Lissajous(1822 to 1180).