Lissajous Figures

Lissajous figures are complex, symmetric patterns created when two sinusoidal waves—like vibrations or oscillations—are combined at right angles, each with its own frequency and phase. When these waveforms are plotted on an oscilloscope or graph, the result is a unique, colorful shape that reflects the relationship between the two signals. These figures help visualize how different frequencies and phase differences influence wave interactions, often used in physics, engineering, and music to analyze vibrations, signals, or musical tones. The shapes can range from simple circles and ellipses to intricate, star-like patterns.