A Lissajous curve is a complex pattern formed by the intersection of two perpendicular harmonic oscillations. These curves are typically represented on a graph, where one oscillation is plotted along the x-axis and the other along the y-axis. The shape of the curve depends on the frequency ratio and phase difference of the two oscillations. Lissajous curves can be generated using an oscilloscope or a parametric equation. They are often used in physics and engineering to visualize waveforms and analyze the behavior of oscillating systems. The curves can take on various shapes, including loops and intricate designs, depending on the parameters used.