Lissajous figures

Lissajous figures are produced in two dimensions when the x and y coordinates are given by two sine waves, which may have any amplitude, frequency and phase. x(t)=a sin(ωt+δ); y(t)=b sin(t)

When the two sine waves are of equal frequency and in-phase, you get a diagonal line to the right . When the two sine waves are of equal frequency and 90 degrees out-of-phase you get a circle. If the two sine waves are in phase but the frequency of the horizontal sine wave is twice the frequency of the vertical sine wave you get the pattern similar to infinity symbol.