Lissajous curve is built from parametric equations where the x and y coordinates are sinusoidal. The resulting motion can produce harmonic, complicated math graphs which eventually terminate in a point.

In this case, Lissajous curve was created by a combination of sin and cos waves. Here you can see how 2 signals are mixed.

 

 

In my experiment with Lissajous curve, I also found these beautiful polygonal patterns.

 

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