3D Lissajous Figures

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These 3D Lissajous figures are parametric curves, where each of x(t), y(t), and z(t) is a sine function. If the ratios of their frequencies are rational, the curve will always eventually close. If one or two of the ratios is irrational, the curve will never close and eventually will fill a 2D or 3D region. Click and drag to rotate the 3D graphic.

Contributed by: Stephen Wolfram (March 2011)
Open content licensed under CC BY-NC-SA


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