WOLFRAM|DEMONSTRATIONS PROJECT

Lissajous Figures

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horizontal frequency
1
vertical frequency
1
relative phase
π
4
length
100
show axes
Lissajous figures are parametric curves where both x(t) and y(t) are sine functions. If the ratio of the frequencies is rational, the curve will always eventually close. If it is irrational, the curve will never close and eventually fill a region.