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Lissajous Pattern


A Lissajous curve in mathematics, also known as Lissajous Figure or Bowditch curve is the graphical representation of the following system of parametric equations.

x = A sin(at + δ)
y = B sin(bt)

These curves/patterns are highly sensitive to the values of a and b, particularly to the ratio a:b. For a ratio of 1, and δ = \frac{π}{2} radians, the figure is a circle. Similarly, for a = b and δ = 0, the figure is a line.
Another simple Lissajous figure is the parabola (\frac{b}{a} = 2, δ = \frac{π}{4}).



Fun Fact

The title sequence by John Whitney for Alfred Hitchcock's 1958 film Vertigo is based on Lissajous figures.

Last update: December 25, 2021