Parametric equations
A Lissajous curve has the form
- A and B are the amplitudes on x and y. This figure keeps A = B, so the orbit stays inside a square.
- a and b are the frequencies. The ratio a:b is the ratio of those two controls, and it sets the crossings and the complexity.
- δ is the phase difference. It sets the symmetry and the sense of rotation or opening.
Interaction
- Frequency a: change the integer frequency on x and watch the crossings of the ratio a:b
- Frequency b: change the integer frequency on y. The ratio a:b is these two controls
- Phase δ: drag the phase difference. The orbit deforms continuously between a locked shape and a twisted one
What to notice
- Only the reduced ratio matters: 2:4 draws the same curve as 1:2. The larger the reduced pair a:b, the more lobes and crossings, and the more of the square the curve covers. A simple ratio stays more symmetric.
- changes how the figure sits against the axes. It does not change the ratio a:b.
- With A = B the orbit stays inside a square, which makes different ratios a:b easy to compare.
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