OneTaskBy Tim King · Updated
Lissajous Curve Generator
Plot Sine-Ratio Figures Online, Free PNG
OneTask is free, with no sign-up, and built by one person.
If this tool saved you time, a coffee helps keep new ones coming.
How the Lissajous Curve Generator works
This Lissajous curve generator draws figures from two sine waves. A Lissajous figure is what an oscilloscope shows when you feed one sine wave to the horizontal input and another to the vertical. The shape depends only on the ratio of the two frequencies and the phase between them. Set those with the sliders, watch the figure redraw, and save it as a PNG.
Lissajous curve generator: what to know first
The curve is x = sin(a·t + φ), y = sin(b·t). When a and b are whole numbers the curve closes and repeats, and the number of lobes tells you the ratio: a figure with a lobes across and b lobes down means the frequencies are in the ratio a:b. The stats line shows the ratio in lowest terms, since 6:8 draws the same curve as 3:4.
Frequencies. Ratio 1:1 is a circle, an ellipse or a diagonal line depending on the phase. 1:2 is a figure eight or a parabola. 3:4 and 3:2 are the shapes on physics posters. Large coprime ratios such as 13:17 fill the frame in a tight weave. Ratios that share a factor reduce to a simpler one, so 4:8 is just 1:2.
Phase shifts the horizontal wave relative to the vertical. At 0° and 180° a 1:1 figure collapses to a diagonal line; at 90° it is a circle. For other ratios the phase tilts and folds the figure without changing its lobe count. Sweep it slowly to see the curve appear to rotate in three dimensions, the effect that made Lissajous figures a staple of early computer graphics.
Shape. Fill frame stretches the figure to the export's aspect ratio, which is what you want for a wallpaper. Square keeps the amplitudes equal so the figure is the true mathematical shape, centred in the frame.
Colour and export. Rainbow shifts the hue along the curve so you can follow the path; Single takes one hue from the seed, and Regenerate only changes that hue because the shape is fully determined by the sliders. Save PNG re-plots the curve at the chosen size, so lines are crisp at 4K. The stats line shows the reduced ratio and the number of lobes on each axis, which is the quickest way to check that two different slider settings really do give the same figure.
FAQ
What is the difference between a Lissajous curve and a spirograph?
A spirograph curve comes from a circle rolling on a circle, so it has rotational symmetry around the centre. A Lissajous curve comes from two straight-line oscillations, so its symmetry is mirror symmetry across the axes. They can look similar at a glance but the families do not overlap.
Why does 2:4 look the same as 1:2?
Because the ratio is what matters, not the individual numbers. The page reduces the ratio in the stats line so you can see at a glance when two settings are equivalent.
How do I get the "3D rotating" look?
Set a 1:1 or 1:2 ratio and export several images with the phase stepped by 10° or so. Each frame looks like the previous one rotated slightly around a vertical axis.
Can I use this to check an oscilloscope?
Yes, as a reference: feed two signals in, count the lobes on the scope, and compare with the figure here for the ratio you expect.
See also: all Generative Art tools, Images, Audio, Video & Screen, PDF, SVG, Simulations & Screensavers, Chart Makers, 3D Model Viewers, Drawing Pads, Mockups & 3D Making, Diagram Makers, 3D Science, Tracker Music.
Related tools
Spirograph Generator
Set the ring, gear and pen offset; the curve draws until it closes.
Harmonograph Generator
Damped pendulum figures; set frequencies, detune and damping, save the spiral.
Rose Curve Generator
The r = cos(kθ) flower; set n and d, save the petals as PNG.
Wallpaper Generator
Random abstract backgrounds, six palettes, saved at desktop or phone size.
Abstract Art Generator
Random shapes, lines, blocks and splatter in five palettes, seeded.