The elegant loops you see on an oscilloscope. Combine two perpendicular oscillations and vary their frequency ratio and phase.
Lissajous CurvesLive
harmonic motion in two axes
Controls
Combine two perpendicular sine waves. The frequency ratio a:b sets the number of lobes; the phase δ morphs the shape — the patterns you see on an oscilloscope.
Reading this result: Reduced to 3:2, the curve closes into a stable 3-by-2 lobe figure; because the ratio is a whole-number fraction it never drifts, and the phase δ only morphs and rotates that fixed pattern.
Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.
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How it works
A Lissajous figure plots x = sin(a·t + δ) against y = sin(b·t). The integer ratio a:b sets how many lobes appear, and the phase δ continuously morphs the shape. They visualize the relationship between two harmonic oscillations — used historically to measure unknown frequencies.
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Ask the AI about this model
The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
Yes. Lissajous Curves runs entirely in your browser using your device's own compute, so local use is free forever. You only pay Compute Tokens if you scale a job to the cloud.
Do I need to install anything?▾
No. Everything runs client-side in a modern browser — no downloads, no license, no account required to start.
Can I save or share my simulation?▾
Create a free account to save projects, and use a shareable embed or minted DOI to publish a live, interactive version anywhere.
How accurate are the results?▾
The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.