Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Students · Lissajous Curves

Lissajous Curves for a Taylor approximation

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a Taylor approximation live below — adjust the inputs and watch it respond, right in your browser.

Lissajous CurvesLive

harmonic motion in two axes

Controls

Speed1×

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.

Presets

Frequency a (x)

Frequency b (y)

Phase δ (×π)

▶ Run in Python

Data Inspector

Ratio3:2

Phase0.50π

Closedrational

Governing equation

x = A sin (3 t + 0.50 π), y = B sin (2 t), 3 : 2

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.

or unlock everything with Pro →

Also for:Researchers Educators Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Lissajous Curves

Lissajous Curves for compound interest Lissajous Curves for a population curve Lissajous Curves for a loan payoff Lissajous Curves for a logistic map Lissajous Curves for a Fibonacci sequence Lissajous Curves for a fractal tree Lissajous Curves for a Fourier series Lissajous Curves for a Monte-Carlo pi estimate

Frequently asked questions

Is this good for students?: Yes — this version of "Lissajous Curves for a Taylor approximation" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.