For K-12 Students · Lissajous Curves
Lissajous Curves for a fractal tree
Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a fractal tree live below — adjust the inputs and watch it respond, right in your browser.
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.
Presets
Data Inspector
Ratio3:2
Phase0.50π
Closedrational
Governing equation
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.
More with Lissajous Curves
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Frequently asked questions
- Is this good for k-12 students?
- Yes — this version of "Lissajous Curves for a fractal tree" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.