Level 5-1

Lissajous Explorer

Change the frequency ratio and watch beautiful Lissajous patterns emerge. Discover the relationship between a, b, and curve shape.

0 /9 Stars

0 /3 Tasks

Tasks

Move the sliders and discover beautiful Lissajous patterns. Earn up to 3 stars per task!

Make a figure-eight (set a = 1, b = 2). Task 1

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Create a 3:2 Lissajous pattern (a = 3, b = 2). Task 2

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Make the simplest Lissajous — a circle (a = b = 1). Task 3

Explore

Start with Double the Frequency to see how changing the frequency ratio reshapes the curve, then explore phase shifts and combined ratios.

Tip: In Lissajous curves (x, y) = (sin(a·t + δ), sin(b·t)), the ratio a/b determines the pattern shape and δ (phase) rotates it.