Lissajous Curves Grid
Controls
Grid Size: 8x8
Cell Size: 80px
Animation Speed: 1.0x
Phase Shift: 0.00π
Waveform Editor
Drag points to customize the selected waveformEach cell shows a Lissajous curve with frequency ratio A:B (row:col). Sine wave creates circles on diagonals. Try 3:2 or 2:3 ratios with phase shift π/2 (0.50π) to see hexagons! Triangle wave creates hexagon-like shapes. Square wave creates rectangle-like shapes.
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About Lissajous Curves
Lissajous curves are complex harmonic motions created by combining two perpendicular sinusoidal oscillations. The shape depends on the frequency ratio and phase difference between the two oscillations.
Formula:
x(t) = A × sin(a×t + δ)
y(t) = B × sin(b×t)
Where a:b is the frequency ratio shown in each cell (row:column).
x(t) = A × sin(a×t + δ)
y(t) = B × sin(b×t)
Where a:b is the frequency ratio shown in each cell (row:column).