Lissajous Explorer

Curve Parameters

Frequencies (a, b, c)

Amplitudes (A, B, C)

Phase Shifts (δ)

Damping (λ)

Visuals

Color

Line Thickness

Grid Thickness

Grid Brightness

Glow Intensity

Anti-Aliasing

Animate Phase Shift

Enable Audio

Camera

Information

This explorer simulates 3D Lissajous curves based on the following parametric equations for damped harmonic motion:

Parameters

Frequencies (a, b, c): The integer ratios between the oscillation frequencies on each axis. These determine the fundamental shape and number of "lobes" of the figure.

Amplitudes (A, B, C): The maximum displacement of the curve along each respective axis.

Phase Shifts (δ): The initial angle (in radians) of each oscillation. This effectively "rotates" the figure in 3D space by changing its starting point.

Damping (λ): Controls the rate of exponential decay of the amplitude, causing the figure to spiral inwards over time. A value of 0 results in an undamped, stable figure.