Lissajous Curves

Definition

Lissajous curves are geometric graphs of a system of parametric equations that describe complex harmonic motion, produced when x and y coordinates oscillate with sinusoidal frequencies and a phase difference.

Key Characteristics

• Defined by x = A * sin(at + d), y = B * sin(bt)
• Frequency ratio (a/b) determines the number of loops and visual symmetry
• Phase delta (d) rotates the curve in apparent 3D space

Applications

• Oscilloscope graphics and laser vector art
• Parametric path drawing in creative computation
• Synthesizer phase visualization

Related Concepts

• harmonograph
• damped-harmonic-oscillation

Related Entities

• jules-antoine-lissajous
• karl-sims

Mentions in Source

• “Lissajous curves visually demonstrate the ratio of frequencies between orthogonal oscillatory axes.” — harmonograph-simulation-and-mathematical-drawing