Lissajous Curve Visualizer

This project is a simple web-based application that visualizes Lissajous curves. Lissajous curves are parametric equations that describe complex harmonic motion, often used in physics and mathematics to study waveforms and oscillations. Learn more about Lissajous curves on Wikipedia.

Features

• Interactive Controls: Adjust parameters such as:
  • ωx (frequency along the x-axis)
  • ωy (frequency along the y-axis)
  • θ (phase shift)

How It Works

The Lissajous curve is defined by the following parametric equations:

• x = a * sin(ωx * t + θ)
• y = b * sin(ωy * t)

Where:

• a and b are the amplitudes.
• ωx and ωy are the angular frequencies.
• θ is the phase difference.

The application uses the HTML5 <canvas> element to draw the curve and JavaScript to handle the animations and user interactions.

How to Use

1. Open the index.html file in any modern web browser.
2. Use the sliders on the right side of the screen to adjust the parameters:
   • ωx: Frequency along the x-axis.
   • ωy: Frequency along the y-axis.
   • θ: Phase shift.
3. Watch the Lissajous curve update dynamically on the canvas as you adjust the sliders.

Screenshots

Lissajous curve with ωₓ = 1, ωᵧ = 2, and phase shift θ = 0.

Lissajous curve with ωₓ = 1, ωᵧ = 1, and phase shift θ = 120.

Lissajous curve with ωₓ = 2, ωᵧ = 3, and phase shift θ = 0.

Acknowledgments

This project is inspired by the mathematical beauty of Lissajous figures and their applications in physics and engineering.