Fork of Fork of 3D Cube of Spheres
This interactive 3D visualization explores wave equations, rendering a 10x10x10 grid of spheres whose size and color represent wave amplitude at each point. Users can switch between Helmholtz, membrane wave, Schrödinger, and wave packet solutions through a dropdown menu, adjusting wavenumber and animation speed. Built with Three.js and OrbitControls, the animation computes numerical solutions to each equation in real time, mapping amplitude to sphere scale and hue. The rotating, zoomable view responds to click-and-drag interactions, with lighting provided by directional and ambient light sources.
AI-generated descriptionWave Equation Explorer
This interactive 3D visualization allows you to explore various wave equations in physics and mathematics.
Features
- Multiple wave equations: Helmholtz, membrane waves, Schrödinger equation, and wave packets
- Interactive controls: Adjust wave parameters in real-time
- 3D visualization: Explore the wave behavior from any angle
Wave Equations
Helmholtz Equation
The Helmholtz equation is used in physics to describe standing waves:
∇²ψ + k²ψ = 0
Where ∇² is the Laplacian operator and k is the wavenumber.
Membrane Wave
A classical wave equation representing vibration of a membrane:
∂²ψ/∂t² = c² (∂²ψ/∂x² + ∂²ψ/∂y²)
Schrödinger Equation
The time-dependent Schrödinger equation describes how the quantum state of a physical system changes:
iħ ∂ψ/∂t = -ħ²/(2m) ∇²ψ + Vψ
Wave Packet
A wave packet combines multiple waves to create a localized wave:
ψ(x,t) = A e^(-(x-x₀)²/(2σ²)) e^(i(kx-ωt))
Usage
- Use the dropdown menu to select different wave equations
- Adjust the wavenumber slider to change the wave frequency
- Modify the animation speed with the speed slider
- Click and drag to rotate the view
- Scroll to zoom in and out
Technical Details
This visualization uses Three.js for 3D rendering and implements numerical solutions to the various wave equations. The wave amplitude at each point is represented by both the size and color of the spheres.
Performance Note
The visualization creates a full 3D grid of spheres (10x10x10 by default), which may affect performance on less powerful devices. If you experience lag, try reducing the grid size in the config object.