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Fork of 3D Cube of Spheres

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NNita
Last edited Mar 31, 2025
Created on Mar 31, 2025
Forked from 3D Cube of Spheres

A 3D grid of spheres animates a solution to the Helmholtz wave equation, with each sphere’s radius and color representing the wave amplitude at that point in space. The visualization uses Three.js with WebGL rendering and OrbitControls for camera navigation. Spherical Bessel functions and spherical harmonics compute the wave values, which oscillate over time to show standing wave patterns in three dimensions.

AI-generated description

Helmholtz Wave Equation Visualization

This visualization demonstrates the Helmholtz wave equation in 3D space. The equation is a partial differential equation that describes wave propagation:

∇²A + k²A = 0

Where:

  • ∇² is the Laplacian operator
  • A is the wave amplitude
  • k is the wave number (related to frequency)

Visualization Details

In this visualization:

  • Each sphere represents a point in 3D space
  • The size/radius of each sphere represents the wave amplitude at that point
  • The color spectrum (blue to red) also indicates the wave value
  • The animation shows how the wave evolves over time

Mathematical Implementation

The visualization uses solutions to the Helmholtz equation in spherical coordinates:

  • Spherical Bessel functions for the radial component
  • Spherical harmonics for the angular components
  • Time-dependent oscillation factor

These components are combined to create a physically accurate representation of standing waves in 3D space.

Controls

  • Use your mouse to rotate the view
  • Scroll to zoom in and out
  • Click and drag to pan
MIT Licensed

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