Visualize Skill: Interactive 3D Math & Science Visualizer

Takes any concept from mathematics or science and creates an interactive, visually stunning, browser-based 3D visualization using Three.js, packaged as a single self-contained HTML file.

The visualization is grounded in real mathematical formulations and physical laws—not just decorative graphics, but a live, interactive simulation or geometric construction that users can rotate, zoom, tweak with sliders, and inspect in real time.

Inputs

The user provides:

1. Concept: Any mathematics or science concept. For example:
   • Math: Eigenvalues & Eigenvectors, 3D Linear Transformations, Gradient Descent on Surfaces, Curl & Divergence of Vector Fields, Riemann Surfaces, Möbius Strip & Topology, Fourier Epicycles in 3D, Lorenz Attractor & Chaos, Spherical Harmonics, Minimal Surfaces (Helicoid/Catenoid).
   • Science: Lorentz Force, Gravitational Orbits & Precession, Double-Slit Wave Interference, Maxwell-Boltzmann Distribution, VSEPR Molecular Geometry, Quantum Harmonic Oscillator, DNA Replication Fork.
2. Depth: One of three simple depth levels (default to Intermediate if not specified):
   • Simple (Level 1 — Intuition & Big Picture)
   • Intermediate (Level 2 — Mechanics & Equations)
   • Advanced (Level 3 — Deep Dive & Rigorous Internals)