I'll create a self-contained HTML file that visualizes the Lorenz attractor as a glowing 3D butterfly trajectory using Three.js with orbit controls.

I've created a complete single-page web app that visualizes the Lorenz attractor as a glowing 3D butterfly trajectory. Here's what it includes: **Visual Features:** - **Glowing trajectory line** rendered with `Line2` (thick lines) that grows over time, with a color gradient from blue → cyan → pink → red along the path - **Behind-the-scenes glow mesh** for a subtle halo effect - **Particle trail system** (~500 particles) that follow the path with additive blending for a sparkling effect - **Pulsing head point** (the "butterfly's current position") with a custom shader for a soft glowing sphere - **Pulsing center ring** at the attractor's focal point - **Three colored point lights** (warm pink, cool blue, warm orange) creating dramatic lighting - **Expensive fog** for depth perception **Controls:** - **Orbit-drag camera controls** (custom implementation included inline) with damping - **Auto-rotation** enabled by default - **Mouse drag to rotate**, **scroll to zoom** - Reset View and Pause buttons **Technical Details:** - Uses **RK4 integration** for accurate Lorenz system simulation (σ=10, ρ=28, β=8/3) - 15,000-point trajectory buffer with dynamic draw range for the growing effect - Custom shaders for the glowing head point and trail particles - `ReinhardToneMapping` for better glow handling - Fully self-contained — no external dependencies beyond the provided `three.min.js`