The user wants me to create a single-page web app that visualizes the Lorenz attractor as a glowing 3D butterfly trajectory. The key requirements are:

1. Use the pre-provided three.min.js (global THREE)
2. Visualize the Lorenz attractor
3. Make it a glowing 3D butterfly trajectory
4. Draw over time (animated)
5. Orbit-drag camera controls (orbit controls)
6. Everything in a single index.html file
7. No external resources, CDNs, or network requests
8. CSS in <style> tag, JS in <script> tag

The Lorenz attractor is defined by these differential equations:
dx/dt = σ(y - x)
dy/dt = x(ρ - z) - y
dz/dt = xy - βz

Common parameters are:
σ = 10
ρ = 28
β = 8/3

I'll need to:
1. Set up a Three.js scene with a dark background
2. Create points/lines for the trajectory
3. Use a glowing effect (maybe with additive blending and point colors)
4. Animate the drawing over time
5. Add orbit controls for camera interaction (but since we can't use external resources, I'll need to implement basic orbit controls manually)

Let me create this file.

I've created a single-page web app that visualizes the Lorenz attractor as a glowing 3D butterfly trajectory. Let me summarize what I built:

1. A Three.js scene with a dark background and fog for depth
2. The Lorenz attractor implemented with the classic parameters (σ=10, ρ=28, β=8/3)
3. A multi-layered glow effect using:
   - A line with additive blending for the main trajectory
   - A points mesh with additive blending for the glowing dots
   - A glow mesh with larger, more transparent points for the outer glow
   - A bright "head" sphere with a point light that follows the current point
4. Color gradient based on position and time (hue cycling)
5. Custom orbit controls implementation (since we can't use external resources) that supports:
   - Mouse drag to rotate
   - Scroll wheel to zoom
   - Touch support for mobile
   - Auto-rotation when not dragging
6. UI elements showing point count and time step
7. Instructions for user interaction
8. Responsive design with window resize handling

The trajectory draws over time, creating the classic butterfly shape of the Lorenz attractor, with a beautiful glowing effect that makes it look like it's emitting light.