The user wants me to create a single-page web app that renders the Mandelbrot set with:
1. Smooth color gradient
2. Full-screen canvas
3. Click-and-drag to pan
4. Mouse-wheel to zoom
5. All in one self-contained index.html file
6. No external resources, CDNs, or network requests

Let me create a complete implementation with:
- Canvas filling the entire viewport
- Mandelbrot set rendering algorithm
- Smooth coloring using escape time with smooth coloring technique
- Pan functionality with mouse drag
- Zoom functionality with mouse wheel
- All CSS and JS inline

I'll use the standard escape time algorithm for the Mandelbrot set:
z = z^2 + c
where z starts at 0 and c is the pixel coordinate

For smooth coloring, I'll use the technique:
smooth_iter = iter - log2(log2(|z|)) + 4.0

Let me write this out.

I've created a complete single-page web app that renders the Mandelbrot set with all the requested features. Let me verify the file was created correctly.

Done! I've created a complete Mandelbrot set renderer in `/tmp/ws/index.html` with:

**Features:**
- **Full-screen canvas** - Fills the entire viewport and resizes automatically
- **Smooth color gradient** - Uses cosine-based palette with log-log smooth coloring algorithm for continuous gradients outside the set
- **Click-and-drag panning** - Click and drag anywhere to pan the view
- **Mouse-wheel zooming** - Scroll to zoom in/out, centered on the mouse cursor position
- **Touch support** - Works on mobile with touch drag and pinch-to-zoom
- **Keyboard controls** - Arrow keys to pan, +/- to zoom, 'R' to reset
- **Info overlay** - Shows current zoom level and center coordinates

**Technical highlights:**
- Pure JavaScript with no external dependencies
- Uses `Uint32Array` for fast pixel manipulation
- Smooth coloring formula: `iter + 1 - log(log(|z|)) / log(2)`
- Cosine-based color palette for vibrant, cycling gradients
- Black interior for points inside the set

Open `index.html` in a browser to explore the Mandelbrot fractal!