Mandelbrot explorer · north-mini-code

The user wants me to create a single self-contained HTML file that:
1. Renders the Mandelbrot set with smooth color gradient
2. Uses a full-screen canvas
3. Has click-and-drag to pan functionality
4. Has mouse-wheel to zoom functionality
5. Must be self-contained - CSS in style tag, JS in script tag, no external resources

Let me create an HTML file that does all of this. I'll write it directly to an index.html file.

I need to:
1. Create a canvas element that covers the full screen
2. Write JavaScript to render the Mandelbrot set
3. Implement smooth color gradients
4. Add click-and-drag panning
5. Add mouse-wheel zooming
6. Make it responsive and full-screen

The Mandelbrot set calculation:
- For each pixel, calculate coordinates in the complex plane
- Iterate z = z² + c where c is the complex coordinate
- If |z| exceeds 2, it's not in the set
- Use iteration count for coloring with smooth gradient

For the color gradient, I'll use a smooth gradient that transitions through colors based on the iteration count.

Let me write this all in one file.

The user asked me to create an interactive Mandelbrot set web app with specific requirements:
1. Full-screen canvas
2. Smooth color gradient
3. Click-and-drag to pan
4. Mouse-wheel to zoom

I've created a comprehensive single-file HTML solution that includes:
- CSS for styling (gradient animation, controls, info displays)
- JavaScript logic for:
  - Mandelbrot set calculation
  - Smooth color gradient animation
  - Mouse drag/pan controls
  - Mouse wheel zoom
  - Touch support for mobile
  - Window resize handling
  - FPS monitoring

The implementation uses canvas block rendering for performance and includes:
- Animated gradient that cycles through colors
- Smooth iteration calculation for better color rendering
- Real-time information display showing position, zoom, and time
- Performance monitoring with FPS counter

The file has been written successfully. I should now open it to verify the content.