The user wants me to create a Matrix digital rain effect as a single-page web app. Let me break down the requirements:

1. Full-screen black canvas
2. Columns of falling green katakana glyphs
3. Trailing fade effect
4. Brighter leading character
5. Everything in a single index.html file
6. No external resources or CDNs

I need to:
- Create a canvas element that fills the screen
- Use JavaScript to animate the falling characters
- Use katakana characters (Japanese characters)
- Create the trailing fade effect by drawing characters with decreasing opacity
- Make the leading character brighter
- Use green colors for the Matrix effect

Let me create this step by step:
1. HTML structure with canvas
2. CSS for full-screen black background
3. JavaScript for the animation logic

I'll use requestAnimationFrame for smooth animation and create multiple columns with different speeds and positions.

Perfect! I've created a Matrix digital rain effect with all the requested features:

1. Full-screen black canvas - The canvas fills the entire viewport with a black background
2. Columns of falling green katakana glyphs - Using Japanese katakana characters plus some alphanumeric characters
3. Trailing fade effect - Each character in the trail has decreasing opacity creating a fade effect
4. Brighter leading character - The leading character is bright white-green with a glow effect, the second character is bright green, and the rest fade to darker green

Additional features I included:
- Random speeds for each column
- Random trail lengths
- Occasional character changes while falling for a more dynamic effect
- Responsive canvas that resizes with the window
- Smooth animation using requestAnimationFrame
- Shadow/glow effects for the leading characters

The effect runs completely self-contained with no external dependencies, just as requested. The file is saved as index.html in the current directory.