The user wants me to create a single-page web app that runs a Gray-Scott reaction-diffusion simulation on a canvas. This should display organic Turing patterns in real time, and the mouse should be able to seed new growth.

Let me break down what I need to do:
1. Create a single HTML file called `index.html` in the current directory
2. The web app should have:
   - A canvas element
   - Gray-Scott reaction-diffusion simulation
   - Real-time animation of organic Turing patterns
   - Mouse interaction to seed new growth
   - All CSS in a <style> tag, all JS in a <script> tag (no external files)
   - No external resources or network requests

The Gray-Scott model is a reaction-diffusion system that produces patterns similar to those found in nature. The basic equations are:

DU/DT = Du * ∇²U - U*V² + F*(1-U)
DV/DT = Dv * ∇²V + U*V² - (F+k)*V

Where:
- U and V are chemical concentrations
- Du, Dv are diffusion rates
- F is the feed rate
- k is the kill rate

I'll need to:
1. Set up the HTML structure
2. Implement the Gray-Scott simulation algorithm
3. Add mouse interaction for seeding
4. Use requestAnimationFrame for real-time rendering
5. Make it all self-contained in one file

Let me create the index.html file with all the necessary code.

The user asked for a Gray-Scott reaction-diffusion simulation with:
1. Real-time organic Turing patterns
2. Canvas that grows patterns
3. Mouse seeding new growth
4. All in a single self-contained HTML file

The code I wrote creates a complete Gray-Scott simulator with:
- Interactive UI controls for all parameters
- Mouse interaction for seeding (click and drag)
- Real-time rendering
- Auto seed option
- Responsive canvas sizing
- Beautiful color coding for chemicals U (blue) and V (red)
- Instruction panel
- Reset functionality

Key features:
- Uses the standard Gray-Scott reaction-diffusion equations
- Implements proper Laplacian calculation for diffusion
- Creates circular mouse seeds when clicking/dragging
- Color mapping for visualization
- Real-time animation loop
- Responsive design that works on mobile and desktop
- Local storage (no network dependencies)

The file is written to /workspace/index.html and should run immediately in any modern browser.