We need to build a single-page web app with Gray-Scott reaction-diffusion simulation. The simulation should run on a canvas, showing organic Turing patterns that grow in real time, with mouse seeding new growth.

We must write everything into one self-contained file named index.html in the current directory. Use CSS in a <style> tag, JS in a <script> tag, inline. No external resources.

We need to produce the file. We'll first check current directory and then write index.html.

Let's start by listing directory to see if there's anything.

We need to create index.html. We'll write the HTML content.

We need to implement Gray-Scott reaction-diffusion. Typically we have two chemicals U and V. The simulation updates using finite difference. Parameters: Du, Dv, feed, kill. We'll have a grid size, maybe 256x256 or 512x512. We'll render to canvas using pixel data.

Mouse seeding: when mouse is pressed or moved, we can set a spot to higher V (or lower U) to seed pattern.

We'll need to implement a simulation loop using requestAnimationFrame.

We'll also allow maybe adjusting parameters via GUI? Not required but could be nice. However, the spec just says run simulation with mouse seeding new growth. So we can keep it simple.

We'll produce a self-contained HTML file.

Let's craft the HTML.

We'll have a canvas element filling the window. CSS to set display: block; width: 100vw; height: 100vh; maybe touch-action: none.

JS: we'll create two arrays for U and V (maybe Uint8ClampedArray for pixel data). Actually we need floating point for reaction-diffusion. We'll use two Float32Arrays.

We'll implement the Gray-Scott equations:

 Laplacian via 5-point stencil: (U_left + U_right + U_top + U_bottom - 4*U_center) / (dx^2). Assuming dx=1.

Update:

U += (Du * laplacian_U - U*V*V + feed*(1-U)) * dt
V += (Dv * laplacian_V + U*V*V - (feed+kill)*V) * dt

We'll set dt = 1.0 maybe.

We'll need to clamp U and V between 0 and 1.

Initialize: U = 1 everywhere, V = 0 except a small rectangle seed in the center (or random noise). Then as mouse moves, we add V at mouse position.

Rendering: map U and V to grayscale or color. Common visualization: show V as brightness, or show U as red, V as blue, etc. We'll do something like: color = (V * 255) for grayscale.

We'll put pixel data into ImageData and putImageData.

We'll also handle mouse move to seed: when mouse down, we add V in a radius around mouse.

We'll also maybe allow clearing with right click or space.

Let's write code.

We'll need to resize canvas on window resize.

We'll implement.

Now we need to write the file. We'll use write tool.

But before writing, we might want to test? Not possible because we cannot run a browser. However we can trust.

Let's create the file.

We'll write the content step by step.

We'll use write tool to create index.html.

Let's do it.

We have created index.html. Let's verify file exists and maybe check a snippet to ensure it's correct.

We'll read first few lines.

We have the file. The task is to build a single-page web app and write it all into one self-contained file named index.html in the current directory. We've done that.

We should ensure there are no external resources. The file uses only inline CSS and JS, no external links.

Thus the task is complete.

We can now respond that we have created the file.

We'll output final.