Fluid simulation

Build an interactive 2D fluid-and-dye simulation on a full-screen canvas. Use HTML, CSS, and JavaScript as needed. Write it to `index.html` in the current working directory using your file tools. Inline your own CSS and JavaScript. Do not use external assets, CDNs, or network requests. No third-party libraries are provided. Required behavior: - Maintain a velocity field and a colored dye field. Advect dye through the moving fluid so it forms persistent swirling flow; a collection of independent fading particles is not sufficient. - Dragging injects dye and momentum in the drag direction. Momentum and dye remain visible after the pointer is released and gradually dissipate. Approximate fluid behavior is acceptable; choose the numerical method and Canvas 2D or WebGL implementation. - Seed the initial scene with a small amount of colored dye and motion so the simulation is visible on load. - Provide a color selector, Pause/Resume, and Clear. Clear removes dye and resets velocity; the next drag can start a new flow. - Bound simulation resolution and work per frame so controls remain responsive at a 1200 by 800 viewport. Verify: Drag through the canvas and sample the flow after release. Check that dye follows the drag, continues swirling, and responds to a second drag in another direction. Use Clear, then drag again to check that a fresh flow can start.