Fluid simulation · gemini-4-argon
Output generated Cost / run $0.3132 Runtime 726.1s
Prompt for this run
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.
TAKE IT TO CODE
A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.
RUN
METRICS
Transcript · 92 messages
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.
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index.html (29641 bytes)Successfully wrote to index.html
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{"action":"open"}Validation failed for tool "browser": - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant Received arguments: { "action": "open" }
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{"toY":350,"action":"drag","y":350,"x":450,"toX":900}Frame 1, +1ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n25 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"click","x":108,"y":140}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n24 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"drag","toX":500,"x":800,"toY":650,"y":250}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n24 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"click","y":395,"x":220}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n25 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"text":"c","action":"keypress"}Validation failed for tool "browser": - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant - action: must be equal to constant Received arguments: { "text": "c", "action": "keypress" }
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{"path":"index.html","edits":[{"newText":" function clearSimulation() {\n pointer.down = false;\n pointer.id = null;\n Successfully replaced 2 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n5 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"click","y":395,"x":220}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n22 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"edits":[{"newText":" canvas.addEventListener('pointerdown', (e) => {\n if (e.button !== undefined && e.button !== 0) return;\nSuccessfully replaced 2 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n7 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"click","x":220,"y":395}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n24 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"x":450,"toY":320,"toX":850,"y":480,"action":"drag"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n22 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"click","y":395,"x":64}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n22 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"edits":[{"newText":" colorPicker.addEventListener('input', (e) => {\n rainbowToggle.checked = false;\n setColorHex(e.taSuccessfully replaced 1 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n10 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"y":395,"action":"click","x":64}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n22 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"path":"index.html","edits":[{"newText":" canvas.addEventListener('pointerdown', (e) => {\n if (e.button !== undefined && e.butSuccessfully replaced 3 block(s) in index.html.
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{"path":"index.html","edits":[{"oldText":" pauseBtn.addEventListener('click', (e) => {\n e.stopPropagation();\n togglePauSuccessfully replaced 1 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n6 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"y":395,"action":"click","x":220}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n22 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"edits":[{"oldText":" const hudPanel = document.querySelector('.hud');","newText":" const hudPanel = document.querySelector('.hudSuccessfully replaced 1 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n10 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"x":220,"y":395,"action":"click"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing.","log: EVENT pointerdown: 220 395 ","log: EVENT mousedown: 220 395 ","log: EVENT click: 220 395 "],"dom":"Eulerian Fluid & Dye\n22 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"path":"index.html","edits":[{"newText":" const hudPanel = document.querySelector('.hud');","oldText":" const hudPanel = documentSuccessfully replaced 1 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n8 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"click","x":220,"y":395}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n21 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"path":"index.html","edits":[{"newText":" let lastActionTime = -1000;\n function canTriggerAction() {\n const now = perforSuccessfully replaced 1 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n9 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"y":395,"action":"click","x":220}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n19 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"edits":[{"oldText":" function handleGlobalPointerOrClick(e) {\n if (hitElement(pauseBtn, e.clientX, e.clientY)) {","newText":"Successfully replaced 1 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n10 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"y":395,"x":220,"action":"click"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing.","log: HIT CHECK: pointerdown 220 395 clearBtn rect: 222.328125 300 308.984375 332","log: HIT CHECK: click 220 395 clearBtn rect: 222.328125 300 308.984375 332"],"dom":"Eulerian Fluid & Dye\n24 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"path":"index.html","edits":[{"oldText":" let lastActionTime = -1000;\n function canTriggerAction() {\n const now = perforSuccessfully replaced 1 block(s) in index.html.
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{"action":"reload"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n8 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"x":260,"action":"click","y":316}Frame 1, +0ms
[Browser image supplied to model]
{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n24 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Idle","images":"attached"}
10 minutes have elapsed. At most 5 minutes remain. Finalize the output as soon as possible: save index.html now, fix only essential issues, and finish.
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{"toX":850,"x":450,"action":"drag","toY":300,"y":450}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n25 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"x":64,"action":"click","y":316}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n24 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nResume\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Paused","images":"attached"}
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{"y":316,"x":64,"action":"click"}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n58 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
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{"action":"click","y":115,"x":110}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n22 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Idle","images":"attached"}
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{"y":316,"action":"click","x":162}Frame 1, +0ms
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{"console":["warning: An iframe which has both allow-scripts and allow-same-origin for its sandbox attribute can escape its sandboxing."],"dom":"Eulerian Fluid & Dye\n16 FPS\nDye Color\n#00E5FF\nCycle hue while dragging\nVorticity (Swirl Confinement)\n28\nDye Persistence\n99.2%\nBrush Radius\n18 px\nPause\nSeed\nClear\nDrag anywhere on the canvas to inject momentum and dye. Keyboard: Space Pause/Resume, C Clear.\nGrid: 240×160\nFlow: Swirling","images":"attached"}
Built a self-contained 2D Eulerian Navier-Stokes fluid-and-dye simulation in `index.html`. ### Features Implemented - **Velocity & Colored Dye Fields**: Uses a grid-based incompressible fluid solver (`240×160` bounded resolution at `1200×800` viewport) with semi-Lagrangian backward-trace advection, Gauss-Seidel Helmholtz-Hodge pressure projection, and vorticity confinement for persistent swirling vortices. - **Interactive Pointer Injection**: Dragging across the canvas injects directional momentum into the velocity field `(u, v)` and colored dye into the `(r, g, b)` channels, which continue swirling and gradually dissipate after release. - **Initial Seeded Flow**: Seeds four opposing multi-colored dye jets on load so swirling flow is immediately visible. - **Controls**: Includes a native color picker, preset color swatches, optional hue cycling while dragging, Vorticity/Persistence/Brush Radius sliders, **Pause/Resume**, **Seed**, and **Clear**. ### Verification Summary - **Checked**: - Verified initial load renders the seeded multi-color swirling fluid with zero console errors. - Dragged across the canvas from `(450, 350)` to `(900, 350)` and then in a second cross direction from `(800, 250)` to `(500, 650)`, confirming dye follows the drag direction, forms persistent swirling vortices, and responds to subsequent drags. - Clicked **Clear** and verified that all dye and velocity reset (`Flow: Idle`) and that dragging again starts a fresh flow. - Clicked **Pause** / **Resume** and **Seed** to verify simulation state toggling and re-seeding. - **Unverified**: Multi-touch pinch/mobile gesture edge cases and long-duration (>5 minute) numerical drift.