Fluid simulation · qwen3.8-max-0902

Let me build a WebGL fluid simulation (Stam-style stable fluids with Jacobi pressure solve) or Canvas 2D. WebGL is better but more code. Let me do WebGL with a simplified version.

Actually a Canvas 2D grid-based Navier-Stokes at, say, 128x128 resolution could work and be simpler to debug. But quality/performance... 1200x800 viewport, grid 160x107 or so. Advection + diffusion + projection with Jacobi iterations ~20. That's 17k cells * 20 = 340k operations per frame — fine in JS.

Rendering: draw dye field to an offscreen ImageData at grid resolution, then drawImage scaled up to canvas with smoothing. That's cheap.

Let me go with Canvas 2D grid simulation. Resolution bound: cell size ~ 6px → 200x133 = 26k cells. Jacobi 20 iterations = 530k ops. Should be OK at 60fps. Let's use cell size 8 → 150x100 = 15k cells.

Let me write it.

Fields: u, v (velocity), r,g,b dye, plus pressure/divergence temp arrays. Use Float32Array.

Steps per frame:
1. Add forces from pointer.
2. Diffuse velocity (viscosity) — can skip or do a few Jacobi iterations.
3. Project (divergence + Jacobi pressure + subtract gradient).
4. Advect velocity (semi-Lagrangian).
5. Project again.
6. Advect dye.
7. Fade dye and velocity (dissipation).

Use staggered? No, collocated grid is fine with projection.

Boundaries: no-slip / free-slip — set velocity normal component zero at walls, dye zero gradient.

Initial seed: a few colored blobs with vorticity.

UI: color selector (swatches + native color input), Pause/Resume, Clear, maybe dye size. Keep simple.

Let me write the code carefully.

Grid indexing: idx = i + j*N where i in [0,N), j in [0,M). N = cols, M = rows.

Advect: for each cell, trace back: x = i - dt*u[idx]*scale. Need velocity in grid units per second. Let's store velocity in grid-cells/second. Then backtrace with dt directly.

Pointer force: drag delta in pixels → convert to cells: dx/cellSize. Force magnitude scaled.

Let me write.

Rendering: ImageData of size N x M, put pixels from dye, then ctx.drawImage(offCanvas, 0,0, W,H) with imageSmoothingEnabled = true. Also draw a slight background.

Handle resize: recreate grids preserving nothing (or resample). Just reinit on resize debounced.

Let me write the file.

Colors: color selector — set of preset swatches plus <input type="color">. Also a "rainbow" option cycling hue.

Let me code it.

Details for Jacobi pressure solve:
div[idx] = -0.5*(u[idx+1]-u[idx-1] + v[idx+N]-v[idx-N])  (with h=1)
Solve Laplacian p = div: p_new = (p_left+p_right+p_up+p_down - div)/4 ... careful signs. Standard: p = (pL+pR+pB+pT + div)/4? Let's define div = -0.5*((uR-uL)+(vT-vB)). Then Jacobi: p = (pL+pR+pB+pT - div*... ). 

Standard Stam: 
div[i] = -0.5*h*(u[i+1]-u[i-1]+v[i+N]-v[i-N]) with h=1/N... Let me just use h=1:
div = -0.5*(uR-uL+vB-vT)
p = (pL+pR+pT+pB + div)/4  — wait, Laplacian p = div means pL+pR+pT+pB-4p = div → p = (pL+pR+pT+pB - div)/4.

Hmm, which? The projection: we want u_new = u - grad p, with div u_new = 0 → div u = Laplacian p. div u = 0.5*(uR-uL+vB-vT) = D. So Laplacian p = D, p = (pL+pR+pT+pB - D)/4.

Then u -= 0.5*(pR-pL), v -= 0.5*(pB-pT).

I'll define D = 0.5*(uR-uL+vB-vT), p = (sum neighbors - D)/4, subtract gradient. Good.

Set p=0 at boundaries (Neumann would be better but Dirichlet at walls is acceptable-ish; actually Neumann: p boundary = p of adjacent interior). I'll copy interior to boundary for p, and set normal velocity 0 at walls.

Vorticity confinement would enhance swirl. Let's add a mild vorticity confinement step — it makes it look great and keeps swirling persistent. Compute curl, then force = eps * (N x grad|curl|).

Let's implement:
curl[idx] = 0.5*((vR-vL) - (uB-uT))
grad of |curl|: dwdx = 0.5*(|c[idx+1]| - |c[idx-1]|), dwdy = 0.5*(|c[idx+N]| - |c[idx-N]|)
len = sqrt(dwdx^2+dwdy^2)+1e-5
fx = eps * (dwdy/len) * c[idx]
fy = eps * (-dwdx/len) * c[idx]
Hmm standard: N = grad|w|/|grad|w||, force = eps * (N × w) → in 2D: f = eps * (Ny*w, -Nx*w). Yes.

Add to velocity.

Dissipation: dye *= 0.995 per frame-ish; velocity *= 0.999.

OK, write.

Also add touch support via pointer events.

Let me write the HTML now.

For performance, typed arrays and flat loops.

Time budget 15 min; let's write it in one go.

Code structure:

```js
const cvs = document.getElementById('c');
const ctx = cvs.getContext('2d');
let N, M, size; // cols, rows
let u,v,u0,v0,r,g,b,r0,g0,b0,p,div,curl,imgData,off,offctx;

function alloc(){...}
function resize(){ cellSize computed; W,H from window; N = clamp(round(W/CELL),...); allocate; seed? }
```

Preserve dye on resize? Simpler: on resize keep fields but re-create; if size changed, just reset. Debounce resize.

Simulation loop with requestAnimationFrame, dt fixed clamp to 1/60 or actual clamped.

Let me write everything.

Pointer handling: track pointer position, compute dx,dy in cells; splat velocity with radius, splat dye with color.

splat(x, y, radiusCells, amountFn): loop over bounding box, gaussian falloff.

For dye splat: add color * falloff (additive, clamp to like 3).

Rendering: putImageData into offscreen canvas at N x M then drawImage scaled.

Alpha: dye amount → color = min(255, r*255). Use alpha 255 with black background.

Also maybe render dye with a slight additive glow. Keep simple: background dark, dye bright.

UI styling: floating panel top-left with swatches, color input, buttons, and a hint text.

Write now.

Edge: `imageSmoothingEnabled = true` on ctx for upscaling — gives smooth look. Good.

Let me also add a "brush size" slider? Not required. Skip; maybe add swirl/force slider? Not required. Keep minimal but add a small "Dye" amount? Skip.

Write file.

Initial seed: create a few splats with different colors and velocities in a rotational pattern, plus a couple of vortex pairs.

Let me produce code.

For clear: zero all fields, then maybe reseed? Spec says Clear removes dye and resets velocity; next drag can start new flow. So clear = all zeros (no reseed).

Pause/Resume: pause stops sim stepping but still renders (or just stops rAF updates). Keep rendering so canvas stays; ignore drags while paused? Better: while paused, don't step physics but still allow? I'll ignore splats while paused too (or queue them, applied on resume). Simplest: ignore.

Now write.

Bounds check in advect: clamp x,y to [0.5, N-1.5].

Advection of velocity uses same semi-Lagrangian.

Let me write the final code.

Also handle DPR for crisp UI — the canvas is the sim, drawn at N x M resolution upscaled, so DPR doesn't matter much; set canvas width/height = window inner size (CSS pixels) maybe * min(dpr,1.5)? Since we upscale from grid anyway, just use CSS pixel size to keep cost low. Actually canvas backing store at CSS size is fine.

Let me write it.

Performance: N x M with CELL=7 at 1200x800 → 172 x 115 = 19780 cells. Jacobi 24 iterations → 475k cell updates per projection, two projections → ~1M. Plus advect/dye. In JS that's maybe 8-15ms. Hmm, borderline. Let's do CELL=8 → 150x100 = 15000, Jacobi 20 iterations, one projection per frame (advect velocity then project once). Typical order: addForces, vorticity, project, advect velocity, project, advect dye. I'll do a single project after advection plus one before — let's just do: forces → vorticity → advect velocity → project → advect dye. One projection, 24 iterations = 360k ops. Fine.

Also skip velocity diffusion (use small numerical dissipation from advection). Good.

Let's write.

Time to write the file.

Note: advectDye dissipation uses dt*60 pow — fine.

One issue: `splat` uses SPLAT array but never clears it; unused, fine.

Bug: in splat, velAmt scaling — `dxCells*w*velAmt` with velAmt ~ forceAmt*0.35/steps + forceAmt*0.12. For steps=1: 12*0.35+12*0.12 = 4.2+1.44=5.64. dxCells for a fast drag might be ~5 cells per frame → u += 5*5.64 = 28 cells/s. That's quite fast but semi-Lagrangian is stable. Actually too fast may cause huge backtrace. dt=0.016, backtrace distance = 28*0.016 = 0.45 cells. Fine.

Hmm, wait: velocity is in cells per second, backtrace uses dt*u → ok.

But is 28 cells/s reasonable? A drag moves dx pixels per frame; in cells it's dx*(N/W). If user drags 100 px/frame (fast), dcells = 100*(150/1200)=12.5 cells. times 5.64 = 70 cells/s → backtrace 1.1 cells/frame. Acceptable but the dye may not keep up. Let's reduce velAmt factor a bit — maybe scale so injected velocity roughly matches the pointer speed: u += dxCells * w * (forceAmt/6). With forceAmt=12 → factor 2. Hmm, still >1.

Actually matching pointer speed means factor 1. Slightly amplifying gives punchy feel. Let's use velAmt = forceAmt*0.08 (=0.96 at 12) plus interpolation division. Let me restructure: total velocity impulse should be about dxCells*factor regardless of steps, so divide by steps: velAmt = (forceAmt*0.09)/steps... but each substep adds at a different location, and total momentum should roughly sum to the full impulse. So per step: factor/steps. And dye similar: dyeAmt total per frame constant → /steps.

Let me simplify: compute once per move: velFactor = forceAmt*0.09/steps, dyeFactor = 0.9/steps.

Also the pointerdown splat with dye 0.9 is fine.

Let me edit that part.

Also: `dyeAmt` clamp R>4 fine.

Another consideration: advectDye's dissipation pow(DYE, dt*60) — DYE_DISSIPATION=0.9965 → at 60fps per frame 0.9965, half life ~198 frames ~3.3s. That's fast fading; "gradually dissipate" — maybe make it slower: 0.999 → half life 693 frames ~11.5s. Let's use 0.9985 (~7.7s half-life). Velocity dissipation 0.9985 → also ~7.7s half life, but vorticity confinement keeps it going. Let's use 0.999 for velocity.

Let me apply edits and then test in browser.

Now test in browser. The browser tool runs index.html.

The scene loads with seeded dye blobs. Good. Next, test dragging: use the browser's drag action, then take a screenshot. Also check the fps text. Let's drag from (400,500) to (700,300).

The drag injected a magenta streak, and the seeded blob got distorted by the flow (swirling). 56 fps. Good. Next, wait a bit and check the persistence of the swirl after release: take a screenshot after a few frames (the motion action displays frames over time). Use the "motion" action? That captures motion frames. Let's just take a screenshot after a short delay — the browser's screenshot is immediate. Use motion to see evolution over time.

After release, the dye keeps advecting/swirling and slowly dissipates. Motion continues between frames. Good.

Observations:
1. The dye looks somewhat dark/faded (magenta streaks turn into a dull maroon). The dye fades to about 50% in 2 seconds. Maybe I should slow the dissipation a bit and boost brightness. DYE_DISSIPATION 0.9986 → per-second factor 0.9986^60 ≈ 0.92. Over 2 seconds ≈ 0.84. But the streaks look darker than expected—this is because the dye spreads out (advection diffusion) and the value of 190*val saturates. The initial streaks were bright (clamped). After spreading, values drop. That's natural.

2. FPS fluctuates between 44–56. Acceptable but could be improved. The main costs are Jacobi 22 iterations over 15000 cells = 330k + advection. Plus rendering. 44 fps on this headless VM is decent. Might be able to reduce ITER to 18. Well, it's fine.

3. Visual "checkerboard/star-shaped" artifacts: I see star-shaped streaks around the blobs (from vorticity confinement?). Looks like small cross-shaped spikes. Probably from the initial global drift sin/cos pattern + confinement. Acceptable.

Next tests: second drag in a different direction, then Clear + drag. Also test pause/resume.

Let me drag in a different direction (e.g., from (900,600) to (500,650)) and take a screenshot.

The second drag created a new streak in a different direction, and the old dye is still faintly visible. Good.

Next, click the Clear button, take a screenshot to confirm it's empty, then drag again with a different color (select the cyan swatch first), and verify the new flow and color selection.

Clear worked — the canvas is completely black. Next, select the cyan swatch (the 2nd one, position around (71,66)) and drag to confirm the new flow.

Cyan has been selected (the swatch is highlighted, and the picker has been updated). Next, drag to create a new flow.

A new cyan flow is starting after Clear. The color selector is working.

Next, testing Pause/Resume: click Pause, drag, confirm no new dye appears; click Resume and confirm it moves again. Quick check: click Pause, take a screenshot of the DOM text (the button should display "Resume"), then take a screenshot after a motion frame to confirm it's static.

The pause button shows "Resume" and is highlighted. The dye field is frozen mid-swirl (vortex rings visible). Next, check whether it stays static: grab a motion frame during pause? The motion action captures 4 frames over about 2 seconds. If paused, the frames should be identical. Let's run motion.

Pause freezes the simulation (frames are identical over about 2 seconds). Resume should restart it. Click Resume and confirm that motion resumes.

Resumed (button is back to "Pause"). The fps label is still showing "paused" but that's because the 0.5-second update hasn't fired yet — no problem.

Remaining checks:
- Console is clean (only sandbox warnings from the harness iframe, not from my own code).
- Resize behavior: might be able to test but optional. The resize handler reallocates and reseeds. Risk: on resize, alloc() resets buf32 to black — no problem.
- One point: in `resize()`, when the size doesn't change, return false early. When it does change, alloc() — but the seeded scene is only reseeded on resize events, not on the initial call (I'm calling seedScene() after resize()). OK.

Potential issue: `handleMove` on pointerdown calls handleMove(e) with st just set (dx=0) → no problem.

Edge case: pointerdown while paused: sets pointer, handleMove returns early due to paused. No problem.

Minor improvement: dye brightness — the scene looked good.

One more check: confirm that resuming actually animates (motion frames should differ). Quick motion check.

Resumed: the dye continues to advect and fade. All required behaviors have been verified.

One concern: the dye fades fairly quickly (the cyan streak becomes quite dark in about 2 seconds). The spec says "gradually dissipate" — this is fine, but the brightness after diffusion looks somewhat dark. The dissipation rate is 0.9986^60 ≈ 0.92/sec, so most of the darkening is due to the dye spreading out. It's within acceptable range, but I could bump up the rendering gain a bit (190 → maybe use a soft tone map). Let me improve it slightly: use r = 255*(1-exp(-R*1.1)) tone mapping for a smoother, brighter look. This is a small change:

let r = 255*(1-Math.exp(-R[k]*1.15)); etc. Math.exp per cell ×3 = 45k exps per frame — no problem.

This makes the mid-range values brighter and looks better. Let me apply it and do a quick re-check with a new seed.

Also, the fps label update after resume is working.

Apply the tone mapping edit, reload, and take a screenshot to confirm the seed is visible.

Wait — the buf32 index: the ImageData buffer is N*M pixels, and buf32[k] corresponds to pixel k. Previously it was using k directly, which is correct.

Reload and check.

The seeded scene loads brighter. Drag once more to confirm that the tone-mapped dye looks good and that the fps is within acceptable range.

Brighter, more vivid dye. On this headless VM, 44 fps (on real hardware it should be faster. The grid is limited to 150×100 = 15k cells, and the per-frame processing is also limited).

All required behaviors verified:
- Velocity + dye field, dye advected by the fluid (streaks bend/swirl, and the seeded vortex deforms) ✓
- Drag injects dye + momentum in the drag direction. Persists after release and gradually dissipates ✓
- Initial seed on load ✓
- Color selector (swatches + custom + rainbow), pause/resume, clear ✓
- Clear resets, and new drags work ✓
- Resolution/workload limits (150×100 grid, 22 Jacobi iterations, dt clamp) ✓
- Console: no errors (only harness sandbox warnings) ✓

Unverified: touch pointer input, window resize re-seeding, rainbow mode, keyboard shortcuts, brush/force sliders — code paths exist but untested. Time is fine (about 6 minutes used). Could quickly test the resize with the browser tool but... can't easily change the viewport. Skip. Quickly test the rainbow toggle? Click the rainbow swatch and drag. A quick check is cheap.

The rainbow swatch is currently selected (has a border). Drag to confirm the rainbow hue cycling.

Rainbow mode cycles hues along the stroke (red → orange gradient visible). All good.

Final state of the file is saved. Wrapping up.

Things I confirmed:
- On load, the seeded scene (5 colored vortices + drift) renders
- Drag injects dye + momentum along the drag direction; streaks follow the pointer
- After release, the dye keeps advecting/swirling (motion frames differ), and gradually fades
- A second drag in a different direction generates a new streak, and the old flow continues
- Clear → canvas goes completely black; a new drag starts a new flow in the selected color
- Color selection: swatches (magenta→cyan verified), rainbow hue cycling also verified; the custom picker is wired up (not directly verified)
- Pause freezes the field (identical frames for about 2 seconds), Resume restarts it
- Grid is capped at 150×100 at 1200×800; fps 44–60 in the headless environment
- No console errors from the app

Unverified: touch/multi-pointer input, window resize re-seeding, custom color picker input, brush/force slider effects, keyboard shortcuts (Space/C), panel collapse. These are simple DOM handlers, so risk is low.