Fluid simulation · qwen3.8-flash

I'll build a stable-fluids solver (Jos Stam style) on WebGL2. Let me look at the directory first.

Empty directory. I'll write index.html with a WebGL2 fluid solver (Stam's stable fluids: advect velocity, add forces, project via Jacobi pressure solve, advect dye, dissipate).

Let me plan the implementation carefully.

Approach: WebGL2 with float textures (EXT_color_buffer_float / renderable float). Simulate at e.g. 256x256 (capped resolution based on aspect) for velocity/pressure, dye at maybe 512. Actually keep it simple: one sim resolution scaled to aspect ratio, capped so max dimension <= ~384. Use RG float for velocity, RGB(A) float for dye, R float for pressure/divergence.

Steps per frame:
1. Input: if pointer down, splat dye + velocity at pointer position based on drag delta.
2. Advect velocity (semi-Lagrangian with dissipation factor for "gradual dissipate").
3. Add force already added via splat.
4. Compute divergence.
5. Jacobi iterations for pressure (e.g. 20-30).
6. Subtract pressure gradient from velocity.
7. Advect dye with velocity, with slight dissipation.
8. Display: render dye texture to screen with a fullscreen quad, maybe add velocity-based shading.

Also add curl/vorticity confinement for nicer swirls — optional but good for "persistent swirling". Let's add vorticity confinement (compute curl, then force). That gives swirls that persist. Keep cost reasonable.

Fallback: if WebGL2 float unavailable, fall back to CPU Canvas2D solver at low resolution (e.g. 96x96 with imageData). That's a decent safety net. Given time budget, I'll implement a compact CPU fallback too. Hmm — that doubles work. The prompt says choose the implementation; a robust WebGL2 with fallback to CPU 2D is nice but risky. I'll implement WebGL2 primary and a simple CPU 2D fallback (Stam in JS on a small grid) — actually the fallback code is ~120 lines. It's worth it for safety in case WebGL isn't available in the test browser. Let me check the browser environment first with a quick test.

Let me first write the WebGL version and test in the browser tool to see if WebGL2 + color_buffer_float works.

UI:
- Color selector: a set of color swatches + a native <input type="color">.
- Pause/Resume button.
- Clear button.
- Maybe a "swirl strength"/ dissipation slider — not required; keep minimal but include dye fade info. I'll add small extra: "Auto-splat" maybe not. Keep required controls plus maybe intensity slider? Don't clutter. I'll include color swatches, color picker, pause/resume, clear.

Display of colors: dye is RGB stored in float texture; splat adds color * amount with gaussian falloff. Clamp with tone mapping (1 - exp(-x)) in display.

Seed initial scene: do several splats with random colors and velocity in the init (before first frame), plus the sim auto-advects. Also seed a gentle initial velocity field.

Pointer handling: pointerdown/move/up with pointer capture; support touch. Map client coords to sim coords.

Paused: stop stepping but keep rendering; still allow input? Requirement: Pause/Resume. When paused, freeze. I'll still allow dye injection? Simpler: when paused, don't step simulation, but continue to render (no update). Splats accumulate and appear when resumed. Actually to be safe, when paused, skip the whole update including splats (but queue?). I'll allow splats to be applied while paused so the user sees injection? Hmm, if paused and no step, the dye texture still updates so the splat shows up in the render — that's fine and demonstrates "injection". I'll apply input splats even when paused (render loop runs, no physics steps). That's reasonable.

Resolution cap: sim res based on aspect: SIM = 192 (velocity) maybe, dye 512? Using two resolutions requires a blit and different texel sizes in advection — standard implementations do that. To keep it simpler and bounded, use single resolution: e.g. width scaled so that max dimension = 256 (with 1200x800 viewport → 256x171 → hmm must be careful about texel aspect). Let's compute: aspect = W/H. If aspect>=1: simH = 220, simW = round(220*aspect) capped at 384... For 1200x800, aspect 1.5 → simW=330, simH=220 → 72600 cells, 30 Jacobi iterations = ~2.2M fragment ops per pressure solve — trivial for GPU. Fine.

Dye at same res is fine; display upscaled bilinearly (looks smooth). Maybe dye at 2x for crispness. I'll use dye = 2x sim res? Advection of dye samples velocity texture (different texel size) — in GLSL with separate textures and normalized coordinates it's fine if I compute offsets in texel units per-pass. Let's just use same resolution for both to reduce bug risk, and use a display that's smooth. 330x220 dye upscaled to 1200x800 will look blurry-ish but smooth — acceptable for fluid look. Hmm, quality matters for "forms persistent swirling flow". Blur is fine, fluids are smooth. But I'd like crisper dye. I'll do dye resolution = 2x sim with careful handling: use `texelSize` uniform per program, and velocity sampling by normalized uv. Semi-Lagrangian advection: newP = uv - dt * vel * texelSize_of_the_field_being_advected? Standard: velocity stored as cell units per second... Let me define velocity in units of "sim-cells per second". Then advecting dye at 2x sim res: displacement in dye texels = vel * (dyeTexelSize / simTexelSize) ... Actually displacement in normalized uv = vel * simTexelSize (since vel in sim-cells/sec → uv/sec = vel/simCells = vel*simTexelSize). Then in the dye pass, sample at uv - dt*vel*simTexelSize — computed from the same uv, so no need for dye texel size for advection offsets. For gradient/diffusion ops in dye, use dyeTexelSize. Simpler: pass `uTexel` of the source field for offsets in each program. Let me do the uniform approach: each program gets `uTexelSize` (of the texture being sampled/processed) and `uDt`.

Advection shader (shared for velocity & dye):
```
vec2 coord = vUv - uDt * vel * uSourceTexel; // uSourceTexel = 1/simCells
```
where for velocity pass uSourceTexel = simTexel, for dye pass also simTexel (since velocity is in sim cells/sec) — same! Great, so both use simTexel. Just need to clamp dt and use bilinear filtering (texture float linear requires OES_texture_float_linear for float32; half-float linear is core in WebGL2? In WebGL2, half-float (RGBA16F) is filterable by default (texture float linear extension needed for 32F). So use RGBA16F/RG16F/R16F for all fields → filterable, and requires EXT_color_buffer_float to render. Half float precision is decent for fluid. Velocities small values ~ fine. Use 16F.

But pressure Jacobi with 16F: pressure values could grow; ok.

Fallback if EXT_color_buffer_float missing: use 8-bit RGBA with encoding? Too much. I'll fall back to CPU Canvas2D solver.

Plan for CPU fallback: grid N x M with Float32Array fields (u,v, u0,v0, r,g,b,...). Stam solver with 20 Gauss-Seidel iterations, resolution ~ capped to total cells <= 6000 (e.g. 96x64). Render into ImageData scaled up. This is real code but let's include a compact version. Given the 15-min budget and that the browser likely supports WebGL2, I'll implement fallback only if time permits. Actually risk: the browser tool environment might lack GPU but have swiftshader — usually fine. Let me test with a tiny probe first.

Let me write the main file now with WebGL2 and then probe. I'll structure code so a WebGL failure shows a message, and add CPU fallback if quick.

Vorticity confinement:
- curl pass (R16F): curl = 0.5*(dvy/dx - dvu/dy) using velocity texture.
- vorticity force pass: N = grad(|curl|) normalized; force = eps * cross(N, grad(curl)); add to velocity * dt.
Cost: 2 extra passes. Include with curl strength slider? I'll fix a constant and maybe expose "Swirl" slider — nice but optional. I'll add a "Curl" slider — small effort, and it demonstrates controls responsiveness. Keep it minimal: I'll add swatch colors, Pause/Resume, Clear, and a "Swirl" range input. Actually the required list is color selector, pause/resume, clear. Extra slider is fine.

Display shader: dye color with slight background gradient, plus optional velocity-based tint. Use:
```
vec3 c = texture(uDye, uv).rgb;
c = 1.0 - exp(-c * 1.6); // tone map
// subtle background
```
Add "bloom-ish" skip. Also add glow of velocity magnitude faintly? Skip for clarity.

Splat shader: additive: `color = texture(src,uv) + uColor * exp(-dist2/radius2)`. For velocity splat use RG texture with vec3 color → need to write into RG16F: use `vec2(splat)`. I'll write one splat program using `uIsDye` flag? Simpler: two programs sharing source, one outputs vec4 (RGBA16F dye) and one outputs vec2 (RG16F velocity). Actually use `out vec4 fragColor; ... fragColor = vec4(value, 0/1)`. For RG16F target, writing vec4 with z,w ignored is fine (only 2 components used). So one program works for both with vec3 uValue: dye → uValue.rgb; velocity → vec2(uValue.xy). Great, single splat program used with different uniforms.

Divergence: from velocity → R16F.
Pressure: Jacobi from divergence + pressure.
Gradient subtract: velocity - grad(pressure) → new velocity.
Curl: velocity → R16F (signed).
Vorticity: needs curl texture and velocity → output velocity add.

Number of FBOs: ping-pong for velocity (2), dye (2), pressure (2), plus single divergence, single curl. Use a helper `createDoubleFBO`.

Also handle canvas resize with devicePixelRatio cap for display (renderbuffer sizes): display canvas at CSS size * min(dpr, 2). Sim grids fixed on resize (recompute aspect, but re-alloc on resize loses contents — acceptable; do a debounced resize that reinitializes and re-seeds? Better: on resize keep sim grid as-is (grid aspect mismatch slightly distorts — fine). I'll create sim grid from initial aspect and only recreate display buffers on resize. Good, avoids losing the sim.

Time step: dt = min(frameTime, 1/30) fixed 1/60 style. Use dt = 0.016 constant-ish scaled. Velocity magnitude in cells/sec: splat velocity = dragDelta(in uv) * ... Let's compute: pointer delta in normalized uv per event; multiply by e.g. 900 → cell units. We'll tune empirically: splat force = delta_uv * FORCE_SCALE where velocity is in sim cells/sec → delta_uv * simCells. Let's just define velocity in "uv per second" units and advection offset = dt * vel (in uv) directly, with uSourceTexel = 1 (i.e. offsets in uv units). Hmm but then divergence/pressure gradient operators need consistent cell spacing. Standard approach: treat velocity in cell units. Let me define velocity stored in "sim cells per second". Advection: coord = uv - dt*vel*uTexel(sim). Pressure poisson: use grid spacing h=1 (cell units): laplacian = (pL+pR+pU+pD - 4p)/h^2, divergence = ((uR-uL)+(vD-uU))/(2h). Jacobi: p = (pL+pR+pU+pD - div)/4. Vorticity similar in cell units. Velocity splat from drag: delta in cells = (dx_uv * simW, dy_uv * simH) times gain ~ (1/dt-ish). We'll tune gain so it feels responsive: vel contribution = deltaCells * 6? Let's think: a drag of 100px horizontally at 1200 wide → dx_uv ≈ 0.083 → cells ≈ 0.083*330 ≈ 27 cells per event. With ~several events per frame. If we set velocity = 27 * 4 ≈ 108 cells/sec, then per frame displacement = 108/60 ≈ 1.8 cells — reasonable flow. Multiply by dt in advection, so ok.

Note y direction: WebGL uv y goes up if we render quad with v coordinate; pointer y is down. To keep it intuitive, I'll flip dy so that drag downward adds downward velocity in the field, and display so that the sim's top corresponds to screen top: sample dye with v = 1 - screenY? Simplest: set vUv such that uv.y = 1 - gl_FragCoord.y/H in display... Actually in the standard fluid demos they just invert pointer y and the sim's y axis is up (matching GL). Then everything drawn via splat uses inverted y and it appears under the cursor. Let's do: uv = (x/W, 1 - y/H) for pointer; and the display quad maps directly. Then the fluid "up" in the y direction is screen up because we inverted pointer y consistently. Advection directions computed with the same convention — a velocity +y moves dye toward uv.y increasing = up on screen. Since we inject velocity from pointer movement with dy inverted, dragging down gives negative y velocity → moves toward lower uv.y = down on screen. Consistent. 

Let me now write the code.

Display shader also draws faint grid/vignette. And maybe show velocity as thin streaks? Skip.

I'll write the file now.

Also: dissipation — velocity dissipation ~0.995/frame-ish scaled by dt; dye dissipation ~0.985 so "gradually dissipate". Use factor per frame: value *= pow(dissipation, dt*60)? Standard: `texture * (1.0 + dt*-dissipation)`. I'll do `exp(-dt*rate)` in shader with uniform `uDissipation` (rate/sec). Velocity rate ~0.18, dye rate ~0.35. Persistent swirls: with pressure projection and vorticity confinement, keeps moving for several seconds. Good.

Clear: zero velocity & dye & pressure via a clear program (or gl.clearTo on FBOs). Also seed: keep small ambient? Clear should remove dye and reset velocity — do exactly that, no auto reseed. Next drag starts new flow.

Seed on load: 4-6 splats with random-ish colors and velocities.

Also handle keyboard? Not needed.

Now, also need to guard: `gl.getExtension('EXT_color_buffer_float')` for rendering to float; `OES_texture_float_linear` needed only for 32F. 16F linear filtering is core in WebGL2? Per spec, texture filtering of half-float is supported (filterable) in WebGL2 core. Yes: in WebGL2, RGBA16F is color-renderable only with EXT_color_buffer_float, and texture-filterable always. Good.

If WebGL2 unavailable → show CPU fallback. I'll write the CPU fallback compactly as a second implementation. Let's decide after probing WebGL availability. I'll write WebGL first, probe, and if it works add a minimal fallback (message + simple CPU solver if time).

Let me write the code.

Sim grid sizing: 
```
const QUALITY = 'balanced' -> 
let SIM_H = 190, SIM_W = round(190 * aspect) clamp [80, 320]... 
```
Let's set: base = 208; if aspect >= 1: simH = base, simW = round(base*aspect); else simW = base, simH = round(base/aspect). Cap max dimension 384. Dye: 2x with cap 768 → dyeW = min(simW*2, 700). Fine, dye is just advection + display, cheap.

For dye advect program, need simTexel for offsets, and its own texel for... nothing else. OK.

Splat radius: in uv terms relative to width: radius = 0.0018 area... Standard: use `uRadius` in uv units (of the target texture space) with aspect correction. Let's implement splat with:
```
vec2 d = uv - uPos; d.x *= uAspect;
float g = exp(-dot(d,d)/ (uRadius*uRadius));
```
where uRadius in uv (0..1 vertical). radius ≈ 0.05 for dye, similar for velocity. But since dye texture is 2x aspect same normalized, fine.

Careful: splat program runs on target texture FBO so vUv covers full target — aspect is canvas aspect which equals sim aspect (same ratio) → good.

Write it.

Programs list:
1. base (quad) vertex shader with vUv.
2. advect (vel, dye): sampler src(field), sampler velocity, uniforms uDt, uTexelSim, uDissipation, uIsDye? Only difference: which texture is velocity. Use two texture units: uTex (the thing being advected) and uVelocity. Same program can handle both! For velocity self-advection, bind velocity read to uTex and same texture to uVelocity — need to bind same texture to two units; that's allowed (not read-writing same). Yes: FBO writes to velocityB while both uTex and uVel sample velocityA. Fine. But texel for offsets always simTexel, so uniform uTexel = simTexel. And for dye we want slight dissipation & maybe lower filtering — same. 

Also exponential splat uses `uAspect`.

3. divergence: velocity → R16F.
4. curl: velocity → R16F.
5. vorticity: curl (abs computed inside) + velocity → velocity, using uCurlTex and uVelocity... needs neighbors of |curl|. Output velocity += dt*force.
6. pressureJacobi: pressure + divergence → pressure.
7. gradientSubtract: velocity + pressure → velocity.
8. splat: src → dst with additive.
9. display: dye (and velocity for tint) → canvas.
10. clear: sets to uColor (multiplicative zero) — reuse splat? Write simple `copy/clear` program.

Also maybe "diffusion" of velocity (viscosity) — skip; numerical diffusion from advection suffices.

Passes per frame: advect vel, curl, vorticity, divergence, 24 jacobi, grad subtract, advect dye, display ≈ 30 draws. Fine.

Ordering: standard: splats → (curl, vorticity) → advect → divergence → pressure → gradient subtract → advect dye.

Now write everything, including the HUD UI, styling.

Color selector: swatches (e.g. 6 colors) + native color input + "mode: rainbow auto-cycle"? Requirement: "Provide a color selector". I'll do swatch buttons with active state, plus `<input type="color">` for custom. The chosen color affects dye injected.

HUD: top-left panel with title, buttons row, color row, sliders (Swirl/curl strength, Fade). Keep tidy, semi-transparent dark panel. Also hint text "Drag to inject dye and momentum".

Now write file. I'll be careful with GLSL ES 3.00 syntax: `#version 300 es` must be first line, `in/out`, `texture()`, `out highp vec4 fragColor`.

Let me write the whole thing.

Display: canvas element sized to window with devicePixelRatio; CSS full screen; the HUD overlays.

Handle resize: recreate display framebuffer/canvas size only.

Implementation details for framebuffer creation:

```js
function createFBO(w,h,internalFormat,format,type,filter){...}
function createDoubleFBO(...)
```
Formats: velocity: RGBA16F? Use RG16F with FORMAT_RG, type HALF_FLOAT. R16F for pressure/div/curl with FORMAT_RED.

Note: rendering to R16F requires EXT_color_buffer_float; if missing, fallback to RGBA16F for everything (needs EXT_color_buffer_half_float in WebGL1, but in WebGL2 EXT_color_buffer_float covers both). I'll write code: if ext available use 16F single/double channel formats; else try RGBA16F with ext... if no ext at all → CPU fallback.

Let's write the code now. Also need `gl.texParameteri` LINEAR for velocity/dye/pressure? Pressure filtering doesn't matter (uses exact neighbors) — NEAREST for pressure/div/curl to be safe (bilinear on neighbor offsets ±texel exactly hits texel centers, fine either way). Use LINEAR for velocity and dye (needed for advection).

CPU fallback: I'll include a compact 2D stable-fluids solver used when WebGL2/float unavailable. Let me write it after main path works, if time permits (probably ~80 lines). Given the browser tool likely has WebGL2, I'll include a simple message fallback and write the CPU solver only if time remains. Actually, robustness: I'll implement the CPU fallback since it also serves as verification alternative... Let's first test WebGL.

Writing the file.

I got sloppy — I wrote an incomplete/messy draft with issues (P.splatRGB not defined, P.copy not defined, unused dbl `reset` referencing clearTo before definition is fine, weird duplicate uniform calls, placeholder stage). Let me rewrite the whole file cleanly and completely, including the CPU fallback and main loop. Better to write a full clean version in one go.

Design final:
- One script: `main()` tries WebGL backend, else CPU backend.
- Programs: add splatRGB (vec3) and splat2 (vec2) and copy.
- Main loop with fixed-ish dt, fps counter, stats via readback (readback every ~30 frames; that stalls GPU — do it sparingly, every 30 frames maybe fine, but readPixels of 64x40 with float conversion... To keep it simple and cheap, skip readback and estimate activity from tracked splats? The stats panel "dye % / speed %" would be nice for verification though — and useful for my own testing via console. I'll expose a `window.__fluid` API for testing: `probe()`, `clear()`, `seed()`, plus a way to simulate a drag from JS (so I can verify with the browser tool's console/type). Actually I can simulate drags via real pointer events dispatch in the browser tool? The browser tool has click/drag actions — drag from x,y to toX,toY should generate pointermove events. Good, real drag works.

For probe, readPixels per frame is a stall; do every 20 frames. Fine at these sizes.

Let me write clean code carefully.

WebGL details:
- formats: velocity RG16F (or RGBA16F fallback), pressure/div/curl R16F (or RGBA16F).
- Note: for RG16F, `gl.readPixels` needs format RG → supported in WebGL2. Yes RG/ RG_INTEGER allowed for RG16F? readPixels implementation format must be RGBA typically; WebGL2 allows format RG for RG16F? The spec table: for internal format RG16F, readableFormats are RG and... Actually WebGL2 says readPixels format must be RGBA unless internal format allows (via getFormats). Safer: for probe, copy fields into RGBA16F/RGBA8 textures and read RGBA. I'll use a probe copy program that handles both (sampling .xy or .xyz and writing vec4) — but I need two different programs since source formats differ. Write `copyDye` (source RGBA) and `copyVel` (source RG) → both output to RGBA16F, read RGBA float. Use a single program with uniform `uMode`? Just sample `texture(...)` and take .xyz — for RG source, .z is 0, .w is 1. So one program works: out = vec4(texture(src).xyz, 1). Good.

readPixels with gl.FLOAT from RGBA16F target: allowed (RGBA + FLOAT is always in the list for WebGL2? The spec: readPixels format RGBA, type FLOAT is supported for all color-renderable formats? In WebGL2, the implementation-format/type pairs must come from the "format and type" table; RGBA+FLOAT is listed as valid. Yes, RGBA/FLOAT is in the table.)

Simplify: allocate probe FBOs once (64x40 RGBA16F) and reuse.

CPU fallback: implement Stam solver:
- grid W,H with total cells cap ~ 8000 (e.g. 110x74).
- fields: u,v,u0,v0,dyeR,dyeG,dyeB + p,div,use Gauss-Seidel (in-place) 18 iters.
- advect semi-Lagrangian bilinear.
- splats gaussian.
- vorticity confinement optional (cheap-ish) — include simple version.
- Render: draw to offscreen ImageData of grid size, then put into a small canvas and drawImage scaled to full canvas with smoothing.
- Boundary: free-slip (set normal velocity 0 at walls) - important for swirl containment.
- Probe: compute mean dye and mean |vel| directly from arrays.

Both backends expose: name, init, resize(rebuild), step(dt), clear, seed, probe, applyInput (drain pending).

Let me structure the frame loop:
```
let last=performance.now(), acc=0;
function frame(now){ let raw=(now-last)/1000; last=now; const dt=Math.min(Math.max(raw,1/240),1/40); if(!state.paused) sim.step(dt); render(); stats; requestAnimationFrame(frame)}
```
For WebGL: step includes splats+render. When paused: still drain pending (apply splats) and render — so I need to separate input/render from physics. Restructure WebGL: `applyInput(dt)`, `physics(dt)`, `draw()`. step(dt) = applyInput+physics+draw. For paused: applyInput + draw only.

Hmm, when paused and injecting dye, the splats show up — good demonstration.

CPU fallback similar.

Advection dt clamp: keep velocities bounded with clamp in splat and a max velocity clamp in advect output (clamp to ±2000 cells/s).

Let me write final file now. Careful and complete.

One more: `dbl` object using getters with swap. Fine.

Splat radius for velocity should be a bit larger than dye: 0.06 vs 0.045.

Tune push gain: dx (uv per step-event) * gain * simW... Let's reason: drag 100px over 1200 width → dx_uv total 0.0833. Interpolated over up to 8 steps: each queued event has dx/steps. Sum per frame ≈ full delta. Velocity added at splat center = dx_uv*gain*simW = 0.0833*12*6*330 ≈ 1980 cells/s. Too high (1980/60 = 33 cells/frame → advection CFL explodes, semi-Lagrangian is stable but smear-y). Reduce: gain factor = state.push * 0.9? Let's target peak velocity ~ 150 cells/s for a brisk drag. 0.0833 * K * 330 = 150 → K ≈ 5.4. So velocity = dx_uv * simW * K where K ≈ push*0.45 (=12*0.45=5.4). And the gaussian adds on top of existing at that texel (overwrite-ish accumulates over multiple events in one frame; each splat adds full value → several events per frame with 8 interpolation steps means sum over 8 events each with dx/steps... total contribution = sum of dx_i * K ≈ total_dx * K = 0.0833*5.4 ≈ 0.45 cells... wait units: dx_i * gain * simW summed = total dx_uv * gain * simW ≈ 150? No: sum over events of (dx_i/steps... ) I set dx = dx/steps in the interpolation, so sum of dx_i = dx total. Then total added = 150-ish... but gaussian overlap at a given texel is only from nearby events. Roughly fine. Then it's just an accumulation of ~150 max at a texel. Good enough; I'll tune after visual check.

Note the splat gaussian multiplies by exp(-d²/r²) with d in uv-scaled units.

Also clamp velocity magnitude in advect: o = vec4(clamp(prev,-2000,2000)*fade) — apply only for velocity; dye positive anyway. Use clamp for both, harmless.

Let me write.

I left a broken/incomplete cpuBackend. Decision: either finish the CPU backend properly or remove it and show a clear message. The requirement is a working app; a half-broken CPU function is dead code but still gets *called* only when WebGL fails. However the code `return { name: ... }` in cpuBackend is unreachable garbage. Better: write a proper, compact CPU backend. But time. Alternatively remove cpuBackend entirely and show a message if WebGL2 unavailable. Since the grader runs in a browser likely with WebGL2, but robustness matters if the headless env lacks GPU. Let me first test WebGL availability in the browser tool. If WebGL works, I'll implement a solid CPU fallback anyway (compact, correct) since it's a real risk with swiftshader lacking float render targets.

Let's test now.

Start a static server (or use file:// directly). The browser tool says "Run index.html" — presumably it opens the file. Let me just call browser inspect/screenshot.

Good news: WebGL2 context works (it got to shader compile). Shader error at line 12 of a fragment shader: "vector field selection out of range" with 'z'. That's FS_SPLAT? Let me see: the failing shader starts with `#version 300 es\nprecision highp float;\n  in vec2 vUv; out vec4 o;` — line 12 issue. Which program? Programs are created in order: advect, splat, div, curl, vort, press, gradsub, display, con, copy.

FS_ADVECT: line numbering: 1 #version, 2 precision, 3 in vec2 vUv; out vec4 o;, 4 vec2 bcl..., 5 uniform sampler2D..., 6 uniform vec2 uTexel..., 7 void main(){, 8 vec2 v..., 9 vec2 coord..., 10 vec3 prev..., 11 o = vec4(clamp(prev...), 3000.0), 1.0);, 12 }. Hmm.

Actually the error is 'z' field selection out of range — selecting .z on a vec2. Where do I do `.z` on a vec2? In FS_SPLAT: `uniform vec2 uPoint, uVA, uVB;` then `vec3 add = (uCh > 2.5) ? vec3(uVA, uVB.z) : vec3(uVA, 0.0);` — uVB.z on vec2 → invalid. Fix: use `uVB.x`.

Let me count FS_SPLAT lines: 1 version, 2 precision, 3 in/out, 4 bcl, 5 uniform sampler2D uSrc;, 6 uniform vec2 uPoint, uVA, uVB;, 7 uniform float uRadius, uAspect, uCh;, 8 void main(){, 9 vec2 d..., 10 float g..., 11 vec4 base..., 12 vec3 add = ... uVB.z → line 12. Yes! That's it.

Fix: `vec3(uVA, uVB.x)`.

Also fix the CPU backend — I'll write a proper complete CPU fallback. Let me first fix the shader and see it run, then decide on the CPU fallback based on remaining time (I have ~13 min). Actually the WebGL path works in this browser, so the fallback is insurance. I'd rather write a correct, compact CPU fallback than a broken stub. Let me do it after verifying the main path.

Also in FS_DISPLAY I have a leftover weird line: `vec2 p = (vUv - c0) * vec2(1.0/ (1.0/g.x), 1.0/(1.0/g.y));` then overwritten by `p = (vUv - c0) * g;`. Clean that up.

Also note: the streak overlay `p` should be aspect-corrected maybe; fine.

Let me fix the shader bug.

Now also replace the broken cpuBackend stub with a proper fallback. Let me write a complete, compact CPU stable-fluids solver using padded (W+2)x(H+2) arrays.

Design (Stam):
- W,H interior cells; arrays size (W+2)*(H+2).
- fields: u,v (velocity), tmpU,tmpV, dyeR,dyeG,dyeB, tmpR,tmpG,tmpB, p, div, curl.
- IX(i,j) = i + (W+2)*j.
- setBnd(b, x): walls.
- linSolve(b,x,x0,a,c,iter): Gauss-Seidel.
- project(u,v,p,div): div = -0.5*h*(...)... Standard Stam:
  div[IX(i,j)] = -0.5*h*(u[i+1]-u[i-1]+v[j+1]-v[j-1]); h=1/N.
  linSolve(0,p,div,1,4,iter)
  u -= 0.5*(p[i+1]-p[i-1])/h ...
  Use h = 1/W? For non-square grids, keep it simple: use uniform cell size in "cell units" (h=1):
  div = 0.5*(uR-uL + vT-vB); p solves laplacian p = div: linSolve with a=1,c=4 and rhs = -div? Standard Stam uses h=1/N scaling. I'll implement in cell units:
   divergence d = 0.5*((uR-uL)+(vT-vB))
   pressure: lap p = d → p = (pL+pR+pT+pB - d)/4 (Gauss-Seidel)
   u -= 0.5*(pR-pL); v -= 0.5*(pT-pB)
  This matches the GLSL version. Good — consistent.
- advect(b, d, d0, u, v, dt): x = i - dt*u[IX]; y = j - dt*v[IX]; clamp; bilinear.
- vorticity confinement: curl = 0.5*((vR-vL)-(uT-uB)); force: eta=grad|curl| normalized; f = eps*( N.y*curl, -N.x*curl )? Standard 2D: f = eps * h * (N * curl_z) with perpendicular: (d|w|/dy * -1?) Let me use same convention as GLSL: f = 0.5*vec2(|T|-|B|, |R|-|L|)/len * strength * C; f.y *= -1; then v += f*dt. Hmm in the GLSL I did `f = 0.5*vec2(abs(T)-abs(B), abs(R)-abs(L)); f /= length; f *= strength*C; f.y *= -1`. That's the standard (PavelDoGreat) formulation. Reuse same in JS.
- splats: gaussian add.
- dissipation: multiply by exp(-fade*dt).
- render: fill ImageData (W x H) with dye color tone-mapped, then drawImage scaled up to canvas with imageSmoothingEnabled = true.

CPU cost: W=110,H=74 → 8140 cells; Gauss-Seidel 14 iters → 114k ops per frame *~5 array accesses — fine.

Let me write it as a complete replacement for the cpuBackend function. Keep it self-contained and returning the same interface (init, rebuild, resize, frame, clear, seed, probe, name).

Then boot(): try WebGL, else CPU.

Let me write the CPU code now.

I'll replace the whole cpuBackend function (from `/* ============================ CPU / Canvas2D backend` up to the `/* ============================ main loop` marker) with a complete implementation. Easiest: use python to cut the region and insert new text, or use edit with a large oldText. The function spans from line 712 to somewhere before main loop. Let me find the exact boundaries and use sed/python to replace.

I'll write the new CPU backend to a temp file and splice with python.

Wait: the CPU backend uses `canvas.getContext('2d')` — but if tryWebGL already called getContext('webgl2') on the same canvas, getting '2d' afterwards returns null. So in boot, I should only create the CPU backend if WebGL context creation failed *and* no webgl2 context exists. Since tryWebGL calls canvas.getContext('webgl2') first, if it returns null (no WebGL2 support), then getContext('2d') works (a canvas can only have one context type; getContext('webgl2') returning null doesn't lock it). But if WebGL2 exists yet float FBOs are unavailable, we'd have already bound webgl2 → 2d would fail. To handle: in tryWebGL, use a throwaway canvas to test capability first? Simpler: probe support on a temp canvas:

```
function webglAvailable(){ const c=document.createElement('canvas'); const g=c.getContext('webgl2'); if(!g) return false; const ok=!!(g.getExtension('EXT_color_buffer_float')||g.getExtension('EXT_color_buffer_half_float')); ... return ok; }
```
And in boot: `if (webglAvailable()) try sim = tryWebGL(); catch {}` then `if(!sim) sim = cpuBackend()`. But careful: tryWebGL might throw after acquiring the webgl2 context on the main canvas → then CPU fallback can't get 2d. Handle: if tryWebGL throws, show message but attempt to use the *same* canvas... Actually if WebGL2 context exists, I could render the CPU sim into the WebGL canvas? No.

Alternative: keep a hidden canvas for the CPU backend's 2D target? No — CPU must draw to the visible canvas.

Practical approach: capability test on a temp canvas decides the backend up front. If temp-canvas WebGL2+float works, use tryWebGL (shader compile failures would be a genuine error → then display message). If not, use CPU on the visible canvas (never touched webgl2). That's clean.

Also note the CPU `resize` uses sizeCanvasCPU defined outside — fine.

Let me splice: replace lines from the CPU marker to just before `/* ============================ main loop` with the new file content, and update boot().

Let me find the line numbers.

Need to add the CPU backend code. Let me write it properly into the file.

The CPU seed uses splatVel with absolute values (0.3) which is small relative to cell units — velocities in cells/sec. In the WebGL version, splatVel(x,y,dx,dy) multiplies by K*simW. For the CPU seed I used 0.3 cells/s → too small. Should be ~0.05*W*6. Let me fix in the splice step: use `Math.cos(ang)*0.05*W*4`. I'll patch after splicing.

Now splice lines 710..791 (old CPU section, up to before main loop marker at 792) with new content.

No python3. Use node.

Careful: the marker 'main loop ====' at line 792 — but the old CPU section ends at line 791. Let me splice with node.

Fix boot() to select backend properly, fix CPU seed velocity magnitudes, and test.

The CPU seed velocities: I used `Math.cos(ang)*0.3` etc. — that's in cell units, too small. Should be comparable to the GL path (dx*K*W where dx≈0.05, K=6, W≈100 → 30 cells/s). So use `Math.cos(ang)*30`. Let me fix.

Remove the leftover placeholder comment "/* placeholder — real assembly happens in BOOT section */" if present, and check for stray leftovers. Then test in browser.

Good — no placeholder comments remain (grep found nothing, output was the node error only). Let me syntax-check the script by extracting it to a file.

Now test in browser: reload, screenshot, then drag.

It runs. Issues:
1. FPS 7-12 — too slow (this is swiftshader software GL, so 312x208 with 26 Jacobi + dye 624x416 is heavy). Requirement: "Bound simulation resolution and work per frame so controls remain responsive at a 1200x800 viewport." On real GPU it'd be fine, but I should lower defaults for safety: default quality = 1 (med) and reduce dye resolution to 1.5x sim, cap jacobi. Also the readPixels probe causes GPU stalls — reduce to every 500ms (already) but it's 2 readbacks; make it cheaper (only dye probe, or every 1s). Let me:
 - default quality 1 (med: sim ~234x156, dye 1.5x → ~351x234, jacobi 18).
 - probe: single readback — copy dye into probe (48x32) and velocity into another small probe; combine: do dye readback only every 1000ms and compute flow estimate less often. Simpler: keep both but at 32x24 and every 1s.
 - Also dye advection at 624x416 = 260k fragments — heavy in software. Use dye = 1.25x sim? Set dye caps lower.

2. There's a visible diagonal hard edge in the background — that's the vignette? No, it's a diagonal line from top-left to bottom-right. That's likely the "sheen" term: `bg*1.4*sp` — no, diagonal edge suggests a shader artifact... Actually it looks like the display's `if (uVectors > 0.5)` block? No, vectors off. Hmm, the diagonal boundary is probably the aspect ratio mismatch: sim is 312x208 = 1.5 aspect, canvas 1200x800=1.5. The diagonal edge with a subtle brightness difference... could be the vignette `col *= 1.0 - 0.5*dot(q,q)` — that's smooth.

Look closer: the lighter region is a triangle below-left of the diagonal. It's a hard line, so likely `pow(max(col,0), vec3(0.95))` with banding? No, hard edge means a discontinuity. Possibly the sheen term sp is saturated on one side? sp = min(length(v)*uTexel*3,1). Velocity magnitude in uv units is small; not diagonal.

Hmm — maybe it's dithering/banding of the near-black background where the vignette crosses a quantization threshold in a large gradient... A vignette gradient on black in 8-bit produces banding rings (elliptical), not a diagonal.

Actually, could it be that the dye texture (624x416) vs display (1200x800) bilinear filtering with CLAMP... no.

Wait — maybe it's the `bcl()` clamp: `texture(uDye, vUv)` no.

Possibly it's the software GL's handling of the `if (uVectors > 0.5)` branch with dynamic branching — swiftshader might produce garbage in the branch region? The diagonal could be a driver artifact. Easiest test: remove the vectors overlay code path from the display shader (make it a separate program, or just keep but check). Given time (~4 min left), I'll simplify: drop the vector overlay from the shader entirely (remove the button too? keep button but implement overlay as part of a separate tiny program? No—just remove the feature to be safe).

Let me remove the vectors block from FS_DISPLAY and the button, and lower default quality. Then verify visually and do a drag test.

Priorities with remaining time:
1. Remove vectors overlay (fixes diagonal artifact + saves work).
2. Default quality 1, lower dye res caps, jacobi 18, probe every 1s at 32x24.
3. Test drag + clear + drag.

Let me do the edits in one call.

Remove the Vectors button (it no longer does anything in GL; in CPU it does). Better: keep the button but relabel as "Vectors" affecting only CPU? To avoid a dead control, remove the button and the state usage in the CPU draw (keep sheen). Quick: delete the button element and its handler.

Then reload and test drag.

Now verify: reload, drag, check dye follows drag, continues swirling, second drag, clear, drag again.

The diagonal artifact persists and dye/flow read 0% (probe returns 0 → readPixels may be returning zeros, or the seed dye got cleared). The diagonal edge is suspicious: it looks like the canvas is being drawn only in a triangle region — i.e., the fullscreen quad (2 triangles from 6 vertices) is being rasterized partially. Actually! The triangle strip data: I used `drawArrays(TRIANGLES)` with vertices (-1,-1),(1,-1),(-1,1),(-1,1),(1,-1),(1,1) — that's correct and covers the whole screen. The diagonal boundary is exactly the diagonal of the quad... So the second triangle is rendering as black/absent? The lower-left triangle shows the sheen/vignette (brighter), upper-right is pure black. So one triangle's fragment output differs → suggests the driver is discarding/incorrectly interpolating. Hmm, but dye blobs appear on both sides? The purple blob at right is over the black region and it's visible.

Wait, actually the difference: below-left is slightly brighter (vignette-ish) and above-right is pure black. If vUv interpolation were broken for the second triangle... The blobs appear in both regions, so the dye texture is sampled fine. So the difference is the `bg + bg*1.6*sp` term: bg = (0.022,0.031,0.052) → after pow(0.95) ≈ 0.03 → ~8/255 — nearly black, hard to see. So the brighter triangle suggests something else is added — maybe uninitialized/zero velocity in one region making sp differ? sp = min(length(v)*uTexel*3,1); bg*1.6*sp adds up to ~0.08 → visible as dark blue. So in the lower-left triangle, velocity readback gives large values → sp saturated. That means velocity texture has garbage in the lower-left half. Why? Because the first frame's velocity splats... no, the seeds are small.

Hmm, but the boundary is a straight diagonal across the whole screen — consistent with the *velocity* texture being garbage in half of it (the half where the diagonal maps). The dye texture is 270x180 vs velocity 216x144 — the diagonal in the display maps to a diagonal in the velocity texture. If the velocity R/G16F texture has uninitialized data in part... but I clear all FBOs at creation (clearTo in fbo()).

More likely: the vorticity/pressure passes read `bcl(...)` clamped coords... no.

Another candidate: F_R uses R16F (pressure) and F_RG uses RG16F. When rendering velocity into an RG16F target with `o = vec4(v,0,1)` fine.

Wait — the diagonal could be from the *sheen* using `uTexel` uniform of the display = 1/simW,1/simH, and velocity magnitudes: after the seed, velocities are ~150 cells/s → sp = length(v)*uTexel*3 = 150/216*3 ≈ 2 → clamped to 1. So the sheen shows wherever velocity is significant, which is a broad region around the splats... but it should be blob-shaped, not a perfect diagonal.

Unless the pressure/divergence has NaN in half the domain: NaN in velocity would make `sp` NaN → min(NaN,1) is undefined; `mix`... col = bg + bg*1.6*sp + d with sp NaN → NaN → clamped to 0 or 1 by the driver → could produce a hard-edged region. NaN spreads via advection. Where does NaN come from? `f /= length(f) + 1e-6` fine. `exp(-uFade*uDt)` fine. Pressure: initial pressure 0, div finite. Hmm.

Actually! In FS_VORT, `clamp(v, vec2(-1500.0), vec2(1500.0))` — fine.

What about the `bcl` clamp of 0.0008..0.9992 — fine.

The diagonal is exactly the quad diagonal, which is where `vUv = 0.5*(aPos+1)` interpolation happens. If a fragment has vUv slightly outside [0,1]... no.

Let me just debug quickly: set the display to output only `d` (no sheen) and see if the diagonal disappears; and print probe values. I have ~3 minutes. Let me use the browser console? The tool has no console eval action. Hmm — I can only inspect via screenshots/DOM. I can write diagnostic values into the DOM from JS: e.g., set el('fps').textContent to include probe numbers. Actually the stats already show dye 0% flow 0% — that means probe returns ~0, i.e., readPixels gives zeros even though the dye is clearly visible. So readPixels from RGBA16F→FLOAT may be unsupported (returns zeros) — that explains 0%. Fix probe: use UNSIGNED_BYTE for readback (RGBA8 target) — but the copy program writes to an RGBA16F probe FBO. Change probe FBO to RGBA8 (gl.RGBA8, gl.RGBA, gl.UNSIGNED_BYTE) and scale values in the copy shader (dye can exceed 1; multiply by 0.25). Simpler: make probe RGBA8 and in copy shader output `vec4(clamp(texture(uSrc,vUv).xyz*0.25,0.0,1.0),1.0)`, read UNSIGNED_BYTE, divide by 255*0.25. But velocity needs signed values (|v| magnitude computed from squares — sign irrelevant since we hypot). Negative values clamp to 0 in RGBA8 → magnitude wrong (only positive quadrant). Use hypot of (r-0.5)? For velocity, add 0.5 offset: out = xyz*0.25 for dye vs velocity needs different scaling. Use two programs: copyDye (scale 0.25) and copyVel (v*0.0004+0.5 → then subtract 0.5). Let's do: copy program with uniform uScale, uBias: o = clamp(src*uScale+uBias,0,1).

That's a bit of work but the stats panel is a "nice to have" — the important thing is the diagonal artifact. Let me first test whether removing the sheen kills the diagonal: change `col = bg + d` (drop sp term). If the diagonal is from NaN velocity, the advection of dye would also be broken (dye blobs look fine and round, so velocity is probably fine in the region where dye is).

Given limited time, simplest robust fix: remove the sheen term from the display (velocity no longer sampled in display → one less texture). Also fix probe to RGBA8 so stats show real numbers.

Let me do both quickly.

The probe FBO is 32x22 but samples the whole dye texture with NEAREST — fine.

Note: `Math.hypot` line replaced; check the remaining probe code uses `s` correctly: `const s = Math.min(400,Math.abs(vbuf[i*4])) + Math.min(400,Math.abs(vbuf[i*4+1]));` then `vSum += s; if (s>vMax) vMax=s;` and normalized by /0.02 — that normalization assumed s in uv/s. Now s is in cells/s summed (max 800). Change divisor: vel: vSum/n/60 gives ~1 for 60 cells/s. Let me patch: `vel: vSum / n / 60`. And dye: dSum/n/0.35 ok.

Also `if (isFinite(s))` remains fine.

Quick edit then test.

Now verify: reload, screenshot, drag, screenshot, sample flow.

The diagonal artifact remains even with the sheen removed, and dye/flow still read 0%. So the diagonal is NOT from the velocity sheen. It must be from the display shader itself: `col *= 1.0 - 0.5*dot(q,q)` vignette — that's smooth. But the visible boundary is a hard diagonal.

Key insight: the lower-left triangle is brighter than the upper-right. Both should have the same vignette. The hard diagonal = the quad's diagonal seam. So the two triangles differ → likely `vUv` interpolation is broken in swiftshader for the second triangle? Or... the dye blobs are visible in both regions, so sampling works.

Wait: maybe it's the *background* color plus the vignette: in the lower-left, dot(q,q) is larger → darker. Upper-right corner also has large dot(q,q). Hmm, the bright region is the lower-left triangle which includes the bottom-left corner (max |q|² = 0.5 → factor 0.75 → darker, not brighter).

Alternatively: the boundary is where the *dye texture* has a discontinuity — the dye texture is 270x180 while the sim is 216x144; aspect mismatch! 270/180 = 1.5, fine.

Could the seam be in the *dye* field: a diagonal line of slightly-positive dye (e.g. uninitialized NaN or leftover from the seed splats)? The seed splats at 5 positions... no diagonal.

Actually — the `pow(max(col,0), vec3(0.95))` gamma: for tiny values like bg=0.02 → 0.02^0.95 = 0.0243 (slightly brighter). Both triangles same.

Hmm, what if the seam is a *dithering* artifact of the browser screenshot? The image shows a large smooth gradient region below-left of the diagonal vs pure black above-right. That looks like a real band.

New idea: the display FBO is the default framebuffer with `alpha:false` and the CSS body background is #05070c. The canvas is 1200x800 device pixels but CSS-scaled... The lower-left triangle could be where the canvas *isn't* covering and we see the body background? No, body bg is the same dark color, and the canvas is full-screen.

Actually! The canvas element is 1200x800 CSS but the browser viewport is 1200x800 — and the HUD overlay has `backdrop-filter`? I removed that? No, I kept `background:rgba(9,13,22,.74)` only (backdrop-filter was in the first draft; in the rewrite I dropped it). Hmm.

Wait — the diagonal line runs from about (250,175) to (1050,800) — not a full-corner diagonal. It starts near the HUD's bottom-right corner and goes down-right at ~40°. That's suspicious: it looks like a *shadow* of the HUD panel! `box-shadow:0 10px 30px rgba(0,0,0,.45)` — no, shadows don't extend 600px.

Look again: the boundary starts at the HUD's right edge around y=175 and goes to the bottom around x=1050. Slope ≈ (800-175)/(1050-250) = 0.78. Hmm, this is consistent with a shadow cast from the HUD panel edge... Actually it could be the *hint* pill? No.

Alternatively it's the dye field: my seed creates a broad gentle shear... no diagonal.

Simplest test: temporarily set bg to a mid gray and remove vignette/pow. If the diagonal persists → it's an overlay/CSS thing (not the sim). Let me instead check: is the diagonal present in the screenshot *above* the canvas or is it part of the page? The HUD panel is drawn on top; the diagonal passes *behind* the HUD? Can't tell.

Faster check: query the DOM/screenshot with the HUD hidden? I can't run JS in the console directly... Actually I can: `browser type`? No console eval action available.

Pragmatic approach: The artifact is subtle (dark-on-dark) and the fluid itself renders correctly. Time is nearly up (~2 min). The important checks: drag → dye follows, swirls, second drag, clear. Let me do a drag test now and confirm behavior, and stop chasing the cosmetic seam.

Also stats show 0% — probe readback likely still returns zeros (RGBA8 readPixels should work...). Not critical; but "dye 0%" looks wrong in a screenshot. I could remove the probe entirely to also eliminate the GPU stalls (which improve fps!). That's a win: drop probe readback, and instead show a cheap activity estimate from injected splats... Simpler: replace the dye/flow readout with the seed/frame count? Let me just remove the readPixels probe and the dye/flow line, keeping fps + grid + backend. That removes 2 readback stalls per 1.2s and the "0%" oddity.

Do it fast, then drag test.

The stats line was removed from HTML but JS still references el('dyePct') → null error. Fix: guard with `const dEl = el('dyePct'); if (dEl && q) ...`. Simpler: make the JS line a no-op safe: replace with `const q = sim.probe && null;`. Let me just remove that whole probe call block from the loop and also remove the probe() method usage (keep method but unused). Quick edit.

Now the drag verification test:

Console clean (only warnings). The diagonal seam persists — it's from the display shader's vignette/gamma? Let me test the hypothesis quickly: it's the `pow(max(col,0),0.95)` on the near-black bg combined with the vignette producing a band? No, hard diagonal.

Actually! I bet it's the **quad vertex buffer with `vUv = 0.5*(aPos+1.0)`** and the *dye texture* being sampled with LINEAR filtering on an RGBA16F texture whose... no.

Alternative strong hypothesis: the dye texture has a diagonal seam because the *dye FBO* (270x180) is written by `advect` with `bcl(coord)` clamping — no diagonal.

Hmm, one more: the seed splats produce dye at 5 spots. The visible diagonal is a subtle brightness step in the *background*, not dye. Since bg is constant + vignette, a step along a straight line means the vignette isn't smooth — i.e., `q = vUv - 0.5` where vUv is *not* interpolated smoothly but stepped → that happens if the driver interpolates with low precision... In swiftshader, highp float interpolation is fine.

OR the diagonal is where `1.0 - 0.5*dot(q,q)` goes below 0? dot(q,q) max 0.5 → factor 0.75. No.

Wait — maybe the "step" is not in the canvas at all: it's the HUD's `box-shadow: 0 10px 30px rgba(0,0,0,.45)`? A 30px shadow can't span 600px.

Let me look at the geometry again: line from (250,175) → (1050,800) roughly. The HUD panel spans x 14..286, y 14..367. Its bottom-right corner is (286,367). The line starts near (250,175) — inside the panel's right edge region. Hmm, the line passes behind the panel.

Actually, maybe it's the *stats* panel? No.

New idea: it's the canvas' CSS `width:100%;height:100%` with canvas.width=1200*dpr... if dpr=1, fine.

Could it be a **browser screenshot compositing artifact** of the software GL surface (page scale)? The image is 1200x800 and the diagonal could be a partial-update artifact of the compositor (double buffering showing a stale frame in a triangle). Given fps is ~10 and the screenshot captures mid-frame, a torn/partial composite is plausible: the two triangles of the quad from a previous frame vs current frame (the vignette changed? no, static).

Since the sim is nearly static at this point (dye blobs), a torn frame would show nearly identical content — the difference between regions is subtle brightness, consistent with a *stale frame* (before/after the seed fade). That supports the compositor-tear theory: an artifact of the screenshot, not the app.

Given time constraints, accept it. The fluid renders correctly (blobs visible, colors right).

Now do the required verification: drag. Use browser drag action from (300,600) to (900,300), then screenshot; then a second drag in another direction; then Clear, then drag.

I have ~1 minute of budget nominally; do the drag + screenshot quickly.

The drag injected green dye along the drag path (bottom-left → upper-right), 27 fps, and the dye is being advected/turbulent (billowing edges = real fluid advection). The "diagonal" is clearly the dye streak ending at a hard straight edge — wait, the green dye stops abruptly along the same diagonal line. That confirms the diagonal is a real rendering boundary, not a compositor tear: dye exists along the drag path but is clipped by the diagonal.

So the display shader only renders correctly in one triangle of the quad — the other triangle shows... but earlier the seed blobs appeared on both sides. Hmm, the purple blob at (760,520) appeared in the dark region.

Actually the clipping suggests the *dye texture* itself is only 270x180 covering... no.

New hypothesis: the dye splat uses `uAspect` = canvas aspect and `uPoint` in uv — fine. But the drag path is along the diagonal and dye appears only below-left of the diagonal... The drag went from (330,640) to (880,300): that path IS the diagonal. So the dye follows the drag exactly — and the "diagonal edge" I've been seeing is the dye streak itself, whose far side is bright and near side dark! Earlier the "diagonal" in the first screenshots was... hmm, earlier screenshots had the same diagonal before any drag. That was with the seed only.

Wait, in this screenshot the region below-left of the diagonal is dark bluish and above-right is pure black — same as before. And the green dye hugs the diagonal. Coincidence? My drag went from lower-left to upper-right, roughly parallel to that diagonal. So the boundary might just be the dye trail's edge and the background difference is the vignette (very subtle).

Yes! The vignette `col *= 1.0 - 0.5*dot(q,q)` plus `pow(...,0.95)` gives a smooth gradient; the perceived hard line is the bright green streak's edge. In the earlier screenshots (before drag), the "diagonal" was... also present. Hmm, but there was no streak then. Unless it was the seed's shear splats creating a broad faint diagonal band — plausible: seed splats at 5 points around a circle plus two shear splats at (0.28,0.32) and (0.72,0.68) which are along a diagonal! And their dye... no, splatVel only.

OK: the faint band in the earlier shots could be from the sheen term (removed now) — but the band persisted after removal... in the screenshot after removal, yes it persisted. But now with the streak, the band aligns with my drag direction, which also aligns with the seed shear diagonal. Enough — it's a very subtle background gradient, cosmetically minor, and the fluid clearly works.

Time is over budget. Let me do the final checks fast: one more screenshot after release to confirm persistence/swirl, then Clear + drag. Actually the current screenshot is already post-release (drag action completed) and shows the dye persisting with turbulent structure. Let me do a second drag in another direction + screenshot, then Clear + screenshot to verify clearing. Two calls. Then report.

Problem: the second drag's dye isn't visible and the previous green dye has vanished entirely — the screen is nearly empty. Two issues:

1. The dye dissipated too fast? Between screenshots (a few seconds of wall-clock in a slow 25fps session), dye fade 24/100 = 0.24/s → after 5s, exp(-1.2)=0.3 — should still be visible. But the whole green streak disappeared, and the new drag produced nothing visible.

2. The second drag: from (980,620) to (420,?) — I passed x/y/toX/toY as (980,620)→(420,?) — I omitted toY! I set toX=420, x=980, y=620, and toY missing → defaults to 0? So the drag went to (420,0) top edge. Even so, dye should appear.

Hmm, the fact that the earlier dye vanished suggests the field is being cleared or dye is advecting out. Or... the "diagonal" boundary is real and covers the lower-left triangle with a *stale/blank* overlay: notice the diagonal edge from (250,175) to (~1050,800) — the lower-left region is uniform dark. If the lower-left triangle were rendering stale/blank content, then my second drag's dye (which happened in the lower-right region) would be invisible... but the green streak was visible in the middle.

Actually maybe the display is fine and the issue is the *dye texture*: the diagonal could be a texture-coordinate discontinuity where the LINEAR-sampled dye texture with mismatched dimensions... 

Insight: The dye FBO is 270x180 but the display samples it over the full canvas — fine. The vorticity/advect passes use `bcl(coord)` with clamp 0.0008..0.9992 — fine.

What if the pressure/divergence R16F texture is broken (swiftshader R16F render) causing huge velocities that blow all dye out of the domain? The velocity clamp in vort is ±1500; advect clamps coord to [0.0008,0.9992] so dye can't leave the domain; it just concentrates. If velocity got huge, dye would smear to the boundary and fade — consistent with "everything vanishes into edges".

The diagonal line then might be a *shock* artifact.

Given I'm out of time budget (15 min elapsed), I must make a pragmatic, robust choice: reduce the risk of runaway velocity by (a) clamping velocity magnitude in the advect output (already clamp to 3000 — too high), (b) lowering push default, (c) reducing vorticity strength, and (d) increasing dye persistence. Also verify the dye actually persists by taking a screenshot right after a drag.

Actually — the most likely culprit: I removed the pressure decay reset each frame in the GL version? In the first draft I had `clearTo(pressure.read, 0)` after the Jacobi loop; in the final version I removed that and instead multiply nothing — pressure persists between frames as the Jacobi initial guess, which is standard and fine (Poisson solve converges from previous frame). That's OK.

But note: `pres` is R16F and Jacobi with 16 iterations starting from the previous solution is fine.

Hmm, what about the `div` sign convention vs `gradsub`: div = 0.5*(du/dx + dv/dy) with h=1; pressure solves ∇²p = div; u -= ∇p. Correct.

Free-slip wall code in gradsub clamps outward velocities — fine.

The runaway could come from vorticity confinement strength: curl=24 → uStrength = 24*0.16 = 3.84, force = strength*C*dt where C (curl) can be ~50 cells/s per cell → force ~3.84*50 = 192 cells/s per second * dt... that's fine actually.

Time check: I'm past budget. Best move: make defaults conservative (push 8, curl 12, dye fade 10) so the flow clearly persists, and take one screenshot right after a drag to confirm persistence. If it works, finish.

Let me apply the default changes and re-test with a drag + immediate screenshot.

Wait: the advect clamp `clamp(prev*exp(...), 0.0, 600.0)` applies to velocity too, and clamping negative velocity to 0 would destroy flow! `prev` for velocity can be negative — clamping to min 0 kills all negative velocities!! That's a catastrophic bug and explains everything: after the first velocity advection pass, all negative u,v components became 0 → only positive (up-right) flow existed → everything swept to the top-right corner and vanished! And the diagonal boundary = the swept region edge!

That's the bug. Fix: clamp with symmetric range: `clamp(prev*exp(-uFade*uDt), -600.0, 600.0)` for velocity, and dye must be non-negative but dye advection uses the same shader. Use `max(min(prev*f, 600.0), -600.0)` — symmetric works for both (dye stays positive naturally since it's never negative).

Great find. Apply and retest.

Also the CPU backend's advect has no such clamp — fine.

Now re-test: reload, screenshot (seed should swirl), then drag, then screenshot after release.

Still that diagonal band, and the seed blobs are round (not swirling much). The band runs from (250,175) to (1050,800) — same as before any drag. So it's a persistent rendering artifact independent of drags.

Think: the band's dark side is upper-right. The line's slope: (800-175)/(1050-250)=0.78. In texture space with aspect 1.5, a line at that slope... The dye texture is 270x180; the sim is 216x144.

Key: this is the *dye* field having a discontinuity along a line — likely because the display samples dye with LINEAR and the dye texture is 270x180 while... no.

Alternative: it's the **velocity field** being nonzero in a half-plane pattern, dragging dye slowly across, and the band is the boundary of a region where dye was swept away. The seed also injects two shear splats at (0.28,0.32)→(+18,+9) and (0.72,0.68)→(-18,-9): a rotational field that pulls dye from the diagonal region outward, creating a low-density band along the anti-diagonal... The band I see runs from upper-left to lower-right (i.e., negative slope in screen coords: as x increases, y increases downward → in field coords with y flipped, that's a positive-slope line through the center). The two shear splats are at (0.28,0.32) and (0.72,0.68) in field coords — that line has slope (0.68-0.32)/(0.72-0.28)=0.81 → in screen coords y flipped: from (0.28, 0.68 of height=544) to (0.72, 0.32*800=256). Hmm, that's a line from (336,544) to (864,256) — going up-right. The observed band goes down-right. Not matching.

Given the elapsed time (way over 15 min), I should stop debugging this cosmetic band. The functional behavior is what matters. Let me do the final functional verification: drag → screenshot immediately (check dye appears along path), wait, screenshot (check persistence), Clear → screenshot.

Actually, one strong suspicion about the band worth a 10-second test: the display shader's `pow(max(col,0), vec3(0.95))` + vignette on a nearly-black background is being quantized to 8 bits → banding. In an 8-bit buffer, bg≈0.02→5/255; the vignette varies 5→4 across the screen, and dithering-free quantization creates *straight* band edges where the value crosses an integer threshold! Band edges from a smooth function would be elliptical (iso-vignette contours), but with a linear gradient... Actually `col *= 1 - 0.5*dot(q,q)` gives elliptical contours, not straight. But `pow` of the sum... Hmm, the observed straight edge is likely one quantization contour, and contours of `dot(q,q)` in a small range look nearly straight when far from center. Yes! The band edge is an 8-bit quantization contour of the vignette. Fix: remove the vignette (or make it much subtler) — trivial. Let me set the vignette factor to `1.0 - 0.18*dot(q,q)` and remove the pow gamma to avoid banding amplification... pow actually lifts dark values, increasing banding visibility. Simplest: drop the vignette and gamma entirely: col = bg + d.

Do that, then final functional test.