Fluid simulation · step-5-preview

Let me build a WebGL fluid simulation. Actually, WebGL2 fragment-shader-based stable fluids (like Pavel Dobryakov's) is the classic approach. But it's a lot of code. Alternatively, a Canvas 2D grid-based Stam solver at reduced resolution would be simpler and controllable. But WebGL gives better quality.

Given constraints (15 min), I'll write a WebGL implementation with fallback... Actually let me do a careful, complete WebGL implementation. But risk of bugs. Alternatively a CPU-based Stam stable fluids solver at ~256x160 grid for velocity + dye at 512x320... that could be slow in JS but manageable? Stam solve at 128x80 is fast. Dye advection via bilinear sampling on a grid rendered to canvas with ImageData. At 200x125 grid for dye, advect each cell with bilinear interpolation and Jacobi pressure solve (20 iterations) — 25000 cells × 30 iterations = 750k ops per frame, fine. Dye advection 25000 cells with bilerp = fine. Then render dye to an offscreen canvas 200x125 and scale up with imageSmoothingEnabled = true. That's a solid approach and quite robust.

Hmm, but visual quality: 200x125 upscaled to 1200x800 will look blurry/smoothed — actually that's fine, looks like a fluid. Interactions remain responsive.

But WebGL would be much prettier. Let me consider: I've got decent recall of the structure of a WebGL stable-fluids implementation. Risk: shader compile errors that take time to debug. I do have browser tools to inspect console, so I can catch errors and fix.

I think the safest high-quality path: WebGL2 with float textures... but WebGL1 with OES_texture_half_float is a hassle. Let's just do the CPU Stam solver — deterministic, no shader debugging, responsive. Use a moderately high resolution for dye: grid 256x160 = 40960 cells. Jacobi pressure 20 iters → 819k cell updates per frame. Each update is ~10 flops in JS. ~8M flops/frame, at 60fps = 480 MFLOPs — JS can do that (typed arrays). Should be OK. Might be ~5-10ms/frame. Acceptable.

Let me use a dye grid of 200x125 (25000 cells) and velocity grid same. Actually let's use same grid for both to keep it simple: N=256 width, 160 height. Hmm, boundary conditions: velocity boundaries set to ± of neighbor.

Better plan: implement the classic Stam "Real-Time Fluid Dynamics for Games":
- velocity field u,v arrays size (W+2)*(H+2) with boundary cells for free-slip/no-slip.
- Dye field 3 arrays (r,g,b).
- Steps: diffuse (skip or do few Jacobi), project (Gauss-Seidel ~20 iters, in-place, fast), advect velocity, project again, advect dye, add forces.

Advection uses semi-Lagrangian with bilinear interpolation.

Init: seed some dye blobs and velocities (e.g., a few rotating vortices, random curl-ish initial velocity plus a couple of big soft dye blobs in multiple colors).

Controls: color selector (a set of swatches + maybe hue input), Pause/Resume button, Clear button.

Drag: on pointermove, compute delta, add velocity along delta (gaussian splat with radius ~ 3-6 cells), add dye with current color (gaussian splat, additive blend slightly fading).

Rendering: draw to ImageData scaled. To make it prettier, apply slight tone mapping: color = dye * exposure, plus maybe gamma. Use an offscreen canvas at grid resolution and drawImage scaled up with smoothing. That's one drawImage per frame — cheap.

Let me also add a subtle background gradient/vignette drawn in CSS behind the canvas canvas... Actually canvas must be opaque-ish; draw background color first (dark navy) then dye over it via globalAlpha=1 drawImage (the dye image has alpha channel too). Let's put dye alpha = 1 where dye exists, else 0. Use separate alpha array or compute as max(r,g,b) clamped. Simpler: dye has rgb and alpha = clamp(density). Actually let's store density per color component, and alpha = min(1, max component). Then drawImage of ImageData with alpha.

Hmm, additive accumulation of dye over time increases density beyond 1; with fade/dissipation it stays bounded. I'll add a small dissipation per frame (multiply by 0.995) and a "density" field to control alpha. Let's keep 4 channels: r,g,b and a (density). Splatting color adds to r,g,b and density a equally.

Rendering: out rgb = dye rgb, alpha = clamp(a). Then colors stay the true injected color. That's cleaner than blending with background. And dissipation scales all 4.

Grid resolution & work per frame bound: fixed grid based on viewport aspect, capped at e.g. 256x160, and cap pressure iterations adaptively to keep frame budget. I'll add a simple adaptive: measure frame time, reduce Jacobi iterations if slow. Keep simple: fixed 20 iterations, plus a perf counter display maybe. Also "Bound simulation resolution and work per frame" — I'll implement: grid computed as min(capW, floor(w/scale)) where scale chosen so grid cells ≈ 4px, capped to max 320x200 (64000 cells). Let me pick scale so grid is ~ 300x200 max. Let me compute: viewport 1200x800 → /4 = 300x200 = 60000 cells. Jacobi 20 iters → 1.2M cell-updates. Fine.

Hmm, 60000 cells × (advect vel 60000×~20 flops + advect dye 60000×~30 + project 20×60000×15 + diffuse optional). Should run ~5-8ms. OK.

Actually I could use a Web Worker... no, keep simple. Let's do a fixed-step with time accumulator, maybe 2 substeps max.

Let me also consider adding a bit of vorticity confinement to keep swirls alive. Nice touch: vorticity confinement force with small epsilon. That helps "continues swirling". Yes, include it.

Also curl noise injection? No, seeded initial motion + drag is enough.

Let me write the code.

Data structures: use Float32Array. Grid dimensions gw, gh (cells), with array size (gw+2)*(gh+2) for velocity with boundary padding. For dye, simpler: just gw*gh without padding. Actually to keep indexing uniform I'll use padded for both: N = (gw+2)*(gh+2), index IX(i,j) = i + (gw+2)*j. i,j in 0..gw+1. Interior 1..gw.

Functions:
- set_bnd(b, x): for velocity, u at i=0 boundary = -u(1) etc (free slip). For dye, copy from neighbor.
- lin_solve with Gauss-Seidel in place: for b=0: x = (x0 + a*(sum neighbors))/den); a=1, so x = (x0 + sum)/4 for diffuse/... For projection we do Jacobi/Gauss-Seidel for pressure: x[i,j] = ( -b[i,j] + x[i-1,j]+x[i+1,j]+x[i,j-1]+x[i,j+1] ) / 4.
- diffuse: skip (use small dissipation instead) or do a few Gauss-Seidel iterations with a = dt*diff*k. I'll skip diffusion for velocity (viscosity = 0) to keep it lively but keep dissipation. Actually slight diffusion smooths nicely; but each diffusion solve with 20 iters is another 1.2M ops. Let's include optional diffuse with 10 iterations on velocity (viscosity small) — or just skip. I'll skip velocity diffusion and rely on numerical dissipation from advection. That's standard for game fluids.

- advect(b, d, d0, u, v, dt): for each cell, backtrace x = i - dt*u, y = j - dt*v (in grid units, accounting for aspect), bilinear sample d0, store into d. Set boundary.

Coordinate mapping: pointer to grid coords: gx = px / canvasW * gw, gy = py / canvasH * gh. Velocity in grid cells per second: vel cells/sec = drag delta in px / canvas * gw / dt. That naturally handles aspect if I use same scale for both axes... but cells are non-square (gw/gh ratio = aspect, cell width in px = 4, cell height = 4 → cell is square in px). Since gw = W/4, gh = H/4, cells are square in pixels. So velocity in cells/sec maps to px/sec by ×4. Free-slip boundaries keep it contained-ish, but fluid can escape and get damped at edges.

Splat radius: 4 cells (~16px) for dye, velocity splat bigger.

Let me write it.

Rendering details for beauty:
- ImageData at (gw+2)×(gh+2)? Just gw×gh. Create ImageData of gw*gh, fill from dye arrays (interior only), putImageData to a small offscreen canvas of size gw×gh, then ctx.drawImage(off, 0,0, cw, ch) with imageSmoothingEnabled = true, imageSmoothingQuality = 'high'.
- Also add a background fill on main canvas before drawing dye: a dark radial gradient. Since dye alpha<1 in low-density regions, background shows through — nice.
- Additionally add optional additive glow: draw the dye image twice with 'lighter' at low alpha for glow. Maybe just once, plus a subtle bloom using a second drawImage with filter blur — Canvas2D filter blur is supported in most browsers; risky on some. I'll use ctx.filter = 'blur(8px)' with try/catch and a second composite pass with 'lighter'. Hmm, could be slow to blur each frame at 1200x800. Let's skip heavy bloom; instead draw the same image scaled with slight offset at low alpha? That creates cheap smear glow. Eh — I'll do a simple thing: draw dye normally, and if ctx.filter supported, draw a blurred copy at alpha 0.35 with 'lighter'. Test performance; if slow, drop.

Actually simpler & safe: skip glow. Focus on required behavior.

Also draw a small "cursor" indicator? Not needed.

Add a HUD with hints.

Let me now handle "Bound simulation resolution and work per frame": 
- grid capped at 320x200 (or maybe 256x160 for safety). Let's target cell size 5px → 240x160. Cap: maxCells = 64000. Compute gw = clamp(round(W/5), 64, 320), gh = round(gw * H/W)... Let me define target cell px = 5, gw = floor(W/5) capped 300, gh = floor(H/5) capped 200. Both even not needed.
- dt clamped to max 1/30; substeps max 2.
- pressure iterations 20 fixed; add adaptive iteration reduction based on measured frame time (if avg frame > 22ms, reduce to 12, etc.). I'll implement a simple adaptive iters between 8 and 24.
- Use requestAnimationFrame loop.

Also on resize, resize canvas to window size (device pixel ratio capped at 1 to keep work bounded... use dpr=1 for perf; retina looks slightly soft but fluid is smooth). Use CSS full-screen canvas, backing store = clientWidth × clientHeight (dpr 1). Good.

Initial seed: create a few dye blobs with different colors at nice positions, and velocities: apply a rotational swirl field, e.g., two vortices: for each cell, v += amplitude * perpendicular vector to center. Also add a couple of "jets".

Color selector: array of swatches; clicking sets current color. Also an input type=color for custom. Rainbow option: hues vary over time? Keep simple: swatches + color input.

Clear: zero dye and velocity. Must not pause. After clear, next drag starts fresh flow — yes.

Pause/Resume: button toggles; when paused, still render (so canvas shows last frame) but no stepping. Show status.

Let me write the file now.

One more consideration: "Dragging injects dye and momentum in the drag direction" — I'll compute per-move delta and apply force along delta, with splat radius scaled so quick vs slow drags inject more (proportional to delta but capped).

Also add auto-decay of velocity (viscous damping multiply 0.995) and dye dissipation 0.997.

Edge case: pointerdown then pointerup without move → small dot of dye. Fine.

Let me write the code carefully.

Structure of JS:

```js
const canvas = ..., ctx = ...
let gw, gh, stride, size;
let u, v, u0, v0, dr, dg, db, da, dr0, dg0, db0, da0;
```

Use separate arrays for rgb and a. That's 8 float arrays of 64000 → fine.

Better: use one array of 4-length per cell (dye as Float32Array of size N*4) — but advect per-channel would be awkward. Keep 4 separate arrays.

Actually to reduce work in advection of dye: I can advect all 4 channels in the same loop with the same bilinear weights — compute indices and weights once. 

Let me write helper:

```js
function IX(i,j){ return i + stride*j; }
```
with stride = gw+2, and cells i=0..gw+1, j=0..gh+1. size = stride*(gh+2).

Advect (dye): for j=1..gh, i=1..gw: 
```
const idx = IX(i,j);
let x = i - dt*u[idx]*? 
```
Careful: velocity stored in grid units per second (cells/sec). dt in seconds. So backtrace offset in cells = u*dt. Good.

```
let x = i - dt*u[idx];
let y = j - dt*v[idx];
if (x<0.5) x=0.5; if (x>gw+0.5) x=gw+0.5; ...
let i0 = x|0 ... 
```
Use clamp: i0 = Math.floor(x), i1=i0+1, s1 = x-i0, s0=1-s1. Clamp i0 to [0,gw], i1 = i0+1 clamp to gw.

For dye: no boundary condition class; use clamping sample (which gives no-penetration-ish). Fine.

Advect velocity: same but with bnd: after advecting, call setBnd on u,v.

Projection:
```
div[idx] = -0.5*( (u[i+1]-u[i-1]) + (v[j+1]-v[j-1]) ) / h? 
```
Stam's original uses h=1 in grid units, so div = -0.5*(du+dv), and pressure solve: p = ( -div + pleft+pright+ptop+pbottom )/4, then u -= 0.5*(pright-pleft). Grid spacing 1. Good.

Gauss-Seidel 20 iterations. Let's use Gauss-Seidel (in-place) — converges faster, still fine.

Hmm Gauss-Seidel over 64000 cells × 20 = 1.28M iterations of ~6 array reads/writes → maybe 10ms. Jacobi needs double buffers. Let's just use Gauss-Seidel with a scratch p array.

OK. Also vorticity confinement:
```
curl[idx] = 0.5*( (v[i+1]-v[i-1]) - (u[j+1]-u[j-1]) );
```
Then force:
```
dwdx = 0.5*(curl[i+1]-curl[i-1]); dwdy = 0.5*(curl[j+1]-curl[j-1]);
len = sqrt(dwdx^2+dwdy^2)+1e-5;
nx = dwdx/len, ny = dwdy/len;
u += eps * dt * ( ny * curl );
v += eps * dt * ( -nx * curl );
```
eps ~ 20-40.

Performance: allocate curl array once.

Splat function: given (gx, gy) float grid coords, radius r (cells), color, dye amount, force (fx, fy):
```
for j in [gy-r-1, gy+r+1], i in [gx-r-1, gx+r+1]:
  d2 = (i-gx)^2+(j-gy)^2; if d2 > r2 continue;
  f = exp(-d2/(r2*0.5))? or falloff = (1 - d2/r2)^2
  u += fx*f; dye channels += color*f*amount
```
Use smooth falloff w = Math.pow(1 - d2/r2, 2) multiplied by exp? Simple: w = Math.exp(-3*d2/r2).

Also splat across a swept line between previous and current point for fast drags (interpolate). Yes — do a segment splat with steps = ceil(dist/ (r*0.5)).

Initial seeding: 
- dye blobs: place 5 blobs with colors along the canvas at nice positions, radius ~ 15-30 cells, amount moderate.
- velocity: apply swirl: for each cell, compute relative to two vortex centers, add tangential velocity. Also a general gentle drift.

Then also do a few warm-up steps? Not needed.

Let me write the render:

```js
const img = ctx.createImageData(gw, gh);
```
Then in render loop, write into img.data (Uint8ClampedArray) — for each of gw*gh: idx = 1 + (j+1)*stride + i... careful. Let me precompute a mapping offset array `roff` for each pixel so inner loop is tight: For pixel p (0..gw*gh-1): x=p%gw, y=(p/gw)|0, src = 1 + x + (1+y)*stride. Precompute srcArr = Int32Array. Then loop p.

color: r = Math.min(255, dr*255) etc. alpha = Math.min(255, da*255).

Then off.putImageData(img,0,0); main ctx.drawImage(off,0,0,cw,ch).

Note ImageData requires the data array length gw*gh*4.

Then a subtle vignette/darkening drawn before dye: fillStyle gradient.

Let's write it. Also add a HUD hint text and a small readout of fps.

Also handle pointer events with setPointerCapture, touch-action: none.

Let me write the HTML now.

For the color selector, I'll make a row of swatch buttons and a color input. Also a "size"/brush? Not required. Keep: color swatches, color input, Pause/Resume, Clear. Plus maybe a "Strength"? Not required — skip to reduce risk. I'll add a slider for brush size? No.

Let me write it.

One more: "Momentum and dye remain visible after the pointer is released and gradually dissipate." — damping factors.

Write file now.

Also handle high-DPI: use dpr = min(devicePixelRatio, 1.5)? For perf bound, use 1. Sharpness of dye rendering: the source is only ~240x160 anyway, so dpr 1 loses little. Use dpr = 1.

Hmm, but the background gradient and UI text would look slightly soft. Acceptable. Actually let me use dpr = min(dpr, 2) for the canvas backing store but keep the sim grid fixed. Cost: filling 2400x1600 background per frame with gradient — that's cheap-ish. But full-screen fill at 2x is 3.8M px fill... could be a few ms. Use dpr=1. Good compromise.

Let me write.

Regarding dt: use fixed dt = 1/60 accumulator with max 2 steps.

Now code:

```js
'use strict';
const canvas = document.getElementById('c');
const ctx = canvas.getContext('2d', {alpha:false});
const off = document.createElement('canvas'); const octx = off.getContext('2d');
```

Set sizes in resize().

Params object.

Let me write out the whole thing.

Also need to make sure Clear resets velocity — yes zero arrays.

Also "Seed the initial scene with a small amount of colored dye and motion so the simulation is visible on load." — do seed at init.

Also after Clear, the sim shows background only until next drag. Fine.

Let's write.

I'll also add keyboard shortcuts: Space = pause, C = clear? Optional; add spacebar. Careful not to hijack when typing in color input (no text inputs). Fine.

Write the file.

Edge: ImageData creation per resize.

Let me write final code.

function step(dt):
1. damping: u *= velDamp (0.99 per... make it dt-aware: Math.pow(0.995, dt*60)). Precompute factor per step.
2. vorticity confinement (uses curl from current u,v) then project.
Order (typical): forces → project → advect → project.
Let's do:
 - apply vorticity force (u,v)
 - project (pressure solve, subtract gradient)
 - advect velocity (u0=v source = u; advect into u) — need temp buffers u0,v0.
 - project again
 - advect dye
 - dissipate dye & velocity

Advect velocity: standard: copy u->u0, v->v0, then for each cell sample u0,v0 back-traced. Fine.

Let me code it.

For projection, use arrays p (size), then u -= 0.5*(p[i+1]-p[i-1]).

Now write.

Also note: boundary condition for dye in advect: my clamping handles it. But dye near the edge may smear; also I should keep dye from building at border. Add slight extra dissipation? It's fine.

Let me write the file.

There are some issues to fix:
1. `resize()` sets off.width/off.height which resets the offscreen canvas — but that's fine. However, on resize the offscreen canvas content is cleared; fine since we redraw.
2. `tr.set(tr)` no-op nonsense — remove.
3. In `advect`, the boundary samples: a00 uses i0 which can be 0 or gw+1 (boundary cells) — for dye, boundary cells contain copied values from earlier? Actually dye boundary cells are never set to anything (they're 0) except in the case where i0=gw, i1=gw+1 → a10 = (gw+1) + row which is a boundary cell = 0. That would cause dye loss at right/bottom edges. Let me fix by clamping i1 = min(i0+1, gw) and i0 = min(i0, gw)... Standard Stam clamps the backtrace position within the interior. Let me just clamp x to [0.5, gw+0.5] and compute i0 = min(floor(x), gw), i1 = min(i0+1, gw). If x = gw+0.5, i0 = gw, i1 = gw, s1 = 0.5 — slightly off but harmless. Hmm, better: clamp x to [0.5, gw-0.5]? That would flatten at edges. Let me instead set the dye boundary cells via a copy from interior so boundary samples are valid. That's the cleanest: after advecting dye, setBndDye: dr[boundary] = dr[interior neighbor]. Then sampling boundary cells returns valid values. Let's do that.

4. In `step`, `MIN` is used before its function declaration — function declarations are hoisted, so fine. But `MIN(CFG.dyeFade, CFG.velDamp)` logic is weird: I intended velocity to dissipate slower than dye. Let me simplify: velFactor = pow(0.999, dt*60), dyeFactor = pow(0.9965, dt*60). Use two passes.

5. Vorticity confinement: `u += eps*dt*ny*curl` — with dt = 1/60 and eps=26, factor 0.43. curl magnitudes ~ a few units. OK.

6. The initial swirl magnitude computation: `vv.k * fall / gw * 0.02` times -dy. For dx = 100 cells in a gw=240 grid: -dy*105*0.02/240 = -100*0.00875 = -0.875 cells/sec. That's slow (0.875 cells/s = ~4 px/s). Way too slow! Need much bigger velocities. Dye advection at 240 cells/sec = 1200px/s is fast. Let's target vortex velocities of ~40-80 cells/sec (200-400 px/s). 

Let me redo: for a vortex with radius R (cells) and peak tangential speed S, velocity = tangential * S * exp(-d²/(R²)) where tangential = (-dy/R, dx/R) normalized. Let's just do: vx += -dy * amp, vy += dx * amp, where amp = S / (R²) roughly with exp falloff. With R = 0.2*gw = 48 cells and S = 60: amp = 60/(48*48) = 0.026 per cell per... at d=48: -dy*0.026 = 1.25. Hmm: tangential speed = d * amp = 48*0.026 = 1.25. Not 60. I messed up: amp = S/R = 60/48 = 1.25 → speed at d=R = d*amp = 60. So amp = S/R where R in cells. With R = 0.18*gw.

So: ampx = S_v / R_x where R_x = 0.18*gw, and use tan = (-dy/gw-ish, dx/gw-ish) to normalize for aspect... Since cells are square in pixels, tangential should be (-dy, dx)/d normalized. So: vx += -dy * amp, vy += dx * amp gives tangential speed d*amp, peak at d=R. amp = S/R.

Also add a global drift flow.

Also the drag force: `vx * 0.11` where vx is in cells/sec. Drag delta over dt: e.g., moving 200px in 16ms → gx delta = 200/5 = 40 cells in 0.016s → 2500 cells/sec, clamped to gw*14 = 3360. Then force applied = 2500*0.11 = 275 cells/sec at the splat center, distributed with a Gaussian (w up to 1). That's a huge impulse but spread over a radius-4 disc (~50 cells). Hmm, splat sets u directly (adds). Adding 275 cells/sec to a few cells creates a very sharp jet that will get projected away. Better to scale down: multiply by ~0.03 → 75 cells/sec. Let me use force factor ~0.05 and also normalize by drag distance... Let's compute velocity magnitude in cells/sec but include the natural factor: cells per second of pointer motion. Moving at 600 px/s with 5px cells = 120 cells/sec. So the pointer's own speed in cells/sec is the right scale, NOT delta/dt (which is the same thing actually... delta/dt is exactly pointer speed). Oh right! dx/dt IS the pointer speed in cells/sec. So vx ≈ pointer speed in cells/sec ≈ up to a few hundred. The clamp at gw*14 = 3360 is generous. So the injected velocity should be roughly proportional to pointer speed — factor 1.0 would be physically matching. Using 0.11 gives 10% which is reasonable, or factor ~0.5 for strong response. Let me use 0.35 * clamped speed distributes via falloff. Actually with the Gaussian w ∈ [0.25, 1], effective peak = 0.35 * speed. Let's use 0.4 for snappy response. Hmm risk of instability from the CFL condition: CFL requires dx/dt * ... |u|*dt < 1 cell. With |u| = 300 cells/sec and dt=1/60, that's 5 cells per step — the advection backtrace is unstable/sharp but Stam's advection is unconditionally stable (it's a backward trace with clamping), just produces artifacts. It's fine and actually standard practice. But it will produce a very fast streak. That's expected/fun.

Actually to keep swirls visible longer, maybe cap the injected speed to something like gw*3 = 720 cells/s. Let me cap at 250 cells/sec and use factor 0.6. Let's set maxSpeed = 260.

Let me also reconsider the drag force being spread over the segment: `fx/steps` per splat — each splat adds fx*k... Since drag velocity multiplied by factor. Let's define per-pointer-move: speed in cells/sec → impulse per unit... Simpler: each move adds vx*0.5*w to the cells. Good.

7. Also `brushCells = 4` → 4 cells = 20px radius. A bit small; let's use 5.

8. Rendering: `dr[id]*255` — dr is dye color coefficient; with amount 0.55 and w up to 1, da ≈ 0.55 → alpha 140. Color rgb would be 0.55*cr*255... Actually splat adds cr*amount*w to dr and amount*w to da, so r/alpha = cr. Good, alpha ~140 with rgb ~ (56,214,255) → color appears as that color at 55% opacity over dark bg. That's a bit dark. Let me boost: use amount ~0.9 and add alpha emphasis: draw with alpha = clamp(da*255) but scale the alpha with a gain, e.g., alpha = min(255, da*255*1.6). Or simply use dye amounts ~1.0+. I'll set initial blob a to ~1.2 and drag amount ~1.0, plus alpha gain 1.15.

Let me also handle the "persistent swirling flow" — dissipation is 0.999 for vel (dye 0.9965 per frame). At 60fps, vel decay half-life = 693 frames ≈ 11s. OK.

9. `resize()` also sets off.width/off.height each time — that's needed only when grid changes; but resetting off dims is harmless.

Actually there's a bug: `resize()` sets `off.width = gw` where gw from the closure — fine.

10. Initial `hint` fades after first drag - fine.

11. In `render` the tone-mapping block references unused `m` and does nothing useful; simplify: soft-clip using 1 - exp(-x)? Let's do: r = 255*(1 - Math.exp(-r/255))? That darkens. Simpler: clamp and if >255 compress: v = 255 + (v-255)*0.5 iteratively. Let me just use a soft clip: v <= 200: v; else 200 + (v-200)/(1+(v-200)*0.02). Meh. Let's keep simple clamp with mild compression. Actually simplest: since alpha caps at 255 and rgb can exceed, just clamp rgb to 255. Slight hue distortion in hot spots, acceptable. I'll do a soft-knee for niceness.

12. Big one: `motionGUI` is useless — remove.

13. Seed calls step() which uses `iters` and does projection — fine.

Let me now rewrite the problematic parts via edits. Actually, given the number of changes, let me rewrite the file cleanly.

Also: performance. Per frame at 240x160 grid: 
- vorticity: 2 passes over 38400 = 76k ops each
- project ×2: divergence 38k + iters×38k×~6 + 38k → with 20 iters ≈ 38k*120 = 4.6M array accesses each project → ~9M for two.
- advect vel + 4-channel dye advect: 38k × ~30 ops × 2 = 2.3M.
So ~12M typed-array ops per frame. That's maybe 15-30 ms in JS. Too slow for 60fps with 2 substeps... but only 1 substep is typical (acc >= FIXED once per frame). So ~15-30ms/frame → 30-60fps. Acceptable but let's reduce cost:
- Reduce target cell size to 6px → 200x133 = 26600 cells. Or keep 5px but cap grid at 240x160.
- Reduce iters to 12-16 with Gauss-Seidel (fast convergence). Gauss-Seidel with red-black or in-place ordering converges quickly.
- Skip the second projection? It's needed after advection. Could reduce.

Let me set targetCellPx = 6 → grid 200×133 = 26.6k cells. Dye rendering upscaled 6× — still smooth-ish with bilinear. Hmm, 6× nearest-ish upscale with smoothing 'high' looks a bit blobby but fine and organic.

Compromise: targetCellPx = 5, max 240x160 = 38400, iters default 14, adaptive 8..20. Grid ~240x160 at 1200x800. Cost ≈ 38400*120*2 = 9.2M + others ~ 12M. Let's test in the browser and measure fps. The adaptive iters will handle it.

Let me also multi-pass: use the fact that the advect for dye can be merged... fine.

Let me rewrite the file now with fixes.

Now let me test in the browser. First check console for errors and take a screenshot.

One concern: the velocity advection weight logic with `w10 = s1*t0*(i1!==i0?1:0)`. If i1 === i0 (only at clamped edge), then s1 = x - i0 which for x = gw+0.5 → i0=gw, s1=0.5, so w10 = 0 anyway... wait no, s1 = 0.5 which is nonzero. Setting w10=0 and w11=0 with i1=i0 means we only use a00 with weight w00 = s0*t0 = 0.5*t0. That halves the total weight at the clamped edge — loses 50% near boundary. Hmm. Better approach: when i1 > gw, use i1 = gw and keep s1 = 0 so the weight is zero and w00 = 1. That's what clamping should be.

Cleaner: clamp so that if i0 >= gw, set i0 = gw - 1, i1 = gw, and s1 = x - i0 which will be in (0,1]... For x up to gw+0.5, i0 = gw-1 would be wrong. Simplest robust approach: clamp x to [1, gw] in cell-index terms... Actually the standard Stam approach: x clamped to [0.5, N+0.5] where N=gw, then i0 = floor(x), i1 = i0+1, and the array is padded so i1 = gw+1 is a valid boundary cell (which after setBndDye contains the copied interior value). So for velocity, boundary cells contain negated values, which for dye advection is wrong, but for velocity advection, u at boundary = -u[next interior], so sampling it gives a mirrored value — that's actually reasonable-ish for free-slip but can cause artifact at edges.

Given the falloff and that the velocity field advecting itself at the boundary is minor, using the padded boundary value is the original Stam behavior. But my setBndVel negates, and then the projected/dissipated field's boundary is only used by advect and projection (projection only reads interior: u[id+1] where id=gw → boundary cell gw+1 → negated. That's the correct free-slip boundary for the divergence computation? For free-slip we set u at boundary = -u[interior] which makes the divergence at the boundary... actually the standard Stam code sets the boundary as the negation for the b=1 component, giving a no-through-flow condition. Fine.)

Let me simplify: revert to the plain Stam approach for both advections — clamp x,y to [0.5, gw+0.5]/[gh+0.5] and use i1 = i0+1 (valid index, boundary cell exists). The only loss is at the extreme edge where a dye edge cell may be sampled from a boundary cell — and since I run setBndDye() which copies interior to boundary, boundary cells hold valid dye values. For velocity, boundary holds the negated mirror, which is fine/standard.

That's simpler and correct. Let me change both advect functions back to the straightforward version.

Note: I need to make sure the dye boundary cells are properly copied AFTER advection (they are, setBndDye is called after the copy-back). But during advection, boundary cells of the *source* hold the value from the previous frame's setBndDye — valid.

For velocity: source u0 = copy of u which had setBndVel applied after advection. Valid.

Let me make that edit.

Also potential issue: `stage.addEventListener('pointermove')` — the stage covers the canvas and the UI panel. If the user drags starting on the UI panel... pointerdown on a button won't start a drag (pointerdown on UI panel target = panel, but I listen on stage so it would fire!). The panel is a child of stage, so pointerdown on the panel bubbles to stage → starts a drag. That's an issue: clicking Pause would also dab dye. Minor but let's guard: in onDown, check if e.target is inside #ui → ignore.

Let me fix that too.

Also: pointerdown on a button then move → drag. Guard fixes it.

Let me apply edits.

My advectDye oldText was wrong (I wrote db line incorrectly). Let me re-read the file section.

Weird. The first edit in the earlier batch also failed? No — the earlier batch's edit 1 failed and the whole call was rejected (atomic). So the velocity one was also not applied. But now edit with corrected text still fails... Let me check the exact whitespace. Maybe line 255 has different indentation. Let me use read.

The file content matches what I wrote... The edit failure was likely due to the first edit in the batch changing overlapping content? No — each oldText must be unique. Hmm, the second edit's oldText appears twice? No, "let x = i - dt * u[id];" only in advectDye.

Wait — maybe the issue is that the edit tool validates against the original file, and both my edits contain similar text but not overlapping. Edit 1 oldText starts with "      let x = i - dt * u0[id];" and edit 2 with "      let x = i - dt * u[id];". These are distinct.

In my last (second) call, I only had one edit with the oldText for the dye one — and it failed. The difference between what I wrote and the file: in my oldText I wrote `tdb[id] = db[a] * w00 + db[a + 1]...` — no wait, I fixed that in the second attempt. Let me look at exactly what I submitted in the second attempt:

```
      const w00 = s0 * t0, w10 = (di ? s1 * t0 : 0), w01 = (dj ? s0 * t1 : 0), w11 = ((di && dj) ? s1 * t1 : 0);
      tdr[id] = dr[a] * w00 + dr[a + di] * w10 + dr[a + dj * stride] * w01 + dr[a + di + dj * stride] * w11;
```
vs file:
```
      const w00 = s0 * t0, w10 = (di ? s1 * t0 : 0), w01 = (dj ? s0 * t1 : 0), w11 = ((di && dj) ? s1 * t1 : 0);
      tdr[id] = dr[a] * w00 + dr[a + di] * w10 + dr[a + dj * stride] * w01 + dr[a + di + dj * stride] * w11;
```
Looks identical. Hmm, maybe trailing whitespace somewhere? Or the edit tool is matching against the file with some normalization issue... Perhaps the issue is the tool found the oldText ambiguous? No, error says "Could not find the exact text".

Maybe the issue is my oldText had a subtle difference in line 265 vs file... Let me check a byte-diff by extracting the region to a temp file and comparing with python. Actually simpler: use sed/python to do the replacement programmatically. Let me just use python for these two replacements.

Actually, maybe the issue is that in the second attempt I included the line "      if (i1 > gw) i1 = i0; if (j1 > gh) j1 = j0;" which matches... fine.

Let me just do it with python to be safe.

Actually wait — I wonder if the edit tool compares against a snapshot taken at the start of the message... The first batch's edit 1 (velocity) failed, so nothing was applied. Then my second call had only the dye edit and it failed too. Strange. Perhaps the tool's matching requires the oldText to appear exactly once AND it uses some fuzzy/whitespace normalization. Let me try a much smaller oldText to isolate.

No python. Use node? Let's check node availability.

The first rep succeeded (wrote to s but file not saved), the second failed because the first replacement already removed... wait, the second one is for advectDye: "const di = i1 - i0, dj = j1 - j0;" — but the first replacement changed `let i1 = i0 + 1, j1 = j0 + 1;\n if (i1 > gw)...` only in advectVelocity. So the dye one still has `let i1...` and `const di = ...`. Count 0?? That means the string doesn't match. Hmm... maybe trailing whitespace. Let me grep the actual lines 256-261 with cat -A.

The text matches exactly what I searched for... unless the first `rep` already modified something. OH! The first replacement's newText contains `const i1 = i0 + 1, j1 = j0 + 1;` but the first replacement also happens in advectVelocity only. Hmm, but count for `const di = i1 - i0` should still be 1.

Wait — did the first rep actually succeed? The error was thrown at line 27 which is the second rep. Since the exception was thrown, s was not written. But the second rep's search... Maybe my template literal in the heredoc had an issue: I used backticks inside a bash heredoc with 'EOF' quoted, so no expansion. The JS template literal `      const di = i1 - i0, dj = j1 - j0;\n ...` — the content contains `${...}`? No.

Hmm wait, the second rep's old string I wrote in the fix.js starts with `      const di = i1 - i0, dj = j1 - j0;` — that matches line 257. Unless... the second rep old string I typed in fix.js was actually different: I included lines "const di...", "const w00...", tdr..., tdg..., tdb..., tda... — yes that's what I wrote.

OH WAIT. I see: in the first `rep` the replacement text I typed includes `const i1 = i0 + 1, j1 = j0 + 1;` — and my old_vel text was searched in advectVelocity and replaced. Fine.

Hmm, so why count 0? Let me debug: maybe the new_vel wrote `const a = i0 + j0 * stride;` and... no.

Actually! Maybe the issue is that in the heredoc, the `\n` sequences... no, I used actual newlines in a template literal.

Let me test directly: use grep -F with the string.

So the individual lines match. So my combined string must differ. Perhaps the `tdb` line: in fix.js I typed `tdb[id] = db[a] * w00 + db[a + di] * w10 + db[a + dj * stride] * w01 + db[a + di + dj * stride] * w11;` — matches. Hmm.

Wait... I bet the issue is that in fix.js, the second rep's old string was constructed with a nested template literal? No...

Let me just re-check fix.js content.

My bad: I forgot the line `      const s1 = x - i0, ...` and `      const a = i0 + j0 * stride;` in the dye block (I started at `const di...` then jumped to `const w00`, skipping s1/a lines). In the file, between `const di` and `const w00` there are those two lines. That's why it failed. Also the first rep succeeded but wasn't saved — good, so the file is still original.

Rather than continue with fragile patches, let me just rewrite the entire file with the corrected advect functions. I'll use `write` again with the full corrected content.

Also note my weird `w01.replace('dr','da')` hack in fix.js — remove that; I'll write the clean version.

Let me write the final file completely.

The console is clean. No errors. FPS 24-31 — the sim is heavy (frameSmooth is presumably high so iters dropped to 10-13). But the screenshot shows... nothing? No dye visible. Wait, the screenshot shows no dye at all. Odd. The seed() ran 24 steps of 1/60 — perhaps the dye got dissipated? Or... let me check: fps shows 24-31, so it's running. But the dye is invisible.

Wait — maybe the issue is the render: `imgData` was created via `octx.createImageData(gw, gh)` before... but `off.width = gw; off.height = gh` was set AFTER allocate() and createImageData — no, order: allocate() then resizeCanvas() then off.width=gw. putImageData(imgData, 0, 0) on a canvas of gw×gh — should be fine.

Hmm, but wait: on the resize handler I call allocate() again which creates imgData from the new octx — fine.

So why is nothing visible? Let's think: maybe the seed dissipation. 24 steps with dyeFade 0.996 → 0.996^24 = 0.907. Not the issue.

Maybe the dye alpha: da initial = 1.10 at blob center * gain 1.15 → 322 → clamped 255. Should be visible.

Unless... putImageData is being drawn but the alpha is... Hmm, is the ImageData actually written? `d[o+3] = a` where a is a float (not integer!) — Uint8ClampedArray assignment truncates. Fine.

Wait, could the issue be that the canvas context has alpha:false, and drawing an image with alpha over it... that should composite normally.

Hmm, maybe the issue is `desynchronized: true` causing issues? Unlikely.

Let me check the fps counter: "fps 31" but the stats show solve 13 and fps 31 — but in the inspect output it says "fps 24". So the sim is running at ~24-31 fps. But no dye...

OH WAIT. I see it. In `frame()`, `render(canvas.width, canvas.height)` is called. And `drawBackground` fills with bgGrad. But maybe the whole render isn't happening because... hmm.

Actually, let me reconsider: maybe the dye IS being drawn but the simulation is so slow (24fps with 10-13 iters) and... no, dye should still show.

Let me test by dumping some state to console. I can't easily access the closure. Let me add a temporary debug hook: expose window.__sim = {u,v,...}. Actually simpler: take a screenshot after a longer wait — maybe the frame was captured at t=0 before seed completed? No, the flow is synchronous.

Hmm, but wait: the browser tool's screenshot at "+0ms" — it reloaded and took the screenshot immediately, maybe the first frames. But seed() is synchronous before the first rAF. Unless the screenshot was taken during... The fps shows 24/31 meaning many frames passed.

Actually hold on. Let me re-read the render function's alpha handling: `a = da[id] * 255 * gain` where gain=1.15 → da=1.1 → 322 → clamped to 255. Then d[o+3]=255. And r = dr[id]*255 = 0.22*1.1*255 = 62, g = 236, b = 255. That's a bright cyan. Should be clearly visible!

Unless... `dr[a]*w00 + ...` — in advectDye, hmm.

Unless the whole thing is that ImageData for the *small* canvas... Let me verify by taking a screenshot after waiting. Let me use the "motion" action to get frames, or just re-inspect after a delay.

Actually — I wonder if the issue is the seam: `ctx = canvas.getContext('2d', {alpha:false, desynchronized:true})`. With alpha:false, drawing a semi-transparent source is composited against the existing opaque backdrop — fine.

Let me just check by capturing another screenshot now (some time has passed).

Nothing visible. The fps dropped to 14 which means the sim is running but no dye shows. Let me debug: expose state to console. Let me add `window.__dbg = {get: () => ({...})}`. I'll temporarily add a debug endpoint.

Possible root cause: `imgData = octx.createImageData(gw, gh)` — but `off.width` is set after allocate(). createImageData doesn't depend on canvas size. OK.

Hmm! Wait. Maybe the problem is `render()` uses `pxIndex[p]` and `da[id]`... all fine.

OH. I think I see it! In `advectDye` I copy back with `for (let id = 0; id < N; id++) { dr[id] = tdr[id]; ... }`. And `tdr[id]` — fine.

Hmm, what about `dissipate`? fv = pow(0.999, 1) = 0.999, fd = 0.996. Fine.

What about `project()`? It modifies u,v. Fine.

Let me think about the initial velocity magnitude. Vortex peak = 62 cells/sec. That's fine.

So the dye should be there... unless the alphablending makes it disappear. Wait — is `drawImage(off, 0, 0, w, h)` failing? If `off` is 240x160 and we draw at 1200x800 — fine.

Hmm, is `ctx.save/restore` needed? No.

Wait... maybe the problem is that the entire `render()` output is drawn but then... the fps display updates, so the loop runs.

Let me consider: is the canvas perhaps covered by something? #hint is centered but pointer-events none and small. The screenshot shows nothing else.

Hmm, is it possible that the canvas is actually 1200x800 but `render` writes into imgData of gw*gh = 38400 pixels... and putImageData(imgData, 0, 0) puts it into `off` (240x160). Fine.

Let me actually verify with a debug dump. I'll add to the code: `window.__dbg = {u, v, dr, da, ...}` — but they're reassigned on reallocate; use getters. Let me add a function at the end of the IIFE:

window.__probe = function() { return {gw, gh, maxDa: max(da), maxU: max(u), sumDye: sum(dr) }; }

Actually simpler and quicker: add a temporary line in the boot section. Let me patch with node sed-like edit and then use browser console via inspect to evaluate. Let me add:

window.__probe = () => {
  let md=0, mu=0;
  for (let i=0;i<N;i++){ if(da[i]>md) md=da[i]; if(Math.abs(u[i])>mu) mu=Math.abs(u[i]); }
  return {gw,gh,md,mu, px0: pxIndex[0], img: imgData ? imgData.width+'x'+imgData.height : null, off: off.width+'x'+off.height};
};

Then run `__probe()` in the browser. The inspect tool has an "inspect" action — but does it let me run JS? It returns DOM + console. Maybe I can inject a script through... Let me check what "inspect" returns: {"console":..., "dom":..., "images":...}. Possibly it executes a JS expression I provide? There's no parameter for JS. Hmm, the key action can send keys; I could use the browser address... no.

Alternative: use console.log in the code to print debug info, which the inspect tool reports in the "console" array. That works! Let me add a temporary console.log in frame() every 60 frames with debug stats.

Let me add temporary debug code, reload, and read the console output.

Excellent debug info!

- md (max dye density) = 0.248 → alpha = 0.248*255*1.15 = 73. Visible but faint. Hmm, the dye was seeded with 1.10 at the center but after 24 steps it's down to 0.248? That's a 4.4× drop. The dissipation is only 0.9×. So the advection is diffusing/decaying the dye fast!

Wait — actually the seed splat has radius 30 cells with amount 1.1 at center, but the dye is concentrated in a small area and advection spreads it. But 4.4× drop in density after 24 steps with velocity ~62 cells/sec... In 24 steps of 1/60 s = 0.4 s, the dye moves 25 cells ≈ its radius. So the blob spreads over ~2× area → density drops ~2×. Plus softening of the splat profile (the splat is sharp; bilinear advection smooths it). OK.

- mu (max |u|) = 12732 cells/sec!! That's insanely large — the CFL is massively violated. This is why the dye smears and why fps is low-ish. Where does the huge velocity come from? Vorticity confinement! With curl ~ large and eps = 22 * dt = 0.366, the force added is eps * n * curl which can be large. Or the vortices with peak 62 → tangential speeds of 62, but after projection + vorticity confinement it blows up.

Let's think: curl[id] = 0.5*((v[i+1]-v[i-1]) - (u[j+1]-u[j-1])). With u~62 over 2 cells... no wait, the vortex speed varies smoothly: over 2 cells (0.02 of R), the derivative is tiny. Hmm, curl = 0.5 * Δv/Δx - Δu/Δy. For a smooth vortex with tangential speed T = d*amp, curl = 2*amp*fall (roughly), which is small.

But at the boundary cells the u,v jump (negated mirror), creating large curl near the boundary → huge vorticity force at the boundary → instability. That's likely the culprit: my setBndVel negates the boundary values, and gradient computations near the boundary use (u[id+1] - u[id-1]) which spans a jump of 2× the interior value at the boundary cell. For a strong vortex touching the edge, this creates high curl, and then vorticity confinement amplifies.

Also the seeding applied the vortex field with `u[id] += vx*0.9` including near the boundary (cells 1 and gw) so the mirror negation is fine, but the vortices' falloff means near boundary velocity is small. Hmm, but 12732 is huge. Let's consider the first vorticityConfinement: dwdy/dwdx uses curl[id+1] - curl[id-1]; near a boundary where curl is huge and noisy, the normalized direction varies wildly, giving a large force (eps * curl, with curl large). Then projection should remove divergence, but the magnitude can grow in a feedback loop.

Also `Math.sqrt(dwdx²+dwdy²)+1e-5` — if curl is spiky, len ~ small relative to curl, so force ≈ eps*curl which is huge. Vorticity confinement as written: u += eps*(dwdy/len)*curl — the magnitude is eps*|curl| which for a large curl is a huge kick.

So: clamp. Standard implementations compute force = eps * (nx, ny) * curl where the curl magnitude is bounded by the local gradient scale... Many implementations use the same formula and it works because curl is small. I should:
1. Limit vorticity confinement to smooth regions and use a bounded formulation: force = eps * clamp(|curl|, 0, cmax) * n. Let me clamp curl magnitude used in the force to e.g. 5 (cells/sec² scale).
2. Reduce eps.
3. Also compute the curl of the *source* velocity only within the interior and treat boundary cells carefully.

Alternatively drop vorticity confinement entirely and rely on the fact that Stam's advection is numerically diffusive... but then swirls die out quickly, which hurts the requirement "continues swirling". Keep it but clamp.

Also the huge max speed of 12732 explains why the fps is 14-24 (numerical diffusion/no, fps depends on iters) — actually the fps being 14 at one point is concerning. The sim cost is fixed per step; iters dropped to 8 (min) yet fps is 14-32. That means each frame is taking 20-60ms even at 8 iters. Hmm, that suggests the actual bottleneck isn't the solver but something else. Grid = 240x160 = 38400 cells.

Cost per step: 
- vorticity: 2 passes × 38400 = 76.8k iterations with sqrt
- project: 38400×(iters+1)
- advect vel: 38400 with bilinear (4 mults ×2) 
- advect dye: 38400 × 16 mults
- copy back: 4×N = 230k array writes
- dissipate: 8×N = 307k array writes

Total per step ≈ 76.8k×15 + 38.4k×17 + 230k + 307k ≈ 1.15M + 0.65M + 0.5M ≈ 2.3M typed array ops. That should take ~5-10 ms in JS. Hmm. The dissipate and copy-back loops are full-array (N = 262×162 = 42.5k) so 8×42.5k = 340k.

Actually the real cost may be the `render()`: the pixel loop is gw*gh = 38400 iterations with clamping — fast. putImageData + drawImage of a 240x160 image scaled to 1200x800 with high smoothing: that's 960,000 pixels bilinear — should be fast, but `desynchronized` canvas with a large drawImage each frame might be slowish. Plus a full-screen 1200x800 radial-gradient fill each frame.

The measured fps fluctuated 14-32 in the tool's reporting — but note the browser may be throttled by the headless environment. Let me measure more precisely with a timing probe in the console log (e.g., log the average time of step vs render).

Let me also address the fundamental issues:
1. The dye density being 0.248 → too faint. Increase seed amounts and render gain. Better: since advection is diffusive, I should keep alphaGain ~1.5 and boost the seed. Also, the visible alpha at 0.248 → 73/255 = 29% opacity over dark bg — visible but weak. The screenshot shows nothing visible though! Something's off. Even 29% alpha of a bright cyan over dark navy should be clearly visible in a screenshot.

So there IS a rendering problem. Let's think again...

AH WAIT. I bet I know: `ctx = canvas.getContext('2d', { alpha: false, desynchronized: true })` — hmm no.

Actually: `d[o] = r` where r is a float like 62.3. Uint8ClampedArray handles it. `d[o+3] = a` with a = 73.4 → 73.

putImageData(imgData, 0, 0) → off is 240x160 with a transparent background; the ImageData replaces the region — that's fine, it's an alpha-replaced blit.

drawImage(off, 0, 0, w, h) → draws the 240x160 RGBA scaled up with smoothing over the background gradient.

Wait... could `imageSmoothingQuality = 'high'` + `desynchronized: true` be causing an issue? Let me just test with a debug that draws a solid color rect and see. Actually, easier: log the pixel values from the offscreen canvas after putImageData, e.g., read back a pixel via octx.getImageData at the dye location.

Let me add to the debug: read pixel (10,10) and (gw*0.3, gh*0.38) from octx.getImageData(1,1,10,10).

Hmm, getImageData on a 240x160 canvas is cheap. Let me add a debug that reports the average of the center of the main canvas... Actually, simplest: use ctx.getImageData(600, 400, 1, 1).data from the main canvas to check what's actually rendered. Let me add that.

Also check: maybe the issue is that the dye max is 0.248 but spread so much that the *whole* field is covered with a very low density (a0 at center = 0.0091 — that's tiny!). So the dye blobs flattened out into extremely thin, wide sheets? With velocity 12732 cells/sec, the dye gets advected 12732/60 = 212 cells per step → the semi-Lagrangian backtrace samples from way outside → clamps to the edge → smears the dye toward the boundary. Yeah, the runaway velocity is destroying the field.

So fixing the runaway velocity is the priority. And then the dye should be much denser (higher alpha), and the "nothing visible" issue should resolve too since alpha would be ~0.5-1.0.

Let me fix:
1. Vorticity confinement: clamp curl magnitude and reduce eps to ~6, and use a more stable formula: 
   force = eps * dt * (n * min(|curl|, curlMax)). Let curlMax = 8.
2. Also guard the whole velocity field: after step, clamp |u|,|v| to a max (e.g., 3*gw? no). Better: clamp to maxSpeed*1.5 or so. A cheap safety net: in step, after project, clamp each cell to a max magnitude (like 600). Let's set velLimit = min(gw,gh)*3 (=~480). Clamping in a loop is cheap-ish (another pass over N). I'll fold the clamp into the dissipate loop to avoid an extra pass.
3. Increase dye amounts: seed a=1.6, and alphaGain 1.3.

Also let's reconsider vorticity strength: with eps=6 and dt=1/60 → 0.1 per unit curl. Fine.

Also the boundary jump issue in the curl computation: curl[id+1] where id=gw is the boundary cell with mirrored velocity → big jump → spurious curl near edges. That's inherent to the free-slip mirror. My setBndVel sets the u boundary = -u(next interior), which means at the boundary the normal velocity reverses. In the curl formula for the boundary cell (id = gw), curl uses u[id+1] (boundary) and u[id-1] (interior). That's the standard Stam approach, though, and vorticity confinement is applied only to interior cells, which use curl at interior cells — but curl at interior cell gw uses v[gw+1] (boundary). So yes, spurious curl at the last interior column.

An alternative that avoids the negation: set boundary cells to copy the adjacent interior value (free-slip tangential, and the normal component set to zero). For the free-slip/outflow condition in a Galerkin sense, setting u boundary = 0 (zero normal velocity) is actually the standard "no-slip wall" and is very stable, and it makes curl near boundaries smoother. Hmm, but then the flow reflects off walls.

Actually, the classic Stam free-slip is: for i=0 (left boundary), u[0][j] = -u[1][j] would be no-flux for the u component at a vertical wall... wait, for a vertical wall the normal component is u itself, and no-penetration means u[0][j] = -u[1][j] gives zero flux through the wall after advection (a particle at the boundary moving right hits the mirror and moves left). And v[0][j] = -v[1][j]? For a tangential component at a vertical wall, free-slip would be v[0][j] = v[1][j]. Negating v at the left/right walls is a no-slip condition. Both are used. Negating v at vertical walls creates a spurious jump in v at the wall → spurious curl.

To be smoother, I'll use: at vertical walls (i=0, i=gw+1): u = -u_interior (no penetration), v = v_interior (free slip). At horizontal walls (j=0, j=gh+1): v = -v_interior, u = u_interior. This is the true free-slip and produces smooth tangential behavior. 

That's a good fix. Then curl near boundaries is 2× the interior value without sign flip issues... Actually with free-slip, the wall is a streamline, so the vorticity is 2× the interior — acceptable.

Then the pressure solve at the boundary: div at the interior uses the boundary value which is a mirror; that's the standard treatment.

Let me implement:
```
function setBndVel() {
  const S = stride, W = gw + 1;
  for (let j = 1; j <= gh; j++) {
    const r = j * S;
    u[r] = -u[r + 1];        u[r + W] = -u[r + gw];   // no normal flow
    v[r] =  v[r + 1];        v[r + W] =  v[r + gw];   // free slip tangential
  }
  for (let i = 1; i <= gw; i++) {
    v[i] = -v[i + S];        v[i + (gh + 1) * S] = -v[i + gh * S];
    u[i] =  u[i + S];        u[i + (gh + 1) * S] =  u[i + gh * S];
  }
}
```
This is consistent free-slip.

Hmm, one caveat: with a tangential velocity at the boundary, advection of dye across the wall... the boundary cells are copies so the dye doesn't get mirrored. Fine.

4. Also, the huge mu=12732 — after fixing #1 and #2, the max speed should be a few hundred. Let's also reduce the vortex peak to ~45 cells/sec and keep CFG.maxSpeed = 260.

Also: I should double-check the perf issue. Let me add timing to the debug log: measure the ms spent in step and in render per second. Let me add a `tStep`/`tRender` accumulator.

Also, note the browser tool might be in a slow environment. Let's measure.

Additionally, the fps reporting: `frameSmooth` starts at 16 and adapts.

Let me apply all these fixes now, plus keep the debug instrumentation temporarily (I'll remove it at the end).

Actually, I realize there might be another significant problem with the huge velocity: `splat` adds fx = vx*0.55 where vx up to 260 → 143 cells/sec at the center. Fine.

Let me now make the edits.

Now update the debug to include timing and also report the average rendered alpha. Let me also check the rendered pixel: add `ctx.getImageData` sampling. Actually let's add to the debug block: measure ms per step and render via performance.now accumulators.

Let me patch the debug block.

Now the dye is visible and swirling. It looks nice — cyan vortex on the left, pink on the right, and there's a flow.

But the dye looks "grainy/pixelated" — the upscaling from 240x160 to 1200x800 with smoothing produces visible blocky artifacts (the classic issue: bilinear upscale of a 5x cell creates a blocky look). It looks like a low-res texture being blown up. Actually the screenshot looks like a "mosaic" pattern. Because imageSmoothingQuality 'high' on a 5× upscale should be smooth... The blockiness might be from the headless renderer's scaling implementation.

Hmm, actually the screenshot looks mottled/noisy — like each 5x5 block has varying brightness. That's because the dye field has high-frequency content and the upscale is bilinear (nearest-ish for 5x?). The visual is acceptable but not great. 

Also `mu: 420` — the velocity is now clamped at the limit (420), meaning it's still hitting the ceiling. Hmm, that means the vortex peaks of 42 cells/sec... no. mu=420 means some cell has speed 420. The clamp is engaged. That's probably at an early frame during seed (the drift + vortices?) or vorticity confinement pushing. Hmm, with the seed at 42 cells/sec and the drift of 6, how could it reach 420? Possibly the pressure solve with free-slip boundaries and the drift creating a global flow: the constant u += 6*sin(...) across the whole domain creates divergence → the projection creates a strong compensating pressure gradient... Still shouldn't reach 420.

Hmm, maybe at frame 1 (the first DBG log) the velocities are still at a transient from the seed's 24 steps. Vorticity confinement with the drift (a shear flow) can create strong curls. It's plausible that the confinement + clamp equilibrium is at the ceiling.

Whatever the cause, the flow looks good in the screenshot. But a speed of 420 cells/sec = 2100 px/sec is very fast; at 5px/cell it moves the whole blob across the screen in <1s. In the screenshot the flow looks like a nice vortex, so it seems OK.

Actually wait. Let's reconsider: maybe mu=420 is exactly at the limit = clamping is active → the sim is saturating, which could cause blocky dye artifacts (dye advected far per step). The dye does look a bit "smeared/spread thin" in places. Let me reduce the velocity ceiling to ~150 and reduce vorticity a bit, then check the look. Also maybe reduce the seed's 24 settle steps.

Let's first check the perf numbers: tS=0, tR=0 at the first log (the accumulators were initialized in that same block). Let me reload and read again to get the timings from the second log.

Also fps ~23-30 in the headless environment. I want to know where the time goes. Let me get a second DBG line.

Actually, the debug logs only print at i%30==1, and I reset the accumulators after printing... The first log at i=1 prints zeros. The reload happened and the console shows only the first log. The tool probably only reports the latest console lines. Let me wait a bit and screenshot to get more logs. Or better: use the "motion" action which runs frames for a while and returns motion frames + console.

Let me use the motion action to let it run and get more debug output.

Key findings:

1. The dye decays extremely fast: `md` goes 1.289 → 0.512 → 0.364 → 0.259 → ... → 0.034 over ~10 × 30 frames = 300 frames = 5 seconds! That's way too fast. The dissipation factor 0.996/frame over 300 frames = 0.30. But md drops by 38× over 300 frames. So advection is numerically diffusing the dye heavily, spreading it thin.

Also `px` (center pixel) = [23,23,42] which is background — so the middle has almost no dye. And the last screenshot shows nothing visible at all. So the dye vanishes in ~5 seconds. Way too fast. That's a problem: "persistent swirling flow".

Why is the dye diffusing so fast? Because the velocity is at the clamp ceiling (420 cells/sec = 2100 px/sec). With dt = 1/60, the backtrace distance = 7 cells per step. The bilinear interpolation with a large displacement each step acts like a box filter of 7 cells → strong smoothing. Plus the flow is fast so the dye spreads over a large area quickly.

So the root cause: velocity is way too high in the seeded scene. Why? Let's figure out. Seed: vortex peak 42 cells/sec, drift 6. After 24 settle steps, mu = 420 (the clamp).

Hmm, that suggests something is growing the velocity by 10×. What? The vorticity confinement with clampped curl of 8: force per step = eps*dt*|curl| = 5*(1/60)*8 = 0.667 cells/sec per step. Over 24 steps that's 16. Not 420.

The pressure projection can amplify velocities, but usually it smooths.

What about the *drift* term: `u[id] += 6*sin(...)` — this adds a non-divergence-free uniform-in-x shear. Projection then works on it: div = -0.5*(du/dx + dv/dy) = -0.5*(-dv/dy) → the pressure gradient accelerates v... no. Hmm, actually the drift shear has zero divergence in the interior (u varies with j, v=0). At the top/bottom walls, u is free-slip (copied), so no divergence. So it should stay ~6.

Wait, could `mu` at the boundary cells be the reported max? My debug loop covers ALL N including boundary cells. The boundary cells hold copies of the interior. Not 420.

Hmm, but which cell has 420? Let me think about vorticity confinement more: `eps = CFG.vorticity * dt = 5/60 = 0.083`. Force = eps * n * curl_max(8) = 0.67 per step. Over 60 steps (1 sec), if applied consistently in the same direction: 40. Not 420.

Hmm... unless the *clamped* w (min |curl|) is fine but len is tiny making n large but normalized (it is normalized). So the force magnitude is bounded by eps*curlClamp = 0.667/step. That's fine.

So where does 420 come from? Perhaps the seed's `u[id] += vx*0.9` where the vortex amp = peak/R. peak=42, R = rf*(gw+gh)*0.5 = 0.20*400*0.5 = 40 cells. amp = 42/40 = 1.05. At a cell with d = 100 cells from the center (outside R), fall = exp(-100²/40²) = e^-6.25 = 0.002. So vx = -dy*1.05*0.002. For dy = -100 → vx = -(-100)*1.05*0.002 = 0.21. Small. Near the center, d=40: vx = -40*1.05*1 = -42.

But hold on: the grid is 240 wide and 160 tall, so (gw+gh)/2 = 200, and R = 0.20*200 = 40 cells. For the blob at (0.30, 0.42) = cell (73, 68). The distance to the top wall is 68 cells, to the left is 73. So R=40 fits. 

So the seed velocity should be ≤ ~42. Yet mu = 420 = exactly the clamp. Something amplifies.

Let me reconsider: is it possible that the first DBG was logged *before* the sim had run (i.e., during the boot at step 1)? The first DBG had md=1.289 which is after the seed's 24 settle steps... but mu was already 420 at that point. So during the 24 seed steps the velocity exploded.

AH WAIT. I think I've got it: the **seed's 24 settle steps** call `step()` → `project()` → but `press` contains values from the previous solve; that's fine.

Hmm, what about `setBndVel` now being free-slip: at the vertical walls, u[bnd] = -u[interior] and v[bnd] = v[interior]. In `project()`, the divergence at interior cell (1,j) uses u[0] = -u[1] (fine) and at (gw, j) uses u[gw+1] = -u[gw]. Fine.

Hmm, so where does 420 come from? Let me instrument: log mu after each of the 24 seed steps, and also find the argmax location. Let me just add a quick check by exposing the state: instead of guessing, I'll log in seed() the max velocity after each step.

Actually — hold on. Let me reconsider the *first* DBG line: it was logged at frame 1, i.e., BEFORE any simulation step in frame()! Because the DBG block is placed after render but the log at i=1 happens on the first frame, which is right after boot's `seed()`. So mu=420 is the state right after seed. And seed ran 24 steps of step(). So yes, the velocity grew to 420 during those 24 steps.

OK so let me instrument the seed to find it. Let me replace the 24-step loop temporarily with per-step logging.

Another suspicion: `vorticityConfinement` uses `curl[id]` computed BEFORE the confinement but `curl` is a full array including boundary cells. The curl at the interior cells adjacent to the boundary uses boundary velocity values. With free-slip, the tangential v at the left wall equals v[1], so v[id+1]-v[id-1] at id=1 = v[2]-v[0] = v[2]-v[1]. Fine, no jump.

But the u component at the boundary: u[0] = -u[1]. So curl at id=1 includes u[id+stride] - u[id-stride] = u at j+1 and j-1 — interior. Fine.

Hmm, so what about the *dwdx, dwdy* using curl at id+1 and id-1 — all interior.

Let me just instrument. Also let me print the location of the max.

Actually, wait. I bet I know! Look at `dissipate()`: `lim = CFG.velLimit` = 420. Before my fix, mu was 12732 — the clamp wasn't there. Now the clamp caps at 420. The dynamics may be *trying* to go higher still. The reported mu=420 means it's saturated at the clamp, i.e., something is driving it beyond 420.

What could drive it that fast? Consider the interaction of the pressure solve with the free-slip boundary at the walls. With free-slip tangential velocity at the walls, the projection's divergence at cell (i,1) uses v[0] = -v[1] (normal blocked) — good.

Hmm, what about the *advection* of velocity: with u0 held at up to 42, and dt=1/60, backtrace = 0.7 cells. No instability.

Let me look at the vorticity confinement formula once more:

u += eps*(dwdy/len)*w where w is the clamped curl.

eps = 5*(1/60) = 0.0833. w = 8 max. So u += 0.0833*n*8 = 0.667 max. Per step. Over 24 steps: 16. Not 420.

Unless... `dt` passed to step is 1/60 — yes, `for (let i = 0; i < 24; i++) step(1 / 60);`.

So the confinement can't be it. What about the seed velocity itself? Let me recompute more carefully:

vx += -dy * vv.amp * vv.s * fall, then u[id] += vx * 0.9.

vv.amp = peak/R. peak=42, R = 0.20 * 200 = 40. amp = 1.05.
At a cell near the vortex center, d ≈ 10: vx = -dy*1.05 = up to ±10.5 → *0.9 = 9.45.
At d = 40: vx = -42.
At d = 80: fall = exp(-4) = 0.018, vx = -dy*1.05*0.018 = 1.5.

So the max is ~42*0.9 = 38. Fine.

Then the drift: u += 6*sin(...). Max 6.

So after seeding, max |u| ≈ 38-44. Then 24 steps → 420?! That's a 10× amplification in 0.4s. The pressure solve (Gauss-Seidel, 12 iters) shouldn't amplify that much... though with only 12 iterations and a strong local divergence (e.g., from the drift shear at the horizontal walls... hmm).

WAIT. I wonder if it's the free-slip boundary + the pressure solve interacting badly. Let's consider the divergence at interior cell (i, 1): div = -0.5*((u[i+1,1]-u[i-1,1]) + (v[i,2]-v[i,0])) where v[i,0] = -v[i,1] (normal blocked at the top wall). So div = -0.5*(du/dx + v2 + v1). If v1 > 0 (flowing down into the wall region... no, at row 1 the v is the fluid's downward velocity), the divergence term = v[i,2]+v[i,1] which could be large. This drives the pressure. But this is standard.

Hmm, let me consider a different possibility: the pressure solve is UNSTABLE in the presence of the "free-slip" mirror because the boundary velocity is not consistent with the discrete divergence. Consider the top wall: v[0] = -v[1]. In the pressure update at cell (i,1): press = 0.25*(press[i-1,1]+press[i+1,1]+press[i,0]+press[i,2]-div). And press[i,0] is a boundary cell that's never updated (stays 0). Fine.

Then u[i,1] -= 0.5*(press[i+1,1]-press[i-1,1]) and v[i,1] -= 0.5*(press[i,2]-press[i,0]) = v - 0.5*press[i,2]. So at row 1, v gets corrected by half the pressure above. Since press[i,0]=0, this creates an asymmetry: the correction at row 1 is half of what it should be, effectively "pushing" fluid into the wall... The classic Stam approach sets the boundary of the pressure to press = div (Neumann) or copies. Hmm, in Stam's original code, the projection loop includes the boundary rows with set_bnd applied to the pressure (b=0 → copies). My project() doesn't set the pressure boundary at all (it stays 0).

This could cause a systematic drift of fluid toward the wall, and since the walls are closed (u/v mirrored with a sign flip → no-through-flow), fluid accumulates at the walls, pressure builds up... but the pressure at the boundary row is forced to 0, so the projection can't satisfy the boundary condition → a persistent imbalance. This could amplify over iterations. Actually, a more likely story: because press[i,0] = 0 always (fixed), and the update at row 1 uses press[i,2] - press[i,0] = press[i,2], the wall acts as a source/sink.

The classic fix: in the pressure solve, iterate over boundary cells too with div[b]=0, i.e., include the padded rows in the solve loop, with the divergence at the boundary cells = 0. Let me extend the pressure loop to include j=0..gh+1 and i=0..gw+1 with divergence = 0 at the boundary (i.e., treat the padded cells as the pressure boundary with a Neumann condition press = neighbor). That's cleaner and standard in many implementations.

Hmm, but honestly, a much more robust approach for this kind of grid: set the pressure boundary to Neumann by iterating the full padded array. Let me do that:

```
for (let j = 0; j <= gh+1; j++) {
  for (let i = 0; i <= gw+1; i++) {
    // at boundary cells, divergence is 0
    press[id] = 0.25*(sum of neighbors - div[id])
  }
}
```
where div at the boundary cells is 0 (already 0 since I only set the interior). This is a proper Neumann BC. Iterating over the padded array costs (262)*(162) = 42.4k cells per iteration instead of 38.4k — 10% more. Fine.

Wait, but there's still the issue that the div at row 1 uses v[i,0] = -v[i,1] (negated). With Neumann pressure at the boundary, the update v[i,1] -= 0.5*(press[i,2]-press[i,0]) where press[i,0] is now a solved value. That's more consistent.

Let me test this hypothesis by instrumenting the seed. Actually, faster: just make the change and re-measure. But I'd like to confirm the cause. Let me instrument seed to log mu per step — quick.

Actually, let me reconsider yet another candidate: `advectVelocity`. The source u0 = u (copy) before advection, then u[id] = sample of u0. With velocity up to 40 cells/sec and dt=1/60 → 0.67 cells. Fine.

Another candidate: THE FORCE from `vorticityConfinement` — I computed eps = 5.0 * dt = 0.083, and the force magnitude is |eps * n * w| ≤ eps*|w| ≤ 0.67/step. But over 24 steps with a consistent direction that's 16. Combined with the feedback from the projection... 

Hmm OK. But there's something important I should check: is `frameSmooth` / `iters` interplay causing multiple steps per frame? No, seed calls step directly.

Let me just instrument. I'll log mu after each seed step and the argmax position.

Also, separately, I must fix the dye's rapid decay. The core problem is that the whole velocity field seems to be at a huge scale, which spreads the dye everywhere instantly. With a proper velocity of ~40 cells/sec, the dye should persist nicely.

Plan:
1. Instrument seed to find the amplification.
2. Fix the pressure boundary.
3. Re-measure.

Let me do the instrumentation.

Confirmed: the initial field is 21.8 (fine), but by SEED2-4 it explodes from *near the bottom-right corner* (237,157 → 235,156 → 234,150). That's the bottom-right corner! A classic sign of the pressure boundary condition problem at the corner.

The growth starts at the bottom-right corner (max gw, max gh) and propagates. So it's the pressure projection near the boundary/corner.

My hypothesis: the pressure at the padded boundary cells is fixed at 0, and the divergence at interior cells adjacent to the boundary includes mirrored velocity values. The projection pushes fluid into the corner, which cannot escape (walls), building pressure that the fixed-zero pressure boundary can't satisfy → runaway.

Fix: iterate the pressure over the full padded array (including the boundary cells) with div=0 at the boundaries. This gives a proper Neumann BC. Let me implement and re-measure.

Also the divergence at cell (gw,j) uses u[gw+1] = -u[gw] → contributing "no flow through the wall" which combined with the mirrored v (free-slip tangential, v[gw+1] = v[gw]) should be consistent.

Let me also handle the corner cells similarly.

Let me rewrite project():

```js
function project() {
  // divergence on the interior
  for (let j = 1; j <= gh; j++) { ... divergence[id] = -0.5*((u[id+1]-u[id-1]) + (v[id+stride]-v[id-stride])); }
  // boundary of divergence stays 0 -> Neumann pressure BC
  for (let k = 0; k < iters; k++) {
    for (let j = 0; j <= gh+1; j++) {
      const row = j*stride;
      for (let i = 0; i <= gw+1; i++) {
        const id = i + row;
        press[id] = 0.25 * (press[id-1] + press[id+1] + press[id-stride] + press[id+stride] - divergence[id]);
      }
    }
  }
  ...
}
```
Careful: at id=0 (corner), press[id-1] is the previous array element (row gh+1's last cell) — out of the logical domain but still a valid array index. To be safe, clamp the neighbor indices. The cost of clamping per cell adds complexity. Alternative: iterate only over the interior + boundary cells but with clamped neighbors using a small extra check. Simpler: iterate the full padded rectangle but for the outermost ring, use only valid neighbors:

I'll do: for j in 0..gh+1, for i in 0..gw+1, and compute neighbors with clamping:
```
const l = (i>0) ? id-1 : id;
const r = (i<gw+1) ? id+1 : id;
const d = (j>0) ? id-stride : id;
const up = (j<gh+1) ? id+stride : id;
press[id] = 0.25*(press[l]+press[r]+press[d]+press[up]-divergence[id]);
```
This is clean and costs a few branches per cell. Fine.

Actually, an even simpler alternative that keeps the interior-only loop: include the pressure boundary cells in the loop but only the ring (a separate loop of O(gw+gh)). And keep the div at the boundary = 0. But the corner cells need inclusion too. Let me just use the clamped-index full loop — it's uniform and simple.

Cost: 42.4k cells × iters. Slightly more than before.

Alternatively, use a dedicated approach: iterate over the interior only, but after each iteration, copy the pressure boundary from the adjacent interior (Neumann). i.e.:
```
// interior Gauss-Seidel
for k: interior update
// Neumann: press[b] = press[interior neighbor]
```
The simplest correct version is the clamped full loop. Let me do that.

Then, also I should double check that the divergence at the boundary cells is 0 — yes, divergence is only computed for the interior.

Let me apply the fix and re-measure SEED.

Better, but still exploding (starting at the right edge, i=239). So the instability is at the vertical wall (i=gw).

Let me think about the divergence at the cell adjacent to the right wall (i=gw,j): 
div = -0.5*((u[gw+1] - u[gw-1]) + (v[.. up]-v[.. dn])) where u[gw+1] = -u[gw] (no-penetration). 

For an incompressible flow with no-through-flow, u[gw+1] should be 0, not -u[gw]! The mirror with a sign flip means fluid is reflected at the wall, which is a *slip wall*; the divergence computed across the wall then reads u[gw+1]-u[gw-1] = -(u[gw]) - u[gw-1]. If u[gw] ≈ u[gw-1] (flow aiming at the wall), then this ≈ -2*u[gw] ≠ 0, producing a large spurious divergence at the last column → the projection creates a strong pressure gradient there → high velocity. That's a positive feedback loop.

The standard Stam treatment uses exactly this mirror (b=1 with negated boundaries), and it works... because in the original, the set_bnd applies to the velocity AFTER projection, and the div used in the projection is computed on the *advected, projected* field, so u[gw] gets pulled toward 0 by the projection each step. But it's known to be a source of boundary artifacts.

Given the observed blow-up, the mirror-with-sign-flip is not stable in my setup. Let me use a cleaner wall: set the boundary velocity to ZERO (both components) at all walls — i.e., a no-slip/free-slip-ish wall where the boundary cells are 0. Then:
- div at the last column: -0.5*((0 - u[gw-1]) + ...) → only nonzero if flow heads to the wall, and the projection will drive u[gw] toward 0... Actually with u[gw+1]=0, the div at (gw,j) = -0.5*(-u[gw-1] + dv) — the projection will then correct. This is much more benign and stable: the "ghost cell zero velocity" gives a no-through-flow (and the tangential derivative is unaffected). Standard "cell-centered no-slip wall".
- Dye at the boundary = copy (setBndDye) → dye piles up near walls, which is fine.
- The tangential free-slip is then approximated: the velocity at the wall is 0, which is no-slip (creates a boundary layer), but with a 1-cell resolution, that's a bit "sticky" at the edges. Acceptable.

Alternatively, I can make the boundary cell equal to the interior cell's tangential component and zero the normal component:
- left wall (i=0): u[0,j] = 0 (normal zero), v[0,j] = v[1,j] (tangential copy)
- right wall: u[gw+1,j] = 0, v[gw+1,j] = v[gw,j]
- top wall: v[i,0] = 0, u[i,0] = u[i,1]
- bottom: v = 0, u = copy.

This is the proper free-slip wall with zero normal velocity. The divergence at cell (gw,j) then = -0.5*((0 - u[gw-1]) + dv). Hmm, when the flow approaches the wall, u[gw] > 0, the projection will produce a pressure that decelerates it. This is the "zero-gradient/normal-zero" treatment and is stable.

Let me implement that and see if the blow-up stops.

Actually, wait. Let me reconsider whether the blow-up comes from the wall at all. The max starts at (239,52) — the right edge, mid-height. Then (236,155) — the bottom-right corner. Then it jumps around the whole domain. So the source is the right edge.

Another candidate: the drift I add at the end (`u += 6*sin`) is a rightward global flow of 6 cells/s. With a right wall, fluid piles up at the wall. With the sign-mirror, this creates a spurious divergence at the last column: u[gw+1] = -u[gw] = -6 (if the flow keeps pushing right) → div = -0.5*(-6 - u[gw-1]) which is large. The pressure gradient then accelerates... this creates the feedback.

Yes! The global drift is likely the trigger, plus the mirrored boundary making it unstable. Let me remove the global drift AND use the zero-normal free-slip wall. Removing the drift is also good: a constant global flow pushes all dye to the wall, which is not desirable anyway.

Let's implement:
1. setBndVel: zero the normal component, copy the tangential component.
2. Remove the drift.

Then re-measure.

Note: with zero normal velocity at the boundary, the wall is blocking, and the dye advection will accumulate dye against walls. Fine.

Let me also double check the corner handling: at the corner cell (0,0), u[0,0] and v[0,0] — I'll set both to 0 there.

Implementation:
```js
function setBndVel() {
  const S = stride, W = gw + 1;
  for (let j = 1; j <= gh; j++) {
    const r = j * S;
    u[r] = 0; v[r] = v[r + 1];      // left: normal zero, tangential copy
    u[r + W] = 0; v[r + W] = v[r + gw];
  }
  for (let i = 1; i <= gw; i++) {
    v[i] = 0; u[i] = u[i + S];      // top
    v[i + (gh + 1) * S] = 0; u[i + (gh + 1) * S] = u[i + gh * S];
  }
  // corners
  u[0] = 0; v[0] = 0;
  u[W] = 0; v[W] = 0;
  u[(gh+1)*S] = 0; v[(gh+1)*S] = 0;
  u[W + (gh+1)*S] = 0; v[W + (gh+1)*S] = 0;
}
```

Hmm, but for the advection of velocity, sampling the boundary cells (which hold a copy of the interior for the tangential component and 0 for the normal) is reasonable.

Let me apply and re-measure.

The instability persists, now starting at the TOP wall (j small, ~3-10). Steps 0-3 are fine (21.5, stable rotation), then at SEED4 it jumps to 38 at (102,3), then 107, 205, 420. So the top wall (j=0/1/2 region) is the trigger.

The divergence at row 1: div = -0.5*((u[i+1,1]-u[i-1,1]) + (v[i,2]-v[i,0])) where v[i,0] = 0. If the flow near the top has v[i,1] < 0 (upward toward the wall)... Hmm.

With the "v[top] = 0, u[top] = u[i,1]" treatment: div at (i,1) = -0.5*(dudx + (v2 - 0)) = -0.5*(dudx + v2). If v2 is upward toward the wall (negative in the y-down convention: v>0 means downward, so an upward flow has v<0)... Let's say v2 = -10 (upward): div = -0.5*(0 - 10) = +5. The pressure gradient correction at (i,1): v[i,1] -= 0.5*(press[i,2] - press[i,0]) where press[i,0] is now a solved value (Neumann). The correction should push v down (positive) to stop the flow into the wall. With press at the boundary solved as a Neumann value, this should work.

Hmm. But wait — the pressure boundary in my Neumann loop: at j=0, press[i,0] = 0.25*(press[i-1,0] + press[i+1,0] + press[i,0] + press[i,1] - 0) — the "dn" neighbor is itself (d>0? j>0 false → dn = id). So it becomes 0.25*(l + r + id + up) → this is a degenerate self-reference. That's not a proper Neumann condition! The correct Neumann BC for a mirror pressure is press[i,0] = press[i,1], but my formulation gives press[0] = (press[left]+press[right]+press[0]+press[1])/4, which is an implicit equation, and it's fine in a Gauss-Seidel sense (it converges), BUT the self-reference effectively adds a spurious 0.25*press[0] term, which is not the correct discrete Laplacian. 

The standard way to handle a Neumann boundary (∂p/∂n = 0) with a second-order scheme is a ghost point: p[ghost] = p[interior] (or the mirrored 2p1 - p2). With the ghost = interior (first-order), the Laplacian at the boundary node is not used; instead you just set p[boundary] = p[interior] after each iteration.

Simplest correct approach: iterate only over the interior cells for the pressure, and then after each iteration apply the Neumann condition: press[boundary] = press[adjacent interior]. This is the cleanest:

```js
for (k) {
  for (j=1..gh) for (i=1..gw) { update }
  // Neumann mirror for the boundary ring
  for (j=1..gh) { press[0,j*S] = press[1,j*S]; press[(gw+1)+j*S] = press[gw+j*S]; }
  for (i=1..gw) { press[i] = press[i+S]; press[i+(gh+1)*S] = press[i+gh*S]; }
}
```
The corner cells: press[0] = press[1], etc. — assign them arbitrarily, e.g., set corners = the average of the two adjacent edge values.

Hmm, but this doesn't really fix the underlying issue if the divergence at the boundary rows is wrong.

Let me step back and think about the real cause of the instability more carefully. The blow-up is triggered at the TOP wall in the latest run, the RIGHT wall in the previous, the corner in the one before. It's a wall-related instability, and the exact trigger varies with what's adjacent.

The core problem: my divergence definition at the interior cells adjacent to a wall uses a mirrored/zero boundary value, which is inconsistent with the pressure solve, creating a persistent large divergence near the wall that the projection can't fix → runaway.

The cleanest and most robust solution: **treat the walls with a "zero-gradient" (outflow-like) ghost cell using the interior value for BOTH components**, which is what many simple implementations do for a bounded domain, plus a light damping near the walls to prevent inflow. Hmm.

Alternative, much more robust: don't use walls at all — make the domain effectively unbounded by damping the velocity field at the boundary ring (a "sponge" layer). This is what many WebGL fluid demos effectively do with no BC (they use a clamped sampling). With no explicit BC, the advection and projection just work on the interior with the boundary cells copied from the interior (Neumann for everything: u[bnd] = u[interior], same for v). Then the divergence at the wall cell uses ghost values equal to the interior → the wall behaves like an "open" boundary where fluid can leave (advection with clamped sampling also keeps it from coming back). Combined with a mild velocity damping in a 4-cell-wide border ring, dye will slowly exit the domain and the field will decay near the edges, which is acceptable (and physically like dye draining away).

Actually the simplest stable classic approach (Stam's original) is:
- set_bnd with b=1 for velocity: `x[0][j] = -x[1][j]` etc. — which is what I had first and which also blew up (mu 12732!). Hmm, in the first version I had the sign-flip mirror for both components and it blew up even worse. So the mirror is definitely the problem.

Let me reconsider. Stam's original code works fine in practice (it's the classic "stable fluids" demo). Why does mine blow up? Possible reasons:
1. My vorticity confinement (extra force) — it's applied to the interior and could push fluid into walls.
2. My splitting order.
3. The `dt` and velocity scale.

Actually, hmm, wait. Let me reconsider the magnitudes. Let me look at the actual divergence values near the wall. Let me instrument: log max |divergence| and its location after step 1 vs step 2.

Actually, hold on. Let me reconsider the seed field: the vortex velocity field is a solid-body-like rotation, which IS divergence-free (approximately, on a uniform grid with free-slip). With amp = 1.05 and a Gaussian falloff, the divergence should be small.

Hmm, unless... the vortices are placed such that the falloff (exp(-d²/R²)) makes it nearly divergence-free. OK.

So the initial div should be ~0, and after the first projection u,v stay ~21. SEED0/1/2 show 21.8 → 21.6 stable. Then SEED4 shows 38 at (102,3) — near the TOP wall. What's special?

The vorticity confinement! At the top wall, curl from the interior can be large near the boundary, and the confinement force pushes fluid perpendicular to the curl gradient... If the max curl is near the top wall, the confinement force pushes fluid INTO the wall, creating a big divergence there. Then the wall BC (v[top]=0) means the pressure can't resolve it → runaway.

Wait, but at SEED3-4 the velocity is only 21-38, not huge. Let's see: 21 → 38 → 107 → 205 → 420. This is exponential growth with a doubling time of ~1 step. So the growth factor per step is ~2. That's a violent instability, and it starts from a modest value.

Let me just directly instrument: log max|div|, max|press|, max|curl|, max speed before/after each sub-step of step(). That will pinpoint which operator diverges.

Let me do that quickly — it's worth the time.

Key insight from the trace: `proj1` leaves div growing monotonically every step even when the input div is 0. The divergence is NOT being reduced by the projection — it grows: 0 → 0.44 → 0.71 → 0.97 → 1.37... The projection is amplifying divergence instead of reducing it! That means my projection sign or the correction is wrong.

Let me check: div = -0.5*(du/dx + dv/dy). Pressure Poisson: ∇²p = div. Solving: p = (sum of neighbors - div)/4? The Poisson equation ∇²p = div discretized: (p_l + p_r + p_d + p_u - 4p)/h² = div → p = (p_l+p_r+p_d+p_u - h²·div)/4. With h=1: p = (sum - div)/4. ✓ That's what I have.

Then the velocity correction: u -= ∇p, i.e., u -= 0.5*(p_r - p_l). ✓ That's what I have.

So with only 12 Gauss-Seidel iterations, the residual is large. But div should DECREASE after projection, not increase! From 0.00 → 0.44 after proj1. That's suspicious: with a divergence-free input, the projection should produce ~0 divergence.

Unless... the boundary treatment is inconsistent: I compute the divergence only on the interior, solve the pressure over the whole padded grid with div=0 at the boundary. The correction loop `u[id] -= ...` runs only over the interior. So after the correction, setBndVel() sets the boundary. Fine.

Why would div grow from 0 to 0.44? Because the pressure solve is under-converged: with a divergence of exactly 0 the correction should be ~0. Hmm, but the initial div reported is the max|div| which was 0.00 at start. After the projection it's 0.44. So the projection INTRODUCED divergence. That means the pressure correction is not a valid gradient-field correction at the cells adjacent to the wall, or the pressure solve is diverging.

Look at the reported div growth: it grows by a factor of ~1.5 every step from proj1. And note "Pstart div" is always the "Pproj2 div" from the previous step. So the projection is generating divergence.

Wait, I wonder about the self-reference in my pressure boundary handling: at j=0, dn = id (self). So press[id] = 0.25*(press[l] + press[r] + press[id] + press[up] - 0). This is an implicit equation: p = (l + r + p + up)/4 → 3p/4 = (l+r+up)/4 → p = (l+r+up)/3. In a Gauss-Seidel sweep, this converges in one pass but adds a "diagonal" term. Effectively the boundary node behaves as if it has a 3-neighbor Laplacian — that's not the correct ghost-cell Neumann, but it's still a stable iteration.

Hmm, the crux: this is a 4th-order-ish inconsistency. Something is systematically wrong. 

With only 5 minutes left, I should take the pragmatic path: **replace the projection with the classic Stam interior-only version including the boundary cells in the iteration using the standard set_bnd(0) treatment** — no. Better: **increase convergence and, most importantly, make the projection not amplify divergence**.

The simplest robust option given time: the projection loop over the interior only (i,j from 1..gw/gh), and set the pressure boundary to 0. And crucially, run MANY more iterations (but that's slow).

Alternative pragmatic option given time constraints: **drop the projection from the main loop and only apply it to the *injected forces*?** No.

Hmm wait. Let me reconsider. Actually, maybe the real bug is much simpler: **the divergence array is a full-size array but the `curl`/`press`/`divergence` arrays... `divergence.fill(0)` is NOT called in my new project()! I removed it?**

Let me check: In the current project(), the first loop computes `divergence[id]` for the interior. I did remove the `divergence.fill(0)` line — no wait, I never had it in the final version... Actually I DID have `divergence.fill(0)` at the top of the original project(). In my fix3 edit I replaced the inner iteration loop only, leaving `divergence.fill(0)` intact. Hmm, the debug reports "div=" max|div| over the interior only, so stale boundary values don't matter.

Let me look at the sign of the correction once more... u -= 0.5*(p[id+1]-p[id-1]).

Hmm, actually let me test the projection in isolation with a synthetic field in Node to find the bug fast. I can extract the project() function and test it. But time is very short (5 min).

Quick test in node: create a small grid, set u,v divergence-free-ish, run project, and check the divergence before/after. Let me do that quickly with a standalone script. Actually, easier: I'll test with the actual page code by running project 60 times on a random field and checking whether div decreases.

Given time pressure, let me instead consider: the most likely bug is that the pressure solve isn't converging at all (12 iterations with the self-referential boundary). Evidence: after proj1, div=0.44 from an input of 0. If the pressure were solved to convergence, the correction would be ~0. So the pressure solve is NOT converging — it's diverging.

The self-reference `dn = id` makes the boundary row an implicit equation. With Gauss-Seidel, this is stable... usually.

OH WAIT. I see it!!! In the pressure loop, for the cell at id where I use `press[l] + press[r] + press[dn] + press[up]`, if i=0 then l = id. And if j=0 then dn = id. So at the corner (0,0), all four neighbors: l=id, r=id+1, dn=id, up=id+stride → p = (id + id+1 + id + id+stride)/4. Self-referential, converges. Still stable.

Hmm, so why is div increasing? Let me think about the corrective update at the cells ADJACENT to the wall:
At cell (1, j): u[1,j] -= 0.5*(press[2,j] - press[0,j]). press[0,j] is solved over the boundary with div=0 → it's the Neumann-ish value. OK.

You know what, maybe the issue is the interaction with setBndVel being called BEFORE the divergence calculation in the next step, and the dy/blah... no.

DECISION: Time is nearly out. Let me take the safest, guaranteed-stable route:

**Remove the projection from the per-step loop entirely and instead maintain incompressibility approximately by construction:** use the "advect + damp + vorticity" only, without projection. Without projection, the field is compressible but visually still looks like fluid dye swirling, and there's no blow-up risk from the pressure solver. But drag-injected momentum would then just accumulate/expand rather than swirl, and the flow would look like "expanding blobs" rather than swirls. Hmm, that's a meaningful quality loss but stability is guaranteed.

Better idea that's cheap and stable: **use a strongly over-relaxed/many-iteration pressure solve but on a coarse scale?** No.

Hmm, hold on, let me reconsider one more time — a classic sign error: in Stam's code, 

div[i,j] = -0.5*(u[i+1,j]-u[i-1,j] + v[i,j+1]-v[i,j-1])
p[i,j] = (div[i,j] + p[i-1,j]+p[i+1,j]+p[i,j-1]+p[i,j+1])/4   ← div ADDED, not subtracted!

Yes! In Stam's original: `p[idx] = (div[idx] + p[idx-1] + p[idx+1] + p[idx-S] + p[idx+S]) / 4` — div is ADDED. 

And then u -= 0.5*(p[i+1,j]-p[i-1,j]).

Let me verify the math: we need ∇²p = ∇·u (where div is defined as -0.5*(du+dv), i.e., div = -∇·u/2... hmm). Stam defines div = -0.5*(du+dv) which is -(1/2)∇·u (for h=1, ∇·u = du+dv). Then he subtracts the gradient of p scaled by 0.5.

Let's derive: we want the corrected velocity u' = u - ∇p to be divergence-free: ∇·u' = ∇·u - ∇²p = 0 → ∇²p = ∇·u = -2·div.
Discrete: (p_l + p_r + p_d + p_u - 4p) = -2 div → p = (p_l+p_r+p_d+p_u + 2 div)/4.

Stam uses p = (sum + div)/4, which corresponds to ∇²p = 2·div... i.e., he solves ∇²p = -2div * ... hmm, let me be careful: with p = (sum + div)/4, we get sum - 4p = -div, so ∇²p = -div. And we need ∇²p = ∇·u = -2div. So Stam's p is off by a factor of 2, meaning his correction is half of what's needed! Indeed, Stam uses u -= 0.5*(pr-pl) which is half the gradient. So his projection only removes half the divergence per call, which is why his code calls project() and the residual shrinks by half each step... 

Hmm, that doesn't explain the growth either, but it means his scheme is mild.

With MY version: p = (sum - div)/4 → ∇²p = div. But we need ∇²p = -2div (as derived above with div = -0.5∇·u). So my p has the WRONG SIGN! I'm solving ∇²p = div where I need ∇²p = -2div. So my pressure is the negative of what's needed → the correction AMPLIFIES the divergence. That's exactly the observed behavior (div grows every step)!

So the fix: either change div to +0.5*(du+dv) and keep p = (sum - div)/4, or keep div = -0.5*(du+dv) and use p = (sum + div)/4 (then ∇²p = -div = 0.5∇·u, giving a correction u -= 0.5∇p where the gradient magnitude is 1/2 of ∇²p... let me just redo the math carefully with the correction factor).

Setup: u' = u - c·∇p. Need ∇·u' = 0 → c∇²p = ∇·u.
Let D = ∇·u (du+dv). 
My discrete correction: u -= 0.5*(pr-pl), so c = 0.5, and ∇ is the central difference.
So we need 0.5·∇²p = D → ∇²p = 2D.
With div defined as div = -0.5*D → D = -2div → ∇²p = -4div.
Discrete ∇²p = (sum - 4p) → sum - 4p = -4div → p = (sum + 4div)/4 = sum/4 + div.

Hmm, that doesn't match Stam either. Let me recheck Stam's div: in Stam's code, `div = -0.5 * ( (u[x+1] - u[x-1]) + (v[y+1] - v[y-1]) )` — yes D/2 with a minus sign where D = the discrete ∇·u.
So div = -0.5 D.
Stam: p = (div + sum)/4 → 4p = sum + div → sum - 4p = -div = 0.5D → ∇²p = 0.5 D.
Correction: u -= 0.5*(pr-pl) = 0.5∇p.
Check: u' = u - 0.5∇p → ∇·u' = D - 0.5∇²p = D - 0.25D = 0.75D. So Stam only removes 25% of the divergence per projection. That's why he needs many iterations or just accepts the residual. Hmm, that seems too weak for his demo... Actually many implementations use `u -= (pr-pl)` (full gradient) with p = (div + sum)/4. Let's check: u' = u - ∇p → ∇·u' = D - ∇²p = D - 0.5D = 0.5D. Still half.

The fully consistent one: p = (sum - D)/4 → ∇²p = D; then u -= ∇p → ∇·u' = 0. ✓ So with D = -2div: p = (sum + 2div)/4 and u -= 0.5*(pr-pl).

So my code should be: press[id] = 0.25*(press[l]+press[r]+press[dn]+press[up] + 2*divergence[id]) — wait let me redo:
p = (sum - D)/4, D = -2div → p = (sum + 2div)/4.
My code: p = 0.25*(sum - div). That has the wrong sign AND a factor of 2 off. → Correct: p = 0.25*(sum + 2*div).

Hmm, but with a factor of 2 the convergence rate per iteration is different but it's still a valid Poisson solve (any consistent ∇²p = D works; the factor only affects the solve's conditioning if inconsistent).

Actually, wait: it doesn't matter what multiple I use as long as the solve is consistent with the correction. Two consistent choices:
(A) div=-0.5D; p = 0.25*(sum + 2div) [solves ∇²p = D]; correct with u -= 0.5∇p. ✓ (fully converges)
(B) div=-0.5D; p = 0.25*(sum + div) [solves ∇²p = 0.5D]; correct with u -= ∇p = (pr-pl). ✓ (fully converges)

I'll use (A) with the existing 0.5 gradient correction.

Hmm, hold on. Let me double check (A): p = 0.25*(sum + 2div) where sum = l+r+d+u. → 4p = sum + 2div → sum - 4p = -2div = D. ✓ ∇²p = D. Then u' = u - 0.5∇p → ∇·u' = D - 0.5∇²p = D - 0.5D = 0.5D. ✗ NOT zero!

Argh, careful: ∇(0.5∇p) = 0.5∇²p. So ∇·u' = D - 0.5∇²p = D - 0.5D = 0.5D. Not zero.
So I need 0.5∇²p = D → ∇²p = 2D → sum-4p = 2D = -4div → p = (sum + 4div)/4 = 0.25*sum + div.

Hmm, so p = 0.25*(sum) + div. Let me double check by considering (B): ∇²p = 0.5D with u -= ∇p: ∇·u' = D - ∇²p = D - 0.5D = 0.5D. Also not zero!? 

Something's off in my reasoning. Let's redo with plain central differences and no 0.5 anywhere:
D_cell = (u[i]-u[i-1]) + (v[j]-v[j-1])  (a one-sided difference, the "flux" divergence)
Standard MAC-style projection (Patankar):
p[i] = (p[i-1]+p[i+1]+p[j-1]+p[j+1] + D_cell)/4  where D_cell = u[i-1]-u[i] + v[j-1]-v[j]... 

The standard staggered-grid Poisson: for each cell, the pressure update is
p[i,j] = (p[i+1,j] + p[i-1,j] + p[i,j+1] + p[i,j-1] + h²·b)/4 where b is the divergence source.

And then u[i] += (p[i-1] - p[i]) (with the full cell spacing, no 0.5).

Stam's formulation uses half-integer velocities (staggered), which introduces the 0.5 factors. His code is the classic and it's known to work "well enough" — the standard interpretation is that his div has a 0.5 factor from the staggered arrangement, and the pressure update p = (div + sum)/4 combined with the correction u -= 0.5*(pr-pl) is self-consistent IN THE STAGGERED SENSE.

Given the classic code works, the safest move is to match Stam exactly:
div = -0.5*(...); p = 0.25*(press[neighbors] + div); u -= 0.5*(pr-pl); v -= 0.5*(pu-pd).

That's exactly Stam's implementation, and it demonstrably produces nice stable fluid. My version's sign is flipped (I had -div instead of +div), which amplifies divergence → the blow-up. That's the bug!

So the fix is a one-character change: `+ divergence[id]` instead of `- divergence[id]`.

But will Stam's half-strength projection give a nice incompressible swirl? In practice, Stam's projection with ~20 iterations removes most of the divergence (each iteration handles the local Poisson solve; the "half strength" concern is about the coupling but empirically the classic demo looks great). Many implementations use exactly this. 

To be safe I'll ALSO increase iterations. And since I have very little time, let me make the sign fix now, test quickly, and finish.

Note: with Stam's sign, my earlier observation that "proj1 introduced 0.44 div from 0" matches: the wrong sign amplified. Let's fix and re-verify.

The console output is identical to before — the browser didn't reload my change? The DBG/SEED log still shows the old P-vort instrumentation which I removed... So the fix5 patch did not take effect in the browser? fix5 reported "ok" but I ran `browser reload` and it failed with "command not found" (the `&&` chain aborted because browser isn't a shell command!). So the file was patched but the browser was NOT reloaded. The `motion` action re-ran the OLD page (still the pre-fix5 version cached in the browser session? Actually the motion action reloads the page from disk, which now has fix5 applied... but the log shows the P() instrumentation which I removed, so it must be the old version).

Hmm, "Frame 1, +0ms" suggests it did reload the page. But then the log shows the P instrumentation... Wait, maybe fix5's second `rep` failed? No — the script printed 'ok', meaning all reps succeeded. So the file no longer has the P instrumentation.

Unless... the browser tool caches. Or maybe `motion` didn't reload. Let me reload properly and check the console again.

Actually, hmm, the console output in `motion` includes the exact same numbers as the previous run — suspicious. Let me reload explicitly and check.

The file IS patched (grep -c returned 0 for the P('start') line, hence exit code 1). So the browser was serving a cached version. Let me reload the browser now.

The projection is now stable: velocity decays smoothly 21.8 → 20.2, and md=1.897 (dye density high). But the image shows *smooth round blobs* — the vortices have dispersed into isotropic blobs. Why? Because the vortex velocity field (peak 42) was mostly canceled by the projection (now correct sign): mu went from 21.8 → 20.2 over 24 steps, i.e., the field is decaying and diffusing without much swirling.

Hmm, but the blobs look smooth/deformed? They look like slightly rotated ovals. There's very little swirl visible.

The issue: the projection is now removing the divergence-free-ish rotation? No — a vortex is divergence-free, so the projection shouldn't kill it. The velocity decays from 21.8 to 20.2 over 24 steps (0.4s) — that's fast decay, ~2%/step. But dissipate is only 0.1%/step. So the projection is removing energy (it shouldn't, other than the compressible part) — hmm, actually the projection does remove the divergent part only. But the *self-advection* of velocity with only 12 pressure iterations... 

Also the dye looks *smoothed* — because the advection's bilinear interpolation with a velocity of 20 cells/s over 24 steps... The dye went from sharp Gaussian blobs to very smooth blobs. That's the numerical diffusion of semi-Lagrangian advection. It's OK but I want more swirl.

The steps are 24 settle steps at 1/60 = 0.4s of evolution, and the dye looks quite smooth. That's expected: bilinear advection is diffusive.

To make it swirl more visibly, I need a stronger vortex that stays coherent. The velocity decays because:
1. The vortices are being advected/diffused.
2. The projection with 12 iterations may be over-damping.

Let me reduce the settle steps from 24 to ~8, increase the vortex peak back up (to ~60), and increase the vorticity confinement a bit (5 → 8). Also the dye should be seeded AFTER a few settle steps so it stays compact and colorful.

Also, time is nearly out. Let me make these final tweaks and remove the instrumentation, then do a final verification of the interaction (drag, clear).

Actually, the safest thing given the time: keep the current physical setup (it's stable!) and just reduce the settle steps to 8 and seed the dye after the settle. Then quickly test the drag interaction.

Let me restructure the seed:
1. Apply the two vortices.
2. Settle for 6 steps (no dye).
3. Add the dye blobs.
4. Settle for 6 more steps.

And raise the peak to 55.

Then remove the debug instrumentation, and test with a drag.

Let me do this now in one edit.

My patch created a mess (IIFE seedTail with leftover debug logging, and the old settle loop). I need to clean up this seeding section. Let me rewrite the whole seeding section properly with a single edit, and also remove the debug instrumentation in frame().

Let me write the replacement text for the whole seeding block and the debug bits. I'll use node string replacement with the full current block from "/* ------------------------------- seeding" to "/* ------------------------------- rendering".

Also remove:
- the DBG block in frame()
- the timing accumulators in frame()
- the `getImageData` in the DBG block (gone with the block)

And the old settle loop inside seedTail must go. Let me do a full section replacement.

Console is clean now. The seeded scene shows colored blobs, but the vortices don't appear to be visibly rotating them (they look static). fps 33 though — good.

Hmm, the blobs look nearly isotropic (slightly elliptical). The swirl is weak. Why? The vortex peak is 58 cells/sec with R = 0.19*200 = 38 cells. The seed settles 10 velocity steps (0.167s) + 10 dye steps. In 0.167 s the dye would move 10 cells — little rotation.

Also, I removed the console debug, so I can't easily check the velocity. The key question is whether the flow is alive on screen. In the screenshot, the blobs look slightly stretched. It's fine but I'd like more visible swirl.

Given the time budget is essentially exhausted (I'm about 5 min over), the priority now is:
1. Verify interaction works (drag injects dye, continues after release, second drag responds, clear works).
2. Make the swirl a bit more visible with a cheap tweak.

Let me do the interaction verification first (the required verification), since that's what matters most. I'll drag across the canvas with the browser drag tool, then screenshot after release, then drag in another direction, then Clear and drag again.

The drag action: action "drag" with fromX, fromY, toX, toY. Let me check the parameter names: "drag" requires x, y (start) and toX, toY. Let me do it.

Let me first do a drag from (300,300) to (900,500).

The drag produced a long streak of dye from left to right, with a swirl/curl at the left end (where the initial dab rolled up). The dye follows the drag direction — good.

Interesting: the seeded dye blobs are gone?! The screenshot only shows the drag streak, not the seeded blobs. That means the seeded blobs have dissipated by now (several seconds elapsed since load). Hmm, that's a concern: at 240x160 with dyeFade 0.996/frame, the seed blobs should last: md=1.9 → after 5s (300 frames): 0.996^300 = 0.30 → md 0.57 → alpha 180. It should still be visible! But the screenshot shows nothing of the blobs.

Wait — maybe the screenshot was taken after the drag, and the drag's streak is bright, but the blobs should still be faintly visible. Let me look again... The screenshot shows ONLY the streak. So the blobs are gone.

Why? Ohh — maybe the frame rate is low (~17 fps) and each frame does multiple steps... no, that doesn't accelerate dissipation (it's per-step, and steps ≈ elapsed time).

Hmm, but actually: the dissipation is applied per STEP, and at 17 fps with acc accumulating, the number of steps per second ≈ 60 (fixed step). So the dye decay is time-based: 0.996^60 = 0.786 per second. So after 5 s: 0.30. So md=1.9 → 0.57 → alpha = 0.57*255*1.35 = 196. Very visible. But it's not there!

Unless the dye is being advected into the walls / spread out. With the vortices spinning for seconds, the dye gets spread into thin filaments over the whole domain, so md drops (density is distributed). The blobs were tight (radius 28 cells); after a few seconds of rotation at 58 cells/s, the dye wraps around and gets stretched into a ring → the peak density drops a lot. Plus numerical diffusion from the semi-Lagrangian advection.

That's physically reasonable but means the "seeded initial scene" fades too quickly. Let me check by taking a screenshot now (after the drag) to see the current state — actually the last screenshot IS the current state, and it shows the streak only.

So the seed faded within ~10 seconds. Is that acceptable? The requirement says "Seed the initial scene with a small amount of colored dye and motion so the simulation is visible on load." It's visible on load (the first screenshot showed nice blobs). Fading over ~10 s is acceptable (dye dissipation is expected). But I'd prefer longer persistence: reduce the dye fade to 0.998 and increase the initial densities.

Given my time is way over budget, let me make one final quick tweak (dye fade 0.998, and a slightly longer-lived seed) and then do the final verification of: release → continuing swirl, second drag, Clear, and a fresh drag.

Actually, the more important check right now: does the flow continue after release and respond to a second drag? Let me take a screenshot now (some time has passed since the drag) to see if the streak still swirls.

Let me do that first, then Clear, then a fresh drag.

Now the screen is empty — the dye has completely faded within ~1-2 seconds of the drag! That's way too fast. Something is wrong with the dye persistence.

The drag streak disappeared entirely in ~1 second. That means the dye is decaying very fast, or being pushed out of the domain (walls with zero normal velocity → dye accumulates at walls, but then setBndDye copies... hmm, the walls have zero normal velocity so dye should pile up, not vanish).

Wait — the drag streak was visible in the drag screenshot and gone ~1s later. The dye decay per second is 0.996^60 = 0.79, so it can't vanish in 1s. Something is destroying the dye.

Possibilities:
1. `da` is being zeroed by something.
2. The dye is being advected out of the domain: the velocity injected was vx*0.55 = up to 143 cells/s... but the walls block it.

OH WAIT. I think I've got it: **`advectDye` reads the source `dr, dg, db, da` and writes into `tdr, tdg, tdb, tda`, then copies back.** Fine.

But look at `dissipate()` — it multiplies dr, dg, db, da by fd. Fine.

Hmm, what about `splat()` being called with `amount`... The drag's dye amounts were fine.

3. **The dye is being pushed to the walls and then... the walls.** With the zero-normal wall, the dye accumulates against the wall, and advection clamps the backtrace to the boundary, so the dye stays. It shouldn't vanish.

Hmm, unless... the number of simulation steps per second is much higher than 60! Let's check: `acc += Math.min(0.1, raw/1000)`. At 17 fps, raw = 58ms → acc += 0.058 per frame. Then `while (acc >= FIXED && steps < 3)`: 1/60 = 0.0167, so 3 steps per frame = 0.05 s of sim time per 0.058 s of real time. That's right.

So the sim time is roughly real time. Then the decay is 0.79/s.

BUT: the drag injects dye with `amt` = min(1.1, 0.3 + dist*0.16) per splat along the segment... the alpha I saw was strong.

Hmm, wait. Let me reconsider: maybe the dye ISN'T decaying — maybe the streak got **flattened against the wall** (the drag direction was to the right, so the dye was pushed to the right wall). Then at the wall... the dye would pile up in a thin layer. With the wall cells holding copies of the interior, the dye at the right edge would remain. But the screenshot shows nothing at all.

Unless the dye was advected to the right wall and then... hmm, `setBndDye()` copies the interior value to the boundary cell. In the advection backtrace, `x` is clamped to [0.5, gw+0.5] and `i0 = x|0` can be gw+1 → samples the boundary cell → which holds the copied interior value. Fine.

Let me think about the alpha: after the drag, the dye at the streak was probably a=0.5-1.0 (bright). To become invisible (alpha < 10) requires a decay of 20×. At 0.79/s that takes 7 s. The elapsed time between the drag screenshot and the next screenshot was maybe 1-3 s (the time for me to respond plus the tool round trip). Hmm, in the headless environment the frames might be slow (17 fps reported) — but the reported fps is measured from the rAF loop.

WAIT. Look at the reported numbers: in the first reload, "fps 25", then "fps 17". The tool's motion frames took ~1 second each. The elapsed real time between my drag and the screenshot could be several seconds. The dye decay 0.79/s over 5s = 0.31 (3×), not 20×.

Hmm, so the dye should still be faintly visible. It's completely gone.

Let me reconsider: is the *velocity* from the drag still huge and pushing the dye out? The drag injected 143 cells/s impulses. With the projection now correct (half-strength per projection, 2 projections per step), and 8-14 iterations, the injected momentum mostly persists. At 143 cells/s, in 1 s the dye travels 143 cells = 60% of the domain width. So the dye gets pushed to the wall and stacked there... but stacking would make it BRIGHTER, not invisible.

Unless... the dye at the wall gets squeezed into a 1-cell layer, and my render loop samples dx = (i - gx) with the splat profile... no.

Hmm, hold on: what if the dye is being advected *through* the wall and lost? In advectDye, the backtrace x is clamped to [0.5, gw+0.5]. If the velocity is large (say 143 cells/s), the backtrace from a cell near the right wall goes to x = i - 143/60 = i - 2.4 — normal. So no loss.

Hmm, what if the whole domain's velocity became large and the dye is being advected in a huge vortex that stretched it to density ~0.01 (invisible)? The drag's momentum (143 cells/s) with no walls to stop it → the fluid rotates and the dye gets sheared into thin filaments over the entire domain within a second or two, dropping the peak density by 10-50×. That's plausible! Shearing a blob into a domain-wide filament reduces its density a lot. Combined with the fade, it could become invisible.

OK. So the dye persistence is the problem. Fixes:
1. Slow the dye decay (0.996 → 0.998).
2. Make the drag inject less speed so the dye doesn't get flung across the domain (the maxSpeed of 260 cells/s = 1300 px/s is very fast; the dye is stretched by shearing).
3. Most importantly: **the render alpha** — the dye alpha is linear in density, so a thin filament is faint.

Given the time I've already spent (well over budget), let me do the essential fixes and finish:
- Reduce CFG.maxSpeed from 260 to 150.
- Reduce the injected force factor from 0.55 to 0.35.
- dyeFadePerFrame 0.996 → 0.998.
- alphaGain 1.35 → 1.6 so faint filaments remain visible.

Then verify: drag → release → swirl visible after a couple seconds; second drag; Clear; fresh drag.

That's a reasonable final tuning. Let me apply and re-verify quickly.

`CFG.maxSpeed` is used but never defined in the CFG object? Let me check — my original file had `maxSpeed: 260` in CFG. grep shows it's used at line 404 but not defined. Let me look at the CFG block.

Ah, I see — in the fix (dyeFade) replacement earlier, I may have accidentally removed it. Let me look at the CFG block.

Good. Now let's do the drag verification again: drag and then observe the flow continuing after release.

I'll drag from (250,600) to (950,250), then screenshot twice (immediately and a bit later).

The drag produced a clear diagonal cyan streak following the drag (bottom-left → top-right). There's also a faint green curl at the top (that's the seeded green blob being stretched) and the seeded blobs remain visible (the pink blob at the bottom-right, the cyan blob at the left being stretched). 

The seeded dye now persists much better. 

Now let me verify the flow continues after release (wait and screenshot), then do a second drag in another direction, then Clear + a fresh drag.

Excellent! After release the streak has curled into a big vortex — the dye keeps swirling after the pointer is released, and it's clearly evolving (rolling into a spiral). This satisfies "momentum and dye remain visible after release and gradually dissipate" and "continues swirling."

Now: a second drag in another direction, then Clear, then a fresh drag.