Fluid simulation · deepseek-v4.1-flash

Let me build a stable fluids simulation (Jos Stam's method) on canvas. Full-screen canvas, velocity + dye fields, pointer drag injection, color selector, pause/resume, clear, initial seed.

Let me write the implementation. I'll use a grid resolution scaled to fit performance, e.g. simulation resolution ~128x... based on aspect ratio, and render via ImageData scaled onto canvas.

Let me write it.

Key components:
- N grid dimensions (width in cells), aspect from window.
- velocity U,V, dye R,G,B (or density with color). To keep colors persistent, use three dye fields.
- solver: add source, diffuse, advect, project.
- pointer input applies gaussian splat of velocity and dye.

Performance: use typed arrays. Resolution N ~ 160. Diffusion iterations maybe 4, pressure iterations 10-20.

Actually to keep framerate at 1200x800, use N=128 or so. Let's pick simulation cell size ~6 px at 1200 -> 200. Hmm. Let's use N based on min? Use fixed grid w = 160, h = round(160*height/width).

I'll implement Stam's stable fluids. For dye I'll advect each channel.

Let me write carefully.

Grid: (N+2) x (N+2) arrays with borders. Index IX(i,j) = i + (N+2)*j... standard Stam uses (i + (N+2)*j) with i in 0..N+1.

I'll store linear arrays length (W+2)*(H+2).

Let me adapt Stam's code with variable dims.

Functions operate on arrays with bounds:
- addSource(x, s, dt)
- diffuse(b, x, x0, diff, dt, iter)
- advect(b, d, d0, u, v, dt)
- project(u, v, p, div, iter)
- setBnd(b, x)

For b: 1 for u (horizontal), 2 for v (vertical), 0 for dye/p.

Let me write JS.

Sizes: let W, H cells. N=W. Actually use W and H separately.

IX(i,j)= i + (W+2)*j.

setBnd(b,x):
```
for j=1..H: 
  x[IX(0,j)] = b==1 ? -x[IX(1,j)] : x[IX(1,j)];
  x[IX(W+1,j)] = b==1 ? -x[IX(W,j)] : x[IX(W,j)];
for i=1..W:
  x[IX(i,0)] = b==2 ? -x[IX(i,1)] : x[IX(i,1)];
  x[IX(i,H+1)] = b==2 ? -x[IX(i,H)] : x[IX(i,H)];
corners average.
```

lin_solve(b,x,x0,a,c,iter).

advect uses dt0 = dt * N (scaled). Standard: dt0 = dt*N. We need dx spacing. Let's use dt0x = dt * W, dt0y = dt*H? Since cells normalized 1/W? Standard Stam: x -= dt0*u[IX(i,j)] where dt0 = dt*N, and u in grid units (cells/sec). I'll store velocity in cells per second, then dt0 = dt (no multiply). Simpler: velocity in cell units per second, x = i - dt*u. Let's do that.

Actually let me just use velocity in "cells per second". Then advect: x = i - dt * u[IX(i,j)]. Good.

diffuse: viscous diffusion optional; can set visc small or 0. Set diffusion for dye small.

Let me implement with a=dt*diff*... For simplicity, diffusion coefficient as given. With grid W, standard a = dt*diff*N*N. I'll just use a small value and tune.

Simplest: skip diffusion (set diff=0), rely on advection+projection. That's fine and stable enough with semi-Lagrangian. But some diffusion helps. I'll add slight dye diffusion.

Let me now code.

Rendering: create ImageData of size W x H, fill from dye fields, then drawImage scaled. Use an offscreen canvas W x H, putImageData, then ctx.drawImage(offCanvas, 0,0, canvas.width, canvas.height) with imageSmoothingEnabled true.

Color select: a few swatches. Dye color multiplies density. Store dye as 3 channels directly (r,g,b density). Add dye = color * amount.

Pointer: on mousedown set down, record prev pos. mousemove apply force: u += dx * force, dye at cell. On each frame while down apply. Actually apply on move events with the delta.

Let's apply force as velocity impulse at cell: v += (dx, dy) * strength, and dye += amount.

Initial seed: add random blobs of dye and a couple of velocity vortices.

Let me set W = 128 base. Actually let me compute to keep ~<= 20000 cells. Set W = clamp(floor(width/8), 96, 200). H accordingly. For 1200 -> 150, H = 100. That's 15000 cells. Fine.

Simulation step each frame: velocity step and dye step with dt fixed 0.016.

Pressure iterations 12, diffusion iterations 6.

Let me write the file.

I need fades: multiply dye by a decay factor slightly < 1 each step so it gradually dissipates. Velocity also damped slightly.

Let me code it all.

Edge handling and coordinate mapping from canvas to grid: gx = x / cssW * W, gy = y / cssH * H.

Let me write.

Now write index.html.

I'll include a fixed top-left control panel with UI.

Let me produce the code.

Careful with project and lin_solve.

Let me write full JS:

```
const canvas = document.getElementById('c');
const ctx = canvas.getContext('2d');
let cssW, cssH, DPR;
function resize(){
  DPR = Math.min(window.devicePixelRatio||1, 1.5);
  cssW = window.innerWidth; cssH = window.innerHeight;
  canvas.width = Math.floor(cssW*DPR);
  canvas.height = Math.floor(cssH*DPR);
  canvas.style.width = cssW+'px'; canvas.style.height = cssH+'px';
  // grid
  W = Math.max(96, Math.min(200, Math.floor(cssW/8)));
  H = Math.max(64, Math.round(W * cssH/cssW));
  allocate();
  seed();
  off.width = W; off.height = H;
}
```

Wait offscreen canvas dims reflect grid; changing on resize reallocates. Fine.

Arrays: size = (W+2)*(H+2).

But allocate on resize resets simulation. Acceptable.

Let me define fields: u,v,u0,v0, dens arrays dr,dg,db, and dr0 etc. p, div.

Step:
```
function velStep(dt){
  addSource(u, u0, dt); addSource(v, v0, dt); // u0 holds impulses
  // diffuse optional
  let visc = 0.0;
  if(visc>0){ diffuse(1,u0,u,visc,dt,ITER); diffuse(2,v0,v,visc,dt,ITER); }
  else { copy u0->u, v0->v } // actually swap
  project(u0,v0,u,v,ITER);
  advect(1,u,u0,u0,v0,dt); advect(2,v,v0,u0,v0,dt);
  project(u,v,u0,v0,ITER);
  // damping
}
```

Hmm need to be careful. Let me follow Stam exactly:

```
function densStep(dt){
  addSource(dr, dr0, dt); ...
  SWAP(dr0,dr); diffuse(0,dr,dr0,diff,dt,ITER); SWAP(dr0,dr);
  SWAP(dr0,dr); advect(0,dr,dr0,u,v,dt); SWAP(dr0,dr);
}
function velStep(dt){
  addSource(u0,u,dt); addSource(v0,v,dt);  // u0 source
  SWAP(u0,u); diffuse(1,u,u0,visc,dt,ITER); SWAP(u0,u);
  project(u,v,u0,v0,ITER);
  SWAP(u0,u); SWAP(v0,v);
  advect(1,u,u0,u0,v0,dt); advect(2,v,v0,u0,v0,dt);
  project(u,v,u0,v0,ITER);
}
```

Stam's SWAP and addSource: addSource(x, s, dt): x[i] += dt*s[i]. And velStep does addSource(u, u0, dt) meaning u += dt*u0 (u0 is source). Then swap.

I'll follow this. But note addSource for dye: addSource(d, d0, dt), d += dt*d0. I'll just directly add to the field arrays rather than a source array to reduce complexity. Actually I need source arrays for the pattern. Let me keep it simple: directly add to u,v,dens from pointer before step. Then velStep doesn't need addSource.

Simplify:
```
function step(dt){
  // diffusion
  if(visc){ diffuse(1,u0,u,visc,dt,ITER); diffuse(2,v0,v,visc,dt,ITER); SWAP(u0,u); SWAP(v0,v); }
  project(u,v,u0,v0,ITER);
  SWAP(u0,u); SWAP(v0,v);
  advect(1,u,u0,u0,v0,dt); advect(2,v,v0,u0,v0,dt);
  project(u,v,u0,v0,ITER);
  // dye
  SWAP(dr0,dr); advect(0,dr,dr0,u,v,dt); SWAP(dr0,dr); // hmm
}
```

Wait advect d from d0. Standard: SWAP(d0,d); advect(0,d,d0,u,v,dt); SWAP(d0,d). After swap d0 holds old d. advect writes new into d from d0. Then swap back. Fine. Similarly for g,b. Diffusion for dye optional.

Let me include dye diffusion small to prevent noise? Skip - advection already diffuses.

Damping: after step multiply u,v by 0.999, dye by 0.995 (dissipate).

Actually I'll apply damping inside step.

Let me set ITER=10.

Now advect with velocity in cells/sec:
```
function advect(b,d,d0,u,v,dt){
 for j=1..H, i=1..W:
   let x = i - dt*u[IX(i,j)];
   let y = j - dt*v[IX(i,j)];
   clamp x to [0.5, W+0.5], y to [0.5,H+0.5];
   i0=floor(x); i1=i0+1; s1=x-i0; s0=1-s1;
   j0=floor(y); j1=j0+1; t1=y-j0; t0=1-t1;
   d[IX(i,j)] = s0*(t0*d0[IX(i0,j0)]+t1*d0[IX(i0,j1)]) + s1*(t0*d0[IX(i1,j0)]+t1*d0[IX(i1,j1)]);
 setBnd(b,d);
}
```

Good.

diffuse:
```
function lin_solve(b,x,x0,a,c,iter){
 for k: for j=1..H for i=1..W:
   x[IX(i,j)] = (x0[IX(i,j)] + a*(x[IX(i-1,j)]+x[IX(i+1,j)]+x[IX(i,j-1)]+x[IX(i,j+1)]))/c;
 setBnd(b,x);
}
function diffuse(b,x,x0,diff,dt,iter){
 let a = dt*diff*W*H;  // standard uses N*N; use W*H approx
 lin_solve(b,x,x0,a,1+4*a,iter);
}
```

I might skip diffusion entirely (visc=0, dyediff=0). That's simplest and stable. Let me skip diffusion. Actually a tiny bit of velocity diffusion is fine but skip for perf.

project:
```
function project(u,v,p,div,iter){
 for j,i:
  div[IX(i,j)] = -0.5*(u[IX(i+1,j)]-u[IX(i-1,j)] + v[IX(i,j+1)]-v[IX(i,j-1)])/ (???);
  p[IX(i,j)]=0;
 setBnd(0,div); setBnd(0,p);
 lin_solve(0,p,div,1,4,iter);
 for j,i:
  u[IX(i,j)] -= 0.5*W*(p[IX(i+1,j)]-p[IX(i-1,j)]);
  v[IX(i,j)] -= 0.5*H*(p[IX(i,j+1)]-p[IX(i,j-1)]);
 setBnd(1,u); setBnd(2,v);
}
```

Hmm the scaling. In Stam, project assumes square N and uses 0.5*N. For rectangular, use 0.5*W for u and 0.5*H for v? Since grid spacing differs (dx=1/W, dy=1/H). Standard formulation: div = -0.5*(du/dx + dv/dy) with dx=1/W... Let's use uniform scaling with cell units. Since our velocity is in cells/sec, gradient in cell units: du = u[i+1]-u[i-1] over 2 cells. Laplacian p: p[i+1]+p[i-1]+p[i,j+1]+p[i,j-1]-4p = ... with a=1, c=4. Then subtract 0.5*(p[i+1]-p[i-1]) from u. This is the standard square-grid version and works for rectangular if we keep same cell units. Yes because cells are unit spacing in our index space. Good, so use 0.5 both. Great, no W/H scaling.

div = -0.5*(u[i+1]-u[i-1] + v[j+1]-v[j-1]).

That's consistent.

setBnd for velocity uses reflection.

Now pointer advection: velocity in cells/sec. When drag with delta (dx,dy) over time, add velocity force proportional to (dx,dy)/dt? Simpler: at each frame, for the cells near pointer, add impulse = (dx,dy)*strength. Since velocity units cells/sec, dx in cells. If we add dx*0.5 each frame it may build up. Let's just add.

I'll accumulate pointer motion between frames: track lastX,lastY in grid coords; on each frame, if dragging, apply force = delta * K to cells in radius, and add dye.

But mouse events may fire multiple times per frame. I'll apply directly in pointermove handler: compute grid pos, delta from previous, add splat. That's immediate and simpler. Then dye shows on next frame.

Splat function:
```
function splat(gx,gy,fx,fy, color, amount, radius){
  let x0=max(1,floor(gx-radius)), ...
  for j..for i:
    let d2 = (i-gx)^2+(j-gy)^2; if d2>r2 continue;
    let w = exp(-d2/(r2*0.5));  // gaussian
    u[idx]+=w*fx; v[idx]+=w*fy;
    dr[idx]+=w*color.r*amount; ...
}
```

fx = dx * forceScale; dx in grid cells.

For rapid responsiveness, apply on pointermove.

Let me set radius ~ 3 cells, amount for dye ~ 0.5 per event. Might get very bright. clamp dye when rendering.

Color: swatches; the selected color as {r,g,b} 0..1. Dye stored additive, render clamps.

Seed: place a few colored blobs and a swirl. Add random.

Render each frame:
```
const img = offCtx.createImageData(W,H);
for j,i: for interior cell (i-? ) Actually dye arrays indexed with border. Map image pixel (px,py) to cell (px+1,py+1).
  r = dr[idx], etc. clamp. Set data.
```
Creating ImageData each frame is costly; create once for W*H and reuse, call offCtx.putImageData.

Wait dye arrays are (W+2)*(H+2) but images W*H. Map.

putImageData to off canvas WxH, then drawImage to main canvas scaled.

Use imageSmoothingEnabled true for nice look. Note putImageData ignores smoothing; drawImage scales.

Colors: dye values ~ can exceed 1. Store as is, render = 1-exp(-v) tone map maybe. Use c = 1-Math.exp(-v*1.2). Good for nice colors.

Let me write file now.

Let me also make sure canvas context for main. Use ctx.imageSmoothingEnabled = true.

Background dark. Add slight fade? No, dye dissipates via damping.

Damping: u*=0.999 each step, dye*=0.997. At 60fps dye half-life ~ 0.693/0.003 ≈ 231 frames ≈ 3.8s. Maybe too fast; use 0.9985 -> ~7.7s. Let's use 0.998.

Also velocity damping 0.998.

Now let's write.

Also pause: stop stepping but keep rendering.

Clear: zero all fields.

Let me write the HTML.

I'll write it in one go.

For the pointer, need to handle both mouse and touch. Use pointer events.

Splat force: fx = dx * 6 maybe. dx is in cells (small, e.g., 1-5). Let's tune: force = dx * 8. Velocity in cells/sec. dt=1/60. advection displacement = dt*v = v/60 cells. If v=40 cells/s, 0.67 cells/frame. That's decent. So force should give velocities up to ~100. dx per event maybe 2 cells. force = dx*15 -> 30. Maybe accumulate. Let's do force = dx*20, clamp.

Actually splatting velocity at a cell repeatedly while dragging builds up. Good.

Let me just pick force 15 and tune after testing via browser.

Now write.

For initial seed, add a couple of vortices and dye blobs.

Let me write code.

I'll structure:

```
const state = {
  W:0,H:0,size:0,
  u:null,v:null,u0:null,v0:null,
  dr:null,dg:null,db:null,dr0:null,dg0:null,db0:null,
  p:null,div:null
};
```

I'll just use module-level vars.

Let me write the complete file.

I'll add a UI panel with color swatches, pause, clear buttons styled.

Let me write.

Note: `SWAP` in JS with typed arrays: need to swap references. Can't swap with a temp easily since they're let variables. Use function swap(a,b)? JS can't swap references. Instead just do manual with temp variable: `let t=u0; u0=u; u=u;`... Actually assignment of local variables in module scope is fine:
```
let tmp = u0; u0 = u; u = tmp;
```
But inside functions referencing module vars, fine.

I'll inline swaps where needed.

Let me define helper `function swapFields(a,b)` not possible. Just inline.

Now step implementation with correct swaps:

```
function step(dt){
  // velocity
  // project
  project(u,v,u0,v0,ITER);
  // advect velocity
  let tu=u0; u0=u; u=tu;
  let tv=v0; v0=v; v=tv;
  advect(1,u,u0,u0,v0,dt);
  advect(2,v,v0,u0,v0,dt);
  project(u,v,u0,v0,ITER);
  // dye
  let t;
  t=dr0; dr0=dr; dr=t; advect(0,dr,dr0,u,v,dt);
  ...
  // damping
}
```

Wait at start project(u,v,u0,v0) uses u0,v0 as scratch p/div. But u0,v0 may hold previous. project sets div and p from u,v. Fine. Then swap u0<->u to get old velocity into u0 for advect. But after project, u0 holds scratch (div-ish), not velocity. Hmm. Standard Stam: project(u,v,u0,v0); then SWAP(u0,u); SWAP(v0,v); advect using u0. After project, u,v still hold velocity (project modifies u,v in place), and u0,v0 hold p,div. Then swap: u0 gets velocity, u gets scratch. advect writes new velocity into u using u0 (old). Good. But advect uses u0 and v0 as the velocity to trace with. After swap, u0=old u, v0=old v. But we did two swaps: u0<->u and v0<->v. So u0 old velocity, v0 old velocity. Good. advect(1,u,u0,u0,v0) — d=u, d0=u0, u=u0, v=v0. That's correct.

Then project(u,v,u0,v0) again. Good.

But wait, I skipped diffusion. Fine.

One issue: project at start every frame might be redundant but keeps incompressible. Keep it.

Let me now handle the initial project so seed velocity is divergence-free.

Now write.

For the render tone mapping and alpha maybe. Canvas stays opaque dark.

Let me also add subtle bloom? no.

Write file.

For decay, note that u0/v0 after step may contain stale; project at next frame overwrites. Fine.

Let's write.

Also handle `visibilitychange` maybe not needed.

I'll set dt = min(0.033, elapsed) clamp. Use fixed 1/60 maybe. Use real dt clamped.

Let me write final code.

Potential performance: arrays length ~ (200+2)*(133+2)=27k, * ~11 arrays = 300k, fine. project iter 10 with lin_solve ~ 27k*10*... fine.

Let me write now.

Let me write the file.

Now let me run it in the browser and inspect. Let me take a screenshot and inspect console.

The initial dye isn't visible. Something's wrong. Let me check. Possibly seed() splats but then... Wait, `SZ = SZ; // no-op` is weird but harmless. The dye tone mapping should show.

Maybe the issue: render() draws but the dye quickly dissipates? No, seed is immediate. Hmm.

Wait, `resize(true)` calls allocate, seed. Then in seed, splat uses u,v,dye arrays. Then loop. But maybe the initial vortex advects dye out of view? At 5 cells/s, over a second 5 cells. Not enough to vanish.

Let me check the tone mapping. Actually wait: in seed, the blobs are at cx + b[0]*W. For W=168, cx=84, b[0]=-0.22 => 47. Fine.

Could `imgData` alpha? We set alpha. Fine.

Hmm, maybe the problem is `offCtx.createImageData` then putImageData, drawImage. Let me check: off canvas default has transparent black; putImageData replaces. Should be fine.

Wait, maybe there's an exception. Console only shows a warning. Let me inspect more. Actually maybe the issue is the render uses dr which after allocate is new and seed splats. But note after seed, `resize` returns; fine.

Actually wait — this is the first frame screenshot maybe before seed? No, seed happens synchronously before requestAnimationFrame.

Hmm, let me check tone mapping: 1-exp(-r*0.9). With r=2.6*Ink... wait splat's last arg is ink=2.6. And inside splat, ink>0 branch: dr += r*ink*w. So r channel of blob 5 (1.0,0.35,0.75) times 2.6 => ~2.6. tone -> 1-exp(-2.34)=0.9. So bright. Should show.

Maybe the issue: `resize(true)` is called, but `gridW`/`gridH` initially 0, so proceeds. Good.

Let me check if maybe the whole `step` corrupts things fast. In step, `project(u,v,p,div)` then swaps u0<->u and advect. But note after first project, we swap u0 and u. Then advect(1, u, u0, u0, v0, dt). Wait parameter names: advect(b, d, d0, u, v, dt). It calls with u0 as both d0 and u (velocity), v0 as v. Fine. Then writes into u.

Hmm but there's a subtle bug: advect reads u0 and v0 while writing d=u. Since d=u and u param=u0, no aliasing problem. Good.

Let me check the actual pixels via inspect. Maybe screenshot was taken too early? Let me take another screenshot after some time. Actually reload + inspect gave frame 1. The screenshot might be from frame 1 before render? The attached image shows black canvas. Let me reload and wait.

Actually, maybe there's a JS error in seed due to `SZ = SZ;`? No.

Let me use browser inspect to get console errors. The reload output only showed a warning. Let me run a screenshot again.

Actually could the issue be that the dye is advected but immediately blown to edges by the project? Let's think: initial velocity field is rotational, divergence-free-ish. Fine.

Wait, maybe the big issue: `SPLAT` adds to dr,dg,db, but `render` reads them. Then loop step advects. But maybe render is drawing to canvas but canvas is behind? No, screenshot shows UI only, canvas black.

Let me check whether canvas dimensions are right. Maybe canvas.width uses dpr and drawImage scales. Fine.

Let me test by inspecting DOM / evaluate. The browser tool doesn't have eval. Let me add a quick check: use bash? Can't run browser JS. Let me just take a screenshot after reload with a delay via multiple calls.

Actually the screenshot probably was captured at frame 1. Let me click to drag and screenshot. But first let's see if initial appears. Let me do inspect then screenshot.

Still black. 50fps, 168x112. So the sim runs but nothing renders. Let me debug.

Possible issue: `offCtx.createImageData(W,H)` returns ImageData with data length W*H*4. We fill. putImageData. drawImage. Should work.

Wait — maybe `imgData` got created but `render` uses `imgData` — yes.

Hmm, maybe the dye is being destroyed by the velocity step. The advect for dye uses `u` and `v` AFTER swapping. Let me trace carefully within step:

Initial: u,v = current velocity. u0,v0 maybe stale.

1. project(u,v,p,div) — fine.
2. t=u0; u0=u; u=t; → now u0 = old velocity (good for advect source), u = old scratch.
   t=v0; v0=v; v=t; → v0 = old velocity, v = scratch.
3. advect(1, u, u0, u0, v0, dt) → writes new u from u0. Good.
   advect(2, v, v0, u0, v0, dt) → writes new v from v0. Good.
4. project(u,v,p,div) → fine.

Then dye: t=dr0; dr0=dr; dr=t; advect(0, dr, dr0, u, v, dt). Writes new dr from old. Good.

So dye should persist. Unless advect for dye produces NaN because velocity is huge. Velocity seeded ~5 plus pressure. Fine.

Wait, is the issue that setBnd on velocity after project causes reflection such that... no.

Let me check render loop more carefully. `render()` writes data. But note: `imgData.data` alpha we set. Then we never reset alpha, fine.

Could `Math.exp(-r*0.9)` be NaN? no.

Hmm. Let me check: maybe seed() runs but then resize is called again with initial=false? No.

Actually! `resize(true)` is called at boot. Then `requestAnimationFrame(loop)`. But there may be a race: the window 'resize' event fires on load? Possibly the browser fires resize, calling resize(false). Since newW/newH equal gridW/gridH it returns early, so seed not re-run. Fine.

Wait, maybe the issue is that `canvas` is full screen but the drawing happens... Let me verify the canvas element size vs internal. dpr min 1.5. cssW 1200 -> canvas.width 1800. drawImage(off,0,0,1800,1200). Fine.

Let me actually check by dragging — maybe the dye from drag shows. If drag shows, then seed is the problem. If drag doesn't show, render is the problem.

Let me drag across the canvas.

Nothing at all. So render is broken. Let me check render.

```
offCtx.putImageData(imgData, 0, 0);
ctx.drawImage(off, 0, 0, canvas.width, canvas.height);
```

Hmm. Maybe `ctx` obtained before canvas resized, still valid. Yes.

Wait — maybe `putImageData` with an ImageData created from `offCtx` whose canvas was size W×H works. Yes.

But maybe the fill loop has a bug: `di` increments 4 per pixel but the outer loop only writes for interior cells. That's fine: W*H pixels.

Hmm, but the issue might be `ctx.drawImage` draws a transparent image because ImageData alpha? We set alpha 255 for all, and also set in render data[di+3]=255. So opaque.

Unless the color values are all near 0. Let me reconsider splat. In seed I call splat(cx+..., 0,0, b[2],b[3],b[4], 2.6). Signature: splat(gx, gy, fx, fy, r, g, b, ink). Yes.

But wait — in `splat`, `if (d2 > r2) continue;` where r2 = rad*rad. Fine.

Hmm, maybe dye gets blown away because the initial velocity is huge relative to grid. Actually let me reconsider project scaling. We used a=1,c=4 for linSolve, and u -= 0.5*(p diff), div = -0.5*(...). That's the standard square-grid. Fine.

Wait, the real bug may be that `step` is called with dt up to 0.05, and sub = round(dtReal/(1/60)). At 50fps dtReal=0.02, sub=1, dt=0.02. Advection x = i - dt*u. u~5 → 0.1 cells. Fine.

So why black? Let me double check that `render` is actually called. The fps update happens in loop, so loop runs. render called each loop.

Maybe `imgData` is null? No, it'd throw.

Hmm, is the canvas being cleared by CSS? No.

Let me reconsider: `off.width = W; off.height = H;` then `imgData = offCtx.createImageData(W,H)`. Fine.

Wait, maybe the CSS `#c { width:100vw; height:100vh }` plus `touch-action` fine.

Let me actually verify by adding a debug: draw a test rectangle. Or better, use the `inspect` action to get more info? The tool's inspect only returns dom/console. No canvas pixel access.

Let me temporarily set a debug by rendering a solid known value. Actually, let me think about `putImageData`. Actually: ImageData's data is a Uint8ClampedArray. We assign rr etc. Fine.

Oh wait! I see it. In render, the tone mapping uses `Math.exp(-r*0.9)`. For r ~ 2.6 → 0.9 fine.

Hmm let me re-examine seed: I set velocity for all interior cells, then splat dye. But the FIRST thing loop does is step, which calls project and advect. If velocity is large and flows out, over the ~1 second before screenshot... but drag also produced nothing immediately.

Unless `render` is drawing onto `ctx` but then something immediately clears? No.

Let me check: maybe `ctx.drawImage(off, 0, 0, canvas.width, canvas.height)` — `off` is a canvas with width W=168. drawImage signature (image, dx, dy, dWidth, dHeight). Fine.

Hold on. Is `imgData` maybe recreated after seed? No.

Let me just test with a standalone minimal check. Actually, let me use the browser inspect with a custom action? Not available. Let me add a temporary overlay text showing a dye value, then inspect DOM.

Actually simpler: maybe the issue is that `data` array is Float32? No it's Uint8Clamped.

Wait, could it be that `offCtx.putImageData` fails silently because the ImageData dimensions don't match? They match W,H.

Hmm. Let me look again at the loop and the use of `dtReal`. At reload, frame 1. Actually the screenshot says Frame 1 each time, even after drag. That's suspicious — maybe the browser tool captures frame 1 only, and the animation isn't advancing? But fps shows 51 fps, meaning many frames ran. The tool description says "motion frames". The screenshot may be a fresh page each time? "Frame 1, +0ms". Possibly it re-navigates on each action? If inspect/reload resets. But drag then screenshot: drag shows frame 1 too. Hmm.

Possibly the screenshot is taken from the initial frame before any rendering happens? But UI shows fps updated (50 fps 168x112), so at least 0.5s elapsed.

Let me reconsider: maybe the rendering IS happening but the dye has already dissipated or been advected off. 50 fps over maybe 1-2 seconds. Damping 0.997^60 ≈ 0.835/s, not enough.

But wait, could the velocity be enormous, causing advect to clamp everything to boundaries and the dye to pile at edges (still visible)? Maybe not.

Let me actually check if the velocity is enormous due to a bug in project. Let me compute: project's linSolve for p with div. Then u -= 0.5*... Should be fine.

Hmm, but there's a subtle aliasing bug: in `step`, after `project(u,v,p,div)`, I swap u0<->u. Now `u` points to old u0 (zeros), `u0` points to velocity. Then `advect(1, u, u0, u0, v0, dt)`. Wait, the 4th arg is named `u` and 5th `v` in advect signature: `advect(b, d, d0, u, v, dt)`. I pass `u0` as velocity u-field and `v0` as velocity v-field. Good.

Then `advect(2, v, v0, u0, v0, dt)`. Good.

Then `project(u,v,p,div)`. Good.

Dye: `t=dr0; dr0=dr; dr=t;` now dr0 = old dye, dr = old dr0 (zeros). advect(0, dr, dr0, u, v, dt). Good.

So sim seems right.

Wait, maybe the bug is that the arrays are Float32Array and `advect` writes but `setBnd` writes to border. Fine.

Let me question whether the initial scene is even created: after `resize(true)`, `allocate()` sets arrays. Then `seed()` calls `clearFields()` then fills. Good.

Hmm, actually maybe `resize` returns early because `initial` is true but gridW/gridH... no, initial true bypasses the early return only? The early return condition: `if (newW === gridW && newH === gridH && !initial) return;`. initial=true so no return. Good.

Let me add a debug pixel test. I'll temporarily modify render to fill a visible rectangle via ctx.fillStyle and see if it shows. But maybe the tool screenshot just always shows frame 1 before render. Let me test by calling inspect after waiting — but actions are discrete.

Alternative: maybe the canvas is rendered but the screenshot is captured before the RAF callback. In that case, I should force a render synchronously at the end of boot. Let me add a synchronous render() call right after resize(true). Then frame 1 screenshot at least shows seed. That's a good idea regardless.

But drag still gave black. Since after drag the page may have reloaded (frame 1). If the tool reloads, then the drag's effect is gone. Hmm, but it says frame 1 +0ms for all, suggesting the tool navigates fresh each call. That means I might be seeing pre-RAF state each time. The fps text updated though... which is set in the RAF loop. So RAF ran. Confusing.

Actually "Frame 1, +0ms" might just be a label of the capture, not a reset. And dom has fps text "51 fps", which only gets set after 0.5s. So the page persists and loop ran. So render should have produced content.

Let me force synchronous render and also check whether the issue is the drawImage of a same-origin offscreen canvas. Should be fine.

Wait... maybe the problem: `ctx.drawImage(off, 0, 0, canvas.width, canvas.height)` but `canvas.width` might be 0 at time of first render? No, resize set it.

Hmm, let me reconsider the possibility that dye values are all zero because `splat` uses `idx` computed but `dr[idx]` etc. Actually let me re-read splat:

```
function splat(gx, gy, fx, fy, r, g, b, ink) {
```
Wait, the parameter names: after fx, fy we have `r, g, b`. But then inside:
```
dr[idx] += r * ink * w;
```
Fine.

But in seed I call `splat(cx + b[0] * W, cy + b[1] * H, 0, 0, b[2], b[3], b[4], 2.6);` where `b` here is the blob array. So r=b[2], g=b[3], b=b[4]. Good.

Now the outer variable `b` is also a parameter name in splat (channel blue). Inside seed, I used `var b = blobs[k];` which shadows nothing problematic.

OK let me just add debug output to the page title / fps text with a dye sample. Actually let me change fps text to include max dye value. Quick edit.

Let me add to render: compute a max and store, and display. But bad to leave. Let me add a temporary debug line. Actually, let me instead expose window.__sim for inspection? The browser tool doesn't eval.

Simplest: temporarily add a bright red DOM element to confirm rendering path, and set document.title to max dye. The inspect returns dom text which includes title? It returned the button texts, likely innerText. Title not included.

Let me put the debug info into #fps text. Modify render to track maxDye and update fpsEl each frame. Let me do a quick edit and reload.

dom still shows "--" for fps, meaning render loop didn't update? Actually the dom string is "--" which is the initial fps text. But earlier it showed "51 fps". Now it shows "--". Hmm inconsistent. Maybe this reload capture is genuinely at frame 1 before RAF. The earlier capture showing 50fps was after some time.

The issue is my debug loop over dr may crash (dr is big, fine). But `window.__mx` should be set.

Let me do inspect (which may wait) to get updated dom.

mx=0.63 means dye exists (max channel). So render writes image data. But the screenshot is black. So the problem is in composite: putImageData/drawImage not appearing.

Wait, canvas.width=1200 (dpr=1). drawImage(off,0,0,1200,800). off is 168x112. Should scale.

Hmm, mx=0.63 after ~1s, dimmer than initial 2.6 but should be visible (tone mapped 1-exp(-0.57)=0.43 → ~110). Should be clearly visible.

So maybe the canvas draw is happening but the screenshot tool captures before composite? Or maybe the canvas element's backing store is cleared after? Or `ctx` is a different context?

Wait — possible major bug: I call `ctx.imageSmoothingEnabled = true;` AFTER putImageData but before drawImage. That's fine.

Hmm, is it possible that `offCtx.putImageData` puts data but then `drawImage` reads from off canvas which is being used as... no.

Let me consider: Is the canvas actually 1200x800 and visible? CSS sets width 100vw. The body background is #05060a. The screw shot shows black everywhere. Dye should show.

Let me test drawing directly to ctx without offscreen: fill the main canvas with a color. Let me temporarily replace render's draw with ctx.fillStyle='red'; ctx.fillRect. Actually let me just add a fillRect at the end of render for debugging, then reload and see red.

Actually wait — maybe the issue is the canvas is covered by something? No.

Another thought: maybe `putImageData` itself works but `imgData.data` is being written with wrong byte indexing because `createImageData` on offCtx returns data length W*H*4, and di increments per pixel, correct.

But mx=0.63 proves dr nonzero. But maybe the render loop computes rr etc but `data[di]` assignment... di starts 0. Fine.

Hold on: the tone mapping for mx=0.63 is 1-exp(-0.567)=0.43. But the max might be at a single cell; most cells near 0. After 1s of advection/diffusion the dye spread thin. Still there should be a blob.

Let me just add a debug fillRect and see if the main canvas shows anything. I'll add at start of render: ctx.fillStyle='rgba(255,0,0,0.3)'; ctx.fillRect(0,0,50,50). If the screenshot shows red, canvas works and the issue is data. If not, canvas rendering issue.

Actually, better: maybe the screenshots are always taken at frame 1 (pre-render) because the tool captures immediately on action, and the visible frame isn't updated. But the fps text updated in the image, so the DOM/composite is current. So canvas should be current too.

Wait, unless RAF renders to a canvas that is then not presented due to the screenshot tool using a separate mechanism. Unlikely.

Let me just try the debug fillRect.

Wait I removed the `var Wp = W + 2;` line but it's used in render! Let me check. In render I used `var Wp = W + 2;` and then `var row = j * Wp;`. I removed it. That will throw ReferenceError -> render crashes -> black! But wait, that was in the NEW version I just made. The original still had Wp. Actually my edit removed it now. Let me re-add. Actually the original render did have Wp. I just accidentally removed it. Let me put it back.

The image shows black canvas still, no red rect visible (it's frame 1 pre-render). The red rect would be at (10,10) under the UI panel maybe. The UI panel covers top-left 0-210px, so the red rect at 10,10 is behind the panel. Oops. Let me move it to center. Also this frame is pre-render. Let me inspect to get the post-render state.

Even the red fillRect isn't visible at (10,10) but that's behind the panel? The panel starts at top:12 left:12 and is ~210 wide, 200 tall. So the red rect (10..70, 10..70) is behind the panel. Let me move the debug rect to center-left, e.g., x=300. Actually the canvas is black; the panel has translucent dark background. If the red rect were drawn, we'd see a reddish tint through the panel? Not necessarily.

Let me move debug fillRect to (400,400) size 100. Then inspect. If visible, main canvas compositing works, and the offscreen drawImage is the issue.

Actually, wait. I bet I know the issue now. `ctx.drawImage(off, ...)` where `off` is a canvas that we also call `putImageData` on. That should be fine.

Hmm, but maybe `off` canvas has width/height set but the ImageData created before? No.

Let me think about whether `imgData` data values are actually being set. mx=0.56 is computed from dr. But maybe the byte values rr are computed to 0 because... no.

Actually, let me reconsider: Maybe the render function throws AFTER computing mx? No, mx computed after drawImage.

Wait, the debug fillRect is after drawImage and before the mx computation. If fillRect worked, we'd see red. And mx gets computed after, and fps shows mx. So render completes. So the red rect IS drawn. But invisible in screenshot → maybe the screenshot doesn't capture canvas content at all, OR the rect is behind panel.

Let me move rect to center and test.

Actually, wait. Let me reconsider the screenshot pipeline. The `dom` reported includes canvas? No. Maybe the screenshot captures the DOM but canvas is drawn by WebGL/2D and should appear. Hmm.

Let me move the debug rect to (500,300) and also make it bigger.

Red rect visible. So main canvas works. The offscreen drawImage is producing black. So `putImageData`/drawImage path has an issue. 

Possibility: `offCtx.putImageData(imgData,0,0)` — maybe imgData's data is not being updated because... Actually mx is from dr, not from imgData. Let me sample imgData directly. But more likely: `offCtx.drawImage` scaling a canvas with transparency... no, alpha 255.

Wait, could it be that `imgData` was created via `offCtx.createImageData` but then we call `offCtx.putImageData`, then `ctx.drawImage(off,...)`. This is standard. Unless the off canvas is tainted? No.

Hmm, let me check: maybe `off` canvas dimensions got set to W,H = 168,112 but then `imgData` created with those. Fine.

Let me sample imgData max and also verify the draw by rendering the off canvas unscaled. Actually, maybe the issue is that `render` is called, but the red rect drawn AFTER drawImage. So drawImage's result is overwritten? No, fillRect only covers part.

Wait, the red rect appears, so the code after drawImage runs. The drawImage result is invisible -> the offscreen image is black/transparent. So either data all zeros (but dr nonzero) or the 2D context drawImage of a small canvas scaled fails.

Let me test rendering imgData directly onto main canvas with putImageData at 0,0 (unscaled) to see if data shows. Actually putImageData ignores canvas transform and draws at grid size in pixels — 168x112 in the top-left. Let me do that as debug: `ctx.putImageData(imgData,0,0)`. But note the main canvas is 1200x800; putImageData at 0,0 would show a 168x112 image (with possibly some transparup edges? no alpha 255). Let's test.

Actually wait, there's a subtle bug: after `putImageData` into offCtx, we call `ctx.drawImage`. But then next frame we call `offCtx.putImageData` again. Fine.

Hold on — maybe the issue is that `imgData` alpha was set in resize AFTER createImageData, but in render we set alpha=255. Fine.

Let me just check by computing max of imgData and displaying. But let me test putImageData on main.

Actually — I suspect the real issue: The `drawImage(off, ...)` with a canvas whose context has `putImageData`. This should work. Let me question the tone mapping: for a single cell with value 0.56, rr = 255*(1-exp(-0.5))=100. That should appear.

Hmm, wait. Maybe the entire dye is concentrated in a tiny number of cells (mx=0.56) and the rest near 0. But even so, a blob of a few cells scaled up 7x would be ~30px, visible.

But actually, after 1 second, the seed dye is advected by the initial velocity. But maybe the velocity is huge and it's all at edges. Let me check the very first frames. The reload capture shows the pre-render black frame. Maybe the dye really is gone within frames.

Let me disable step temporarily (pause = true initially) to see seed. Actually let me test by setting a debug: fill imgData with a gradient to confirm drawImage works. Let me override: instead of dr, set data to a known pattern based on i,j. Let me temporarily modify render to compute rr=gg=bb = (i/W)*255.

Actually simpler: let me test drawing the offscreen canvas filled solid via offCtx.fillStyle. Hmm.

Let me add after putImageData: `if(!window.__once){ctx.putImageData(imgData,0,0); window.__once=1;}` to directly blit data to main and see if data is non-black. But putImageData onto main at 0,0 will be overwritten next frame by drawImage. But within same frame, we putImageData then drawImage; drawImage overwrites whole canvas. Let me put it AFTER drawImage for debug.

I'll modify: replace the red rect debug with:
```
if(!window.__once){ ctx.putImageData(imgData, 0, 0); window.__once = 1; }
```
But putImageData on main canvas at 0,0 draws 168x112 unscaled. That would show. If it shows color, data is fine and drawImage scaling is broken. If black, data is black.

Wait but mx computed from dr is 0.56; imgData should have rr. Let me instead directly compute max of imgData.data to compare.

Let me just do both: compute maxByte of imgData and display. Replace debug.

The second edit oldText didn't match. Let me look at the actual text.

The edit failed because the whole call failed atomically? It says could not find edits[1], so no changes applied. Let me redo both with correct text.

The putImageData at 0,0 isn't visible either → imgData is black. Let me inspect for mb.

mb=0! So imgData.data red channel max is 0, despite dr max 0.64. That means the render loop isn't writing to data. Why? Let me look at the render code now. Maybe the loop body has an issue. Let me read the render function.

The render code looks correct. But mb=0 means data[di] is 0 for all red samples. Hmm, but wait — maybe `imgData` is not the same object we think. Or maybe `dr` values are negative? mx computed as max dr = 0.64, positive. So rr positive.

Unless `imgData.data` is a different length than expected. `createImageData(W,H)` — data length W*H*4. Our loop writes exactly W*H*4 bytes. Good.

Wait, maybe the issue is that `di` indexing writes but data values are floats assigned to Uint8ClampedArray — fine.

Hmm, mb computed after putImageData. But wait, `mb` loop steps q2 += 4, reading data[q2] red. If everything 0, then writes didn't happen.

Could it be that `render` is throwing before the loop? No, mb gets set.

Let me reconsider: maybe `dr` inside render refers to something else? No.

OH WAIT. I see it! In `resize()`, after creating imgData, I set alpha:
```
for (var k = 3; k < imgData.data.length; k += 4) imgData.data[k] = 255;
```
That's fine.

Hmm, could `W` and `H` be something else than grid dims? In resize, `gridW = W = newW; gridH = H = newH;`. Good.

Let me check: is `imgData` perhaps null and render assigning to null... no, would throw.

Wait, maybe there are TWO render functions or the one being called is different? No.

Let me actually check if data writes happen by setting data[0]=123 always as a test. Let me add near mb: data[0]=123 and see if mb becomes 123. Actually mb is computed over the whole array after the loop; data[0] would be overwritten by the loop next frame... within same frame mb reads data[0] after loop. If assignment works, mb>=123. Let me test that.

Actually wait — maybe the bug: `data[di] = rr < 0 ? 0 : rr > 255 ? 255 : rr;`. Could `rr` be NaN? NaN < 0 is false, NaN > 255 is false, so assigns NaN → Uint8ClampedArray converts NaN to 0. So if r is NaN, result 0! And mx would be NaN though... mx computed with `if (dr[q] > mx)` — NaN > 0 is false, so mx stays max of non-NaN. But if some dr are finite and some NaN, mx = finite max. But the finite max is 0.64. Hmm, but the cells with 0.64 should render.

Unless ALL dr are NaN except a few? mx=0.64 finite. So at least one finite. That cell should give rr>0.

Wait, unless the loop never executes because H=0? No.

Hmm, let me just add data[0]=123 test.

Actually, wait! I wonder if `imgData` is being reassigned somewhere. Let me grep imgData.

Let me add a direct test: after the inner loops, set data[0]=123. Then mb check. Let me edit.

Even data[0]=123 gives mb=0! That means `imgData.data` is not writable? Or `imgData.data[q2]` reads back 0 for all. But data[0]=123 then mb loop reads imgData.data[0] which is data[0]. Should be 123.

Unless `imgData.data` is not the same as `data`? `var data = imgData;` then `data[0] = 123` sets property "0" on the ImageData object, not on data's Uint8ClampedArray! Because `data = imgData` — imgData is an ImageData object, not its data array. Then `data[di] = rr` sets numeric properties on the ImageData object itself, which are ignored. That's the bug! I should use `var data = imgData.data;`.

Yes! That's it. Fix: `var data = imgData.data;`. Great catch.

Now let me remove all debug and fix. Let me rewrite the relevant parts cleanly.

Let me revert the render function to clean and remove debug from loop, remove the wait. Let me apply edits:
1. `var data = imgData;` → `var data = imgData.data;`
2. Remove debug lines (red rect, mb, once, mx).
3. Restore fps text.
4. Remove mx computation in render.

Let me do these edits.

Also remove the weird `SZ = SZ; // no-op keep reference` line and the `if (!paused) paused = false;` oddity. And there's another bug: pause btn toggles paused then `if (!paused) { paused = false; }` no-op. Fine but clean.

Also `if (speed < 0.01 && speed === 0) return;` is weird but works. Let me clean it up. Let me make those edits.

Now dye visible. This is the pre-render first frame, showing seed blobs (with little advection). Let me inspect and screenshot after a bit to see swirling. Let me inspect first.

The blobs are being stretched/smudged by the flow. Good — advection works. But the overall swirl is gentle. fps dropped to 32 — a bit low. Target 1200x800 should stay responsive. 32fps is okay-ish but let me optimize. The main cost is likely the linSolve loops (12 iterations) and advect and the damping loop over full SZ. Let's reduce ITER to 10 and maybe grid to 150. Actually 32fps is acceptable "responsive" but let's improve a bit.

Actually note the fps measurement includes my debug overhead? No, debug removed. 32fps. Hmm.

The render loop over W*H each frame plus 11 arrays. The tonemap uses Math.exp 3x per pixel (18816 pixels) = 56k exp calls/frame. That's significant. Could precompute? Fine.

The linSolve does ITER=12 iterations over (W*H) ~ 18k cells, 4 arrays reads, called for project twice = 24 passes, plus advect 5 times (velocity 2 + dye 3) over 18k = 90k, plus damping over 27k*5. Total maybe 1-2M ops/frame. Should be fast, ~10ms. But rendering + putImageData + drawImage scaling 168->1200 might be the cost. 32fps = 31ms. Hmm.

Let me profile mentally: maybe the `setBnd` calls in linSolve per iteration are cheap. The biggest cost might be `ctx.drawImage` upscaling with smoothing on a large canvas each frame (1200x800) — GPU should handle.

Actually maybe the fps shown is low because the page also had initial load. Let me not over-optimize. But requirement says controls remain responsive at 1200x800. 30-50fps is responsive. Let me reduce ITER to 10 and reduce damping cost by skipping? Let me measure again after more time.

Actually, let me check: the screenshot shows the flow. Let me now test dragging. I'll drag and then inspect after some delay to see swirling and second drag.

Also I should re-seed more strongly / add more motion so it's clearly visible. The blobs are somewhat dim after a second. Dye damping 0.997 per step at ~40fps => decays. Fine.

Let me do the drag test. Use browser drag.

The drag injected a streak (cyan) from bottom-left to top-right. Good. But it looks like the drag is only partially applied — the streak goes from ~(300,500) to (800,300). Good. It's a bit dim. The default color is COLORS[4] r=0.20 g=0.75 b=1.0 cyan. Good.

Now let me wait/step and see if it continues swirling after release. The drag ends with pointer up. Let me take another screenshot after a moment. The browser tool each action seems to advance the page a bit. Let me inspect again to let time pass.

The dye has swirled and spread. It's quite dim now. The damping is too aggressive and the tone map makes it faint. The requirement: "Momentum and dye remain visible after the pointer is released and gradually dissipate." Currently it fades quite fast. Let me increase dye brightness and reduce damping a bit, plus boost the initial seed.

Issues to improve:
1. Dye fades too fast (DYE_DAMP 0.997 per step at up to 60fps → half-life ~3.8s, but combined with diffusion/advection spreading it looks very dim in ~2s). Actually 0.997^120 = 0.7 after 2s. That's not the main cause; spreading thins it. The tone map with 0.9 factor saturates only at high values. Let me boost INK and use a stronger tone map (e.g., 1-exp(-v*1.6)) and increase seed brightness.

2. fps ~50-54, fine.

3. The flow could be more visible. Let me increase FORCE? The streak was fine.

Let me increase INK to 1.2, seed ink to 4, dye damp to 0.9985, and tone map factor to 1.4. Also maybe reduce velocity damp to 0.9985 so momentum persists longer.

Also the initial seed vorticity is modest. Let me make it stronger and more varied so dye swirls better. But not too strong.

Let me also reduce resolution slightly to improve fps? 50fps is fine.

Let me apply tuning.

Also, I want to make sure Clear works and a fresh flow can start. Clear zeroes fields. Then drag starts new flow. Good.

One more: after Clear there's no ambient velocity, so a drag creates its own flow and dye. Good.

Let me apply tuning edits.

Also improve initial velocity field to be more varied. Let me leave it. Let me also fix that the drag streak's ink multiplier: `INK * Math.min(1.4, 0.45 + speed * 0.10)`. With INK=1.1 that's ~0.5-1.5. Fine.

Let me reload and test full sequence: initial, drag, second drag, clear, drag. Let me reload.

Now let me wait a bit to see it swirl. Let me inspect.

Now 60fps. Good. The seed blobs are swirling (elongated). But the motion is still relatively weak — the blobs are stretching but not dramatically. That's okay.

Now let me test drag and second drag, then clear.

Let me drag from left to right.

Strong cyan streak injected along the drag. Now let me wait and see it swirl, then do a second drag in another direction. Let me inspect to let time pass.

Now the streak has swirled and folded, showing a clear S-curve. This demonstrates persistent swirling flow after release. Good.

Now let me do a second drag in another direction (vertical). Then screenshot.

Second drag (vertical) injected a clean vertical streak, and the old flow remains. Good. Now test Clear. Click Clear button at approx (139, 99). Then screenshot.

Clear worked — canvas fully black, velocity reset. Now drag again to confirm a fresh flow starts.

Let me also test the Pause button and color selector. I'll drag first.

Fresh flow after Clear works.

Now test color selector: click the red swatch (second, at x~64, y~61) then drag. Actually let me click an orange/red swatch and drag to verify color changes. Swatch positions: 6 swatches starting x~35, spacing ~29. First pink at 35, second red at 64, third orange 93, fourth green 122, fifth cyan 151, sixth purple 180, y=61.

Let me click red (64,61) then drag.

The red swatch is now active (white ring on second swatch). The streak continued swirling. Now drag to confirm red dye.

The red dye was injected. Color selection works. The prior cyan streak is still faintly visible and swirling. Great.

Now test Pause/Resume. Click Pause (bold red? the button at 64,99). Then drag should not inject? Actually dragging unpauses (onDown sets paused=false). So test: click Pause, verify label becomes Resume, then maybe check screenshot shows frozen. Then click Resume. Let me quickly test Pause label.

Actually the onDown handler sets `paused=false; updatePauseBtn();` so any drag resumes. That's fine behavior. But if paused and user drags, it resumes. Good.

Let me test pause click.

Pause button now shows "Resume" (highlighted). The simulation is paused. Note the image shows the swirl frozen. Good.

Let me verify the resume button works and the flow continues. Click Resume. Actually enough. Let me resume so final state isn't paused (doesn't matter for file). But let me verify.

Actually I've verified all required behaviors:
- Initial seeded dye and motion ✓
- Drag injects dye and momentum ✓
- Dye follows drag, continues swirling after release ✓
- Second drag in another direction ✓
- Clear resets ✓ fresh flow ✓
- Color selector ✓
- Pause/Resume ✓
- ~50-60fps at 1200x800 ✓

Remaining unverified:
- Pause actually stops motion (I should confirm but the label changed; frozen screenshot suggests yes, though hard to tell motion from still).
- Mobile/touch path.
- Resize behavior.

Let me click resume to unpause and then check. Also I realize there's one potential issue: when paused, dtReal accumulates? In loop, if paused, we skip step but lastT still updates each frame, so no jump. Good.

Let me resume and do a final screenshot. Also I should double check the code doesn't have leftover debug. Let me grep.

No debug leftovers. Now let me resume and verify the sim continues. Click Resume.

Resumed, label back to "Pause". Good.

Now let me do a final review of the code for any remaining issues. Let me read the full file once to verify.

Potential issue: `resize` on window resize re-seeds, losing current flow. That's acceptable (unspecified). But it could be annoying. Not required.

Potential issue: In `onMove`, `e.preventDefault()` on mousemove only when pointerDown. Fine.

Potential issue: touchstart on canvas calls onDown with preventDefault. Good. But mousedown also triggers for touch? We use both mouse and touch listeners; touch devices may fire both, but preventDefault on touchstart should suppress mouse emulation. Fine.

Potential issue: `project` first call each step is redundant but harmless; actually it's needed to maintain incompressibility before advection. Fine.

Let me double check the initial seed velocity: it's not projected until first step, which projects. fine.

One thing: `local` variable shadowing in advect: parameters `u, v` shadow outer. Fine.

The `FORCE` of 18 and INK multiplier. Good.

Let me check the `clearFields` also resets `p` and `div`. Yes.

The `resize` early-return logic: on resize, if dims change, reallocate and seed. Fine.

Let me verify there are no syntax errors by checking console (only the sandbox warning appears). Good.

I think the app meets requirements. Let me read through the file once to be safe, especially the top portion. Actually I already know it. Let me just double-check the final render function and step.

Everything looks good. One subtle thing: `setBnd` doesn't handle `b===0` for dye at edges explicitly, but it copies neighbor; fine.

The simulation is complete and verified. Let me write a brief report.

Actually, one more consideration: the drag test relied on the browser tool which may dispatch pointer events. It worked.

Let me also verify no external resources: grep for http.