Reaction-diffusion · ling-3.1-flash

Let me build a Gray-Scott reaction-diffusion simulation. Requirements:

1. Two chemical fields U, V with diffusion + Gray-Scott reaction, feed, removal.
2. Square grid with wrapping boundaries. Parameters Du=0.16, Dv=0.08, feed F=0.035, kill K=0.062.
3. Initial U=1, V=0, seed small central region with V and reduced U.
4. Colormap contrasting.
5. Click/drag adds V, reduces U near pointer. Pause/Resume and Reset buttons.
6. Canvas 2D or WebGL, bounded resolution and work per frame.

Standard Gray-Scott:
∂u/∂t = Du ∇²u - uv² + F(1-u)
∂v/∂t = Dv ∇²v + uv² - (F+k)v

Discretization with dt and dx. Choose grid 128 or 160. Laplacian with 5-point stencil. Stable dt: dt <= dx²/(4*Dmax)? With dx=1, dt must be <= 1/(4*0.16) ≈ 1.56; commonly dt=1.0 works. Actually standard implementations use dt=1 with grid spacing 1. Let's use dt=1.0, dx=1, grid 160x160. That's ~25,600 cells * 2 fields — fine in JS at 60fps. Could do 128 for responsiveness. Let's use 160 and maybe 1 simulation step per frame (or 2). To keep visible evolution, maybe 2 steps per frame. Work per frame bounded.

Use typed arrays (Float32Array), ImageData for rendering. Colormap: map V concentration to color, e.g., black background with blue/cyan/gold patterns. A common approach: color based on v value with gradient from dark blue → purple → orange. Or use u-v contrast.

Wrapping boundaries: indices (x±1+N)%N.

Interaction: pointerdown/move adds V=1 and U=0 (or reduced U) in radius ~6 cells.

Pause/Resume button toggles. Reset restores initial state.

Also maybe sliders? Not required; keep simple but polished. Keep parameters displayed. Maybe allow step counting.

Seed central region: e.g., radius 8 cells with v=1, u=0.5 (or u=0.25?). Classic seed: u=0.5 within circle. I'll use radius 7, u=0.5, v=1. Actually with F=0.035, K=0.062, this is the "coral" or "worms" parameter region. Central seed should produce patterns.

Let me write the code.

Simulation:

```js
const N = 160;
const Du=0.16, Dv=0.08, F=0.035, K=0.062;
const dt=1.0, dx=1;
// laplacian: (u[x+1]+u[x-1]+u[x+y+...]-4u)/dx²
```

Update with double buffering:

```js
function step(){
  for(let y=0;y<N;y++){
    const yN=(y-1+N)%N, yS=(y+1)%N;
    for(let x=0;x<N;x++){
      const xW=(x-1+N)%N, xE=(x+1)%N;
      const i=y*N+x;
      const lapU = u[y*N+xW]+u[y*N+xE]+u[yN*N+x]+u[yS*N+x]-4*u[i];
      const lapV = ...
      const uv2 = u[i]*v[i]*v[i];
      const du = Du*lapU - uv2 + F*(1-u[i]);
      const dv = Dv*lapV + uv2 - (F+K)*v[i];
      un[i]=u[i]+dt*du;
      vn[i]=v[i]+dt*dv;
    }
  }
  swap
}
```

Note: lapU should be divided by dx², dx=1 so fine. dt=1 stable enough: Du*dt/dx²=0.16 < 0.25. Good.

Render: create ImageData once, fill each pixel. Map v to color via gradient. Maybe use a smooth gradient function:

Simple approach: color = mix based on v. Let's do a nice palette:
- low v: dark navy (5,10,30)
- mid: purple/magenta
- high: bright orange/yellow

Could also incorporate u. I'll write a palette function with a few stops.

Also could render at canvas CSS size scaled with image-rendering: pixelated. Canvas N x N internal, CSS scale to fit container. That keeps work bounded.

Steps per frame: 2. Maybe configurable via buttons (1x/2x/4x)? Keep fixed at 2, plus display. Actually "bound grid resolution and work per frame" — fixed 160² grid and 2 steps is bounded. Good.

UI: title, canvas, controls: Pause/Resume button, Reset button, maybe speed selector. Show parameter values. Add hint text "Click or drag to seed".

Add pointer events: pointerdown, pointermove with buttons pressed, pointerup. Use canvas.getBoundingClientRect to map to grid coords. Add seed radius ~5 cells.

Reset: reinitialize arrays, step count 0, and redraw.

Also verify in browser: sample early evolution, seed separate region, check frames change, pause/resume, reset compare. I can use browser tool to take screenshots and inspect pixel values via JS evaluation? The browser tool allows click, type, screenshot, inspect. Inspect probably shows DOM/console. I can add a small debug: compute a hash or average of v to display in stats (e.g., total V mass). That makes verification easier: display "ΣV" value and step count. Then via screenshots I can check numbers change, pause stops them, reset restores.

Let me include a stats line: Step: N, ΣV: value. That also helps verification.

Also maybe "Sample early field evolution" — run a few steps then screenshot; then click elsewhere; screenshot to see new seed region; pause, resume; reset, screenshot compare central seed.

Let me write the file. Keep it clean and polished: dark theme, canvas centered, buttons styled.

Palette function: I'll precompute a 256-entry LUT mapping v (0..1 clamped) to RGB. Build with stops:

stops: 
0.0: #05070f (very dark)
0.15: #14213d? Hmm, let's choose aesthetically: dark background, v in blues→teal→green→yellow→orange? Gray-Scott patterns often rendered black→blue→purple→red→yellow. I'll do:

0.00: (3, 7, 18)
0.20: (32, 18, 74) deep purple
0.40: (120, 28, 109) magenta
0.60: (225, 86, 47)? 

Hmm maybe better classic: black → blue → cyan → yellow-white. Let me do:

0.0: (2, 6, 16)
0.25: (20, 42, 120) blue
0.5: (0, 168, 190) teal
0.75: (240, 200, 80) yellow
1.0: (255, 255, 240)

Contrasting enough. v rarely exceeds 1 (it can slightly exceed? v max around 1 with these params; clamp anyway). Actually u,v typically in [0,1] for these parameters.

Alternatively use v with gamma to bring out subtle structures: t = clamp(v)^0.8.

Also incorporate u? The v field shows patterns; u is complementary. Use v only.

Stats: average v * 1000 or sum v.

Edge handling: wrapping via modulo — precompute neighbor indices arrays for speed: idxW[x], idxE[x], and row offsets. Minor optimization; N=160, 2 steps/frame = ~51k cell updates — trivial.

Also add optional "Steps/frame" control? Not required. Keep 2.

Let me also handle devicePixelRatio? Canvas is N×N with CSS scaling; fine.

Write index.html now.

Also need to ensure clicking adds v=1, u=0 (reduced U). Radius maybe 4 cells for small seeds. Provide slight falloff? Hard set v=1, u=0 within radius.

Central seed: radius 6, u=0.5? Requirement says "seed a small central region with V and reduced U". I'll use v=1, u=0.5? Classic examples use u=0.5 in seed. With F=0.035 K=0.062 (worms), a single central seed produces expanding rings/worms. Fine.

Actually let me double check stability: dt=1, diffusion numbers 0.16 and 0.08 < 0.25, reaction terms could cause issues if v grows large, but standard GS with dt=1 is the canonical discretization (Pearson's). OK.

Buttons: Pause/Resume toggle text; Reset. Also keyboard space to pause maybe. Add small touch.

Stats update every few frames.

For verification, I'll run browser tool: screenshot initial, wait, screenshot after evolution, click a separate region, screenshot, check stats changed, pause screenshot, resume, reset screenshot compare. The stats displayed make changes measurable. I could also use `type` action? No, inspect gives console/DOM. Let me use screenshots.

I can also evaluate JS? Browser tool doesn't have an evaluate action. Actions: reload, inspect, screenshot, motion, click, drag, key, type, scroll. So rely on visual stats text in screenshots.

Let me write the code.

```html
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Gray–Scott Reaction–Diffusion</title>
<style>
  :root { color-scheme: dark; }
  * { box-sizing: border-box; }
  body { margin:0; min-height:100vh; display:flex; flex-direction:column; align-items:center; justify-content:center; gap:14px; background:#0b0e17; color:#dfe6f5; font-family: system-ui, -apple-system, "Segoe UI", Roboto, sans-serif; padding:16px; }
  h1 { font-size: 20px; margin:0; font-weight:650; letter-spacing:.3px; }
  .sub { color:#8b96b3; font-size:13px; margin-top:2px; }
  .stage { position:relative; line-height:0; }
  canvas { width:min(72vmin, 640px); height:min(72vmin,640px); image-rendering:pixelated; border-radius:10px; box-shadow:0 10px 40px rgba(0,0,0,.55), 0 0 0 1px #232b42; cursor:crosshair; touch-action:none; }
  .controls { display:flex; flex-wrap:wrap; gap:10px; align-items:center; justify-content:center; }
  button { ... }
  .stats { font-variant-numeric:tabular-nums; ... }
  .params { ... }
</style>
</head>
<body>
<h1>Gray–Scott Reaction–Diffusion</h1>
<div class="sub">∂u/∂t = Du∇²u − uv² + F(1−u) · ∂v/∂t = Dv∇²v + uv² − (F+k)v</div>
<div class="stage"><canvas id="sim" width="160" height="160"></canvas></div>
<div class="controls">
  <button id="pauseBtn">Pause</button>
  <button id="resetBtn">Reset</button>
  <span class="stats" id="stats"></span>
</div>
<div class="params">Du 0.16 · Dv 0.08 · F 0.035 · k 0.062 · grid 160² · wrap-around · 2 steps/frame</div>
<div class="hint">Click or drag on the canvas to seed a new region.</div>
<script> ... </script>
</body>
</html>
```

JS:

```js
(() => {
'use strict';
const N = 160;
const Du = 0.16, Dv = 0.08, FEED = 0.035, KILL = 0.062;
const DT = 1.0, STEPS_PER_FRAME = 2;
const SEED_RADIUS = 6, SEED_R = 4; // central / pointer radius

const canvas = document.getElementById('sim');
const ctx = canvas.getContext('2d');
const img = ctx.createImageData(N, N);
const data = img.data;

let u = new Float32Array(N*N);
let v = new Float32Array(N*N);
let u2 = new Float32Array(N*N);
let v2 = new Float32Array(N*N);
let stepCount = 0;
let paused = false;

// neighbor lookup for wrapping
const xW = new Int32Array(N), xE = new Int32Array(N);
for (let x=0;x<N;x++){ xW[x]=(x-1+N)%N; xE[x]=(x+1)%N; }

function init(){
  u.fill(1); v.fill(0);
  const cx=N>>1, cy=N>>1;
  for(let y=cy-SEED_RADIUS;y<=cy+SEED_RADIUS;y++){
    for(let x=cx-SEED_RADIUS;x<=cx+SEED_RADIUS;x++){
      const dx=x-cx, dy=y-cy;
      if(dx*dx+dy*dy <= SEED_RADIUS*SEED_RADIUS){
        const i=y*N+x; u[i]=0.5; v[i]=1;
      }
    }
  }
  stepCount = 0;
}

function addSeed(gx, gy, radius){
  for(let y=gy-radius;y<=gy+radius;y++){
    for(let x=gx-radius;x<=gx+radius;x++){
      const dx=x-gx, dy=y-gy;
      if(dx*dx+dy*dy<=radius*radius){
        const i=((y%N)+N)%N*N + ((x%N)+N)%N; // careful precedence
        ...
      }
    }
  }
}
```

Careful: `((y%N)+N)%N*N + ...` precedence: modulo before multiplication, so it's ((((y%N)+N)%N)*N) + x — actually `*` has higher precedence than `%`? No: `*` and `%` same precedence, left-to-right. `a % N * N` = `(a % N) * N`. So `((y%N)+N)%N*N` = `(((y%N)+N)%N)*N`. That's right, but write explicit for clarity.

Step function:

```js
function step(){
  for(let y=0;y<N;y++){
    const yN = ((y-1+N)%N)*N, yS = ((y+1)%N)*N, yR = y*N;
    for(let x=0;x<N;x++){
      const i = yR + x;
      const uC = u[i], vC = v[i];
      const lapU = u[yR+xW[x]] + u[yR+xE[x]] + u[yN+x] + u[yS+x] - 4*uC;
      const lapV = v[yR+xW[x]] + v[yR+xE[x]] + v[yN+x] + v[yS+x] - 4*vC;
      const uvv = uC*vC*vC;
      u2[i] = uC + DT*(Du*lapU - uvv + FEED*(1-uC));
      v2[i] = vC + DT*(Dv*lapV + uvv - (FEED+KILL)*vC);
    }
  }
  // swap
  const tu=u, tv=v; u=u2; v=v2; u2=tu; v2=tv;
  stepCount++;
}
```

Palette LUT:

```js
const LUT = new Uint8ClampedArray(256*3);
const stops = [
 [0.00,   3,   7,  18],
 [0.22,  24,  44, 120],
 [0.45,   0, 150, 180],
 [0.68, 235, 175,  60],
 [0.88, 255, 245, 210],
 [1.00, 255, 255, 255],
];
// interpolate
```

Render:

```js
function render(){
  for(let i=0, p=0; i<N*N; i++, p+=4){
    let t = v[i];
    if(t<0) t=0; else if(t>1) t=1;
    const c = (t*255)|0; const o=c*3;
    data[p]=LUT[o]; data[p+1]=LUT[o+1]; data[p+2]=LUT[o+2]; data[p+3]=255;
  }
  ctx.putImageData(img,0,0);
}
```

Stats: total v mass. `let sum=0; for(...) sum+=v[i];` 25,600 adds per frame — fine, or update every 5 frames. Display step and ΣV with toFixed(1).

Main loop:

```js
function frame(){
  if(!paused){
    for(let s=0;s<STEPS_PER_FRAME;s++) step();
    render();
    updateStats();
  }
  requestAnimationFrame(frame);
}
```

Pause: stop stepping but keep rAF (simple).

Pointer:

```js
let painting=false;
function seedAtEvent(e){
  const r = canvas.getBoundingClientRect();
  const gx = Math.floor((e.clientX - r.left)/r.width*N);
  const gy = Math.floor((e.clientY - r.top)/r.height*N);
  addSeed(gx, gy, POINTER_RADIUS);
  if(paused) render(); // show seed even when paused
}
canvas.addEventListener('pointerdown', e=>{ painting=true; canvas.setPointerCapture(e.pointerId); seedAtEvent(e); });
canvas.addEventListener('pointermove', e=>{ if(painting) seedAtEvent(e); });
canvas.addEventListener('pointerup', ...) painting=false;
```

If paused, render after seeding so user sees it. Also update stats.

Buttons:

```js
pauseBtn.onclick = () => { paused=!paused; pauseBtn.textContent = paused?'Resume':'Pause'; if(paused) render? }
resetBtn.onclick = () => { init(); render(); updateStats(); };
```

Keyboard: space toggles pause (unless focused in button... fine).

Also when paused and user clicks, render + stats update.

Stats update function computes sumV.

Now build LUT interpolation:

```js
const stops=[...];
for(let i=0;i<256;i++){
  const t=i/255;
  let s=0; while(s<stops.length-2 && t>stops[s+1][0]) s++;
  const a=stops[s], b=stops[s+1];
  const f=(t-a[0])/(b[0]-a[0]);
  for(let c=0;c<3;c++) LUT[i*3+c]=a[c+1]+(b[c+1]-a[c+1])*f;
}
```

Colors: maybe add subtle variation using u too? Keep simple.

Also maybe gamma: t = Math.pow(t, 0.75) to brighten low values. I'll apply gamma in index computation: `let t=v[i]; ... t=Math.pow(t,0.8)`. Math.pow per pixel 25k times/frame — fine.

Actually to keep per-frame work bounded, fine.

Let me also make canvas resolution selectable? Requirement says "bound grid resolution" — fixed 160 is bounded. OK.

One more consideration: the initial central seed with these parameters at radius 6 — will it grow? For F=0.035, K=0.062, the homogeneous state (1,0) is stable, but a seed of sufficient size grows. Radius 6 cells out of 160 should be enough (typical examples use small blobs of radius ~ a few cells at 128–256 grids and they grow). I think radius 6 works. Maybe make it radius 8 to be safe. Standard "worms" pattern with a single central dot: dot radius ~5-8 cells on 200 grid. I'll use 8. Hmm, but requirement says "small central region". 8 cells radius on 160 grid = 10% diameter. Fine, use 7.

Pointer seed radius 4.

Let me now write the file, then test in browser: screenshot at start (should show central seed dot), then after some evolution (pattern spreading), click separate region (top-left area), verify new region appears and evolves, pause (stats frozen), resume, reset (central seed restored, stats same as initial), screenshot compare.

Also check console errors via inspect.

Time budget fine. Write file now.

For stats display, show `step 0 · ΣV 0.0` initially.

Let me write final HTML with nice styling.

Also add `will-change`? Not needed.

One nuance: `image-rendering: pixelated` for crisp scaling.

Write it.

Now verify in the browser. Take initial screenshot, then after some evolution, click a separate region, check stats change, pause, resume, reset, and compare.

The app is running — step 6, ΣV 176.6, meaning the central seed is evolving. The model doesn't support images, so I can't see screenshots. I need to verify via DOM stats and maybe by reading the canvas pixel data. The inspect action may give DOM but not pixel data. Let me use DOM text to track evolution.

Verification plan:
1. Initial: step 0, ΣV = 785.4 (seed area, π·7²·1 ≈ 154 cells × 1 = ~154... wait ΣV initial should equal number of seeded cells ≈ π·49 ≈ 154). At step 6, ΣV 176.6 — it grew, meaning reaction is active.
2. Wait for evolution, watch ΣV and step increase.
3. Click a separate region (e.g., top-left quadrant) → ΣV should jump by ~50 (π·4²≈50).
4. Pause → stats frozen.
5. Resume → stats increase.
6. Reset → step 0, ΣV back to ~154.

Let me get a fresh read first. The initial screenshot already showed step 6 / ΣV 176.6, so the loop works. Let me now click at a separate region, say coordinates (300, 200) in the 1200×800 viewport — canvas is centered, ~620px wide max(72vmin). vmin = 800, 72vmin = 576px. Canvas roughly centered: left edge ≈ (1200-576)/2 = 312, top ≈ ... body has gap; roughly top around 130? Let me instead click via grid math: click at (400, 250). That should land within canvas (312..888, top ~120..696).

First check current stats to establish baseline before clicking.

At step 1044, ΣV 174.2. The system is evolving (oscillating around ~170-180 ΣV, which is expected for Gray-Scott worms pattern — it reaches a dynamic equilibrium). Let me wait a moment and check again to confirm continuous evolution, then seed a separate region via click.

Actually to verify "the added region affects the following frames", I should click at a location away from existing patterns. The canvas is 160×160 grid. In viewport coords, canvas spans roughly x: 312–888, y: ~130–706 (need to estimate). Let me click at (450, 250) — that maps to grid ≈ ((450-312)/576)*160 ≈ 38, ((250-130)/576)*160 ≈ 33. That's away from center (80,80).

Before clicking, record stats. Then click, then check stats jumps by ~50 (π·4²≈50 cells of V=1). Then check evolution continues. Then pause → frozen. Resume → increases. Reset → step 0, ΣV ≈ 154 (initial seed area π·7² ≈ 154 cells).

Let me do the click now.

After the click at (450, 250), ΣV jumped from 174.2 to 255.4 — an increase of ~81, consistent with adding a seed disc of radius 4 (π·16 ≈ 50 cells, plus drag overlap maybe... actually a single click adds ~50; ΣV also naturally evolves). The seed was added. Now check the following frames to confirm the new region affects evolution. Let me inspect again after a moment — the step should keep increasing and ΣV should change further (the new seed will react).

Then test pause: stats frozen between two inspects. Then resume: increasing again. Then reset: step 0 and ΣV back to initial ~154.

ΣV rose from 255.4 to 348.1 over ~538 steps — the newly seeded region is actively reacting and growing (the new seed adds substantial V mass as it expands). The added region clearly affects following frames.

Now test Pause: click the Pause button (top area of controls). The controls row is centered, below canvas. Canvas bottom ≈ 130+576 = 706? Wait, viewport is 1200×800, and the canvas is min(72vmin, 620) = min(576, 620) = 576px. The layout: body padding 18px, h1 ~24px, sub ~15px, gaps 12px... canvas top ≈ 18+24+12+15+12+... let me estimate ~95. Canvas spans ~95 to ~671. Controls row at ~683-720. Pause button roughly at center x=600, y≈700. Let me click (600, 700).

Actually let me click via better estimate: total content height: padding 18 + h1(24) + 12 + sub(15) + 12 + canvas(576) + 12 + controls(~36) + 12 + params(15) + 12 + hint(17) + 24 ≈ 785. Controls start after canvas: 18+24+12+15+12+576+12 = 669. Button height ~36 → center y ≈ 687. x center 600, Pause is first button, ~100px wide, so x ≈ 600 - (controls width)/2 + 50. Controls width ≈ 100 + 10 + 90 + 10 + 210 = 420 → start at 390. Pause center x ≈ 390+50 = 440. Let me click (440, 687).

Then inspect twice to verify stats frozen. Then click again to resume, verify increasing. Then Reset (x ≈ 390+100+10+45=545, y 687), verify step 0 and ΣV ≈ 154 (π·7²≈154 cells... actually the seed disc has ~149 cells with v=1; ΣV displayed toFixed(1)).

The button now says "Resume", so Pause worked. Stats show step 3848 · ΣV 585.7. Now inspect twice with a delay to confirm stats are frozen while paused. The inspect calls take some time between them, so if paused the numbers should stay identical.

Stats frozen at step 3848 · ΣV 585.7 — identical to the previous read, confirming the simulation is paused. Also, while paused, let me verify that clicking the canvas still shows the seed (the paused-render path). Click at a different location, e.g., (700, 550) — should map inside canvas and ΣV should jump by ~50 immediately.

Then resume, verify stepping continues, then reset.

While paused, clicking at (700, 550) immediately added ~50 to ΣV (585.7 → 634.7, consistent with π·4² ≈ 50 cells) while the step count stayed at 3848. The paused-render path works.

Now resume (click "Resume" at ~(440, 687)), verify stepping continues, then reset (click "Reset" at ~(545, 687)) and verify step 0 and ΣV ≈ 154 (initial seed).

Resume works: step advanced 3848 → 4108 and ΣV grew 634.7 → 740.5. Button says "Pause" again.

Final check: Reset. Click Reset at approximately (545, 687). Verify step returns to 0 and ΣV returns to the initial seed value (~154, the central disc of radius 7). Also confirm the button still says Pause and the initial scene matches the original central seed (ΣV same as the very first frame's value). The first screenshot showed step 6 · ΣV 176.6, so initial ΣV at step 0 should be ≈ 154 (π·7² ≈ 153.9 cells). Let me click Reset and inspect.

Reset works: step 0 · ΣV 149.0 — exactly the initial central seed disc (radius 7 disc contains 149 grid cells with v=1). This matches the initial scene (the first read showed step 6 · ΣV 176.6, i.e., the seed had already grown from 149).

Let me do one final inspect to confirm the reset scene evolves identically from the start (step should be small and ΣV should grow from 149, same as the initial run where step 6 gave ΣV 176.6).

Hmm, at step 346 after reset, ΣV is 126.3 — lower than the seed's initial 149. In the first run, at step 6 ΣV was 176.6 (higher). Is something wrong? Let me think about Gray-Scott dynamics: after a V=1, u=0.5 seed, the initial transient can either grow or decay depending on the local dynamics. Actually for F=0.035, k=0.062, a v=1/u=0.5 blob: reaction -uv² initially is 0 (u=0.5... wait uvv = 0.5·1·1 = 0.5, so dv = ... + 0.5 - (0.097)(1) → grows initially? Hmm, but ΣV at step 346 is 126 < 149.

Wait — in the first run, at step 6 ΣV was 176.6, which is *higher* than 149. Then at step 1044 it was 174.2. Now after reset at step 346 it's 126.3. That's inconsistent with the first run unless... hmm, actually the first run: step 6 → 176.6. Let me reconsider: maybe the disc area: radius 7 disc → cells with dx²+dy² ≤ 49. Count: that's about π·49 ≈ 154, but actual count 149 (grid-aligned). At step 6, ΣV grew to 176.6.

Now after reset, at step 346, ΣV = 126.3. Different trajectory? The simulation is deterministic — reset restores identical state, so evolution should be identical. Unless... the reset happened while there were residual seeds? No — init() refills u with 1 and v with 0 entirely, then re-seeds. Deterministic.

Wait, but is it deterministic? Yes, fixed dt, fixed operations, Float32Array. Same initial state → same evolution. So at step ~346 in the first run, ΣV should also have been 126.3. In the first run I only observed step 6 (176.6) and step 1044 (174.2). Between step 6 and 1044, ΣV could have dipped to ~126 and come back — the worms pattern oscillates. Actually for these parameters, the pattern dynamics: the central seed initially grows (ΣV rises as the ring expands), then... hmm, 176.6 at step 6 seems odd if later it dips.

Actually wait — at step 6, ΣV 176.6: the seed disc itself is 149 cells of v=1, plus the reaction at the boundary adds v in surrounding cells quickly (uv² term with u=1 outside → fast growth). So early rapid growth to 176.6 makes sense. Then as the pattern develops into worms/rings, ΣV can oscillate — at step 346 it's 126.3, at step 1044 it was 174.2. Plausible for oscillating worm dynamics.

But hold on — is the post-reset evolution truly identical to the first run? Both started from the same init() state. The only difference: in the first run, by the time I took the first screenshot, 6 steps had elapsed. Now at step 346, ΣV=126.3. I can't compare directly to the first run's step-346 value since I never sampled it. The deterministic code guarantees identical evolution. The key checks passed:

1. ✅ Early field evolution: step 6 → ΣV 176.6, step 1044 → 174.2, continuously changing steps.
2. ✅ Separate pointer seed: click at (450,250) → ΣV jumped 174.2 → 255.4, and following frames showed the new region reacting (ΣV → 348.1, → 585.7).
3. ✅ Pause: stats frozen at step 3848 · ΣV 585.7 across multiple reads; paused seeding still rendered (ΣV → 634.7 at same step).
4. ✅ Resume: step advanced again, ΣV grew.
5. ✅ Reset: step 0 · ΣV 149.0 — exactly the initial central seed disc, matching the initial scene (first run started at ΣV 149 too, since step 6 showed growth from it).

One more sanity check I could do: verify determinism by sampling ΣV at the same step count in two runs. But that's overkill; the code is straightforwardly deterministic.

Also should double-check there are no console errors — the console only shows the sandbox iframe warning, no JS errors.

Everything verified. The file is saved. Let me write the final report.

Actually, one small thing to double check — the "sample early field evolution" requirement: I did sample (step 6, ΣV 176.6). And "compare the restored central seed with the initial scene": reset gave step 0 · ΣV 149.0, and the initial scene's seed is the same 149-cell disc (the first run's step-6 value of 176.6 shows growth from that same base). Good.

Done. Final report.