Reaction-diffusion · mimo-v2.5

Let me build the Gray-Scott reaction-diffusion simulation. I'll write index.html with inline CSS/JS. Use Canvas 2D with ImageData for a grid of e.g. 256x256, running multiple steps per frame.

Plan: implement with typed arrays, wrap boundaries via index math (use modular indexing with precomputed index arrays for speed, or use padding approach). Simple approach: grid N=256, arrays Float32Array(N*N). Laplacian with wrap using precomputed xm1/xp1 arrays.

Steps per frame: ~12. dt = 1.0, Du=0.16, Dv=0.08 (with dx=1 laplacian kernel standard 9-point with -1 center, 0.2 diagonal, 0.2 orthogonal... actually standard Gray-Scott uses dt=1, Du=0.16, Dv=0.08 with laplacian kernel [[0.05,0.2,0.05],[0.2,-1,0.2],[0.05,0.2,0.05]]). That's stable with dt=1: diffusion number Du*dt = 0.16 < 0.25 for 5-point; with 9-point kernel sum weights = 1 for neighbors, so effective stability Du < 0.25 fine.

Seed: central region radius ~ grid/16 with V=1, U=0.

Color map: map V (0..1) to colors — dark background to bright organic colors. e.g. use U and V: color based on v: smooth gradient.

Interaction: mousedown/mousemove on canvas adds V=1, U=0 in radius ~4 cells (scaled to grid coords).

Controls: Pause/Resume button, Reset button. Maybe also show FPS/step count, and seed another region verification... The verify steps I should do with browser tool: click in a separate region, check following frames change (I can read state via a debug hook, e.g. window.__sim exposing fields and stats). Pause/resume, reset and compare central seed with initial scene (via debug hook comparing arrays).

Add debug hooks: window.__sim = { grid: N, getU(), getV(), stats(), paused, reset() }.

Render: canvas 2D, ImageData N*N, putImageData to offscreen canvas then drawImage scaled to display canvas with imageSmoothing enabled for smooth look. Display canvas size e.g. min(720, viewport).

Let me write the file.

Color mapping: use a palette based on v and gradient of u. Something like:
t = clamp(v*? ) Use: c = v; brightness. Let's do: 
r = 255 * smoothstep... Use combination: base color from v: mix between deep dark blue/purple (0,0,0) to teal to white.

Simple: t = min(1, v*2.2); then r = 20 + 235*t^1.5... maybe give pattern nice contrast: background dark navy (u≈1), V regions bright. Add gradient from laplacian for edge shading? Keep simple but pretty:

palette function: 
t = clamp(v,0,1); s = Math.pow(t, 0.65)
r = Math.round(255*Math.min(1, s*1.4 - 0.1))
g = Math.round(255*Math.min(1, s*1.15 - 0.02))
b = Math.round(255*Math.min(1, 0.25 + s*0.75))
Hmm; let's do a two-tone: dark indigo → bright cyan/white.

Also add slight blue tint from u? u ranges 0..1; background u≈1, so background = indigo (30,20,60)? Actually just color by v.

Let me include: 
bg = (12, 14, 28); mid = (0, 140, 190); hot = (245, 250, 240).
t<0.5: lerp bg→mid with t*2; else lerp mid→hot.

Interaction radius in grid cells: brush radius = max(3, N*0.02) ≈ 6 at N=256.

Also mouse coords → grid: rect scaling.

Steps per frame: adjustable? Keep fixed at 10, plus quality maybe. Add a speed slider? Not required; keep minimal: Pause/Resume, Reset, plus maybe steps slider—optional. I'll add a small "steps per frame" slider for nicety but keep it simple. I'll include it; low risk.

dt = 1.0, laplacian 9-point.

Reset: re-fill U=1,V=0, seed center.

Frame loop: requestAnimationFrame, if !paused, run steps, render. Even paused, render (no-op since same). Render always fine.

Debug verification: expose window.__sim with getU/getV returning copies or views, snapshot, diff metric, and a seedV(x,y,r) function maybe. I can use pointer events via browser click tool; but reading state requires JS eval — browser tool has "inspect" action which runs in page? It says "Run index.html, inspect DOM/console, interact, and see screenshots". Probably `inspect` executes arbitrary JS. Let me check by trying.

Write file now.

Laplacian with wrap: precompute left[i], right[i], up[i], down[i] index arrays. For cell index i = y*N+x: left = y*N + ((x-1+N)%N), etc. Precompute once.

Update loop: use two sets of arrays and swap. Compute:
u2[i] = u[i] + (Du*lapU - u*v*v + feed*(1-u)) * dt
v2[i] = v[i] + (Dv*lapV + u*v*v - (kill+feed)*v) * dt

lapU = 0.2*(orthogonal sum) + 0.05*(diag sum) - u[i]. Wait standard kernel: center -1, orthogonal 0.2, diagonal 0.05. So lapU = 0.2*(L+R+U+D) + 0.05*(diag) - center.

Clamp to [0,1] for safety.

Seed: central circle radius N/16 with V=0.9? Typically V=1, U=0 (or u=0.5,v=0.25). Use U=0.5, V=0.25? Spec says "seed a small central region with V and reduced U" — set V=0.9, U=0.2? Let's use V=1, U=0 to make it strong. Hmm with feed=0.035, kill=0.062, that's the "coral growth" / "mitosis"-ish regime. F=0.055,k=0.062 is mitosis; F=0.037,k=0.06 is solitons; F=0.035,k=0.062 should work — produces something like "u-skate"? Should still produce interesting patterns. Fine.

To make patterns robust, seed a few sub-seeds? Spec says small central region. Keep it; also click adds elsewhere.

Also maybe add slight noise to avoid perfect symmetry stagnation? Not needed; deterministic pattern is fine. Actually perfect symmetry can produce boring stable symmetric patterns, but it still evolves. Add tiny noise (±0.01) to seeded region? I'll add small random perturbation in seed to break symmetry — allowed.

Render resolution: display canvas 512 or so, offscreen N x N putImageData, then drawImage scaled with smoothing.

Let me write it.

UI layout: dark theme, title, controls, stats (frame, avg v, paused indicator), canvas centered.

Canvas sizing: N=256 grid; display size 640 (responsive via CSS max-width; use fixed 640 backing store and CSS width 100%).

Pointer: pointerdown sets drawing=true, capture; pointermove adds; pointerup ends. Also touch support via pointer events.

Now write code.

For verification I'll need stats: avg V, and count of changed cells, and sample values at seeded region. Expose:
window.__sim = {
  N, paused,
  getU(x,y), getV(x,y),
  avgV(), diffFromSnapshot(), snapshot(), isPaused(),
  step(n) — run n steps manually,
  brush(x,y,r)
}

Ok write.

Estimated sim cost: N=256 → 65536 cells, ~10 steps/frame = 655k cell updates/frame, fine in JS.

Let me write the file.

Now run it in the browser and verify. First reload and inspect console.

My sanity-check one-liner had a typo (not the actual file). Let me fix the test script quickly.

The numerics are stable and the pattern grows (avg V increases from seed, spreading). Pattern is slowly growing — with F=0.035, k=0.062 the growth is slow but present. After 4000 steps avg V0.006 — that's slow growth but organic patterns take shape. Let me check the visual spread — is it growing into a "coral"-type pattern? Let me quickly check spread radius at4000 steps.

Actually let's just proceed to browser verification — visuals matter. Let me open the browser.

The pattern spreads outward steadily, growing an organic structure. Good. At 12 steps/frame, 60fps →720 steps/sec, so it takes ~30 sec to reach radius 85. That's a bit slow for a demo but acceptable. Maybe bump default steps per frame higher? At 256² with 9-point laplacian, 30 steps/frame might be OK performance-wise. Let me test perf in browser. Alternatively bump default to 18-20. Let's check in browser first.

Now open browser.

Now open browser.

curl isn't available. Let me just use the browser tool to open index.html directly (probably file:// or it can load local path). Try browser reload/screenshot.

The simulation is running. Frame 60, avg V 0.0022. The pattern is showing a growing ring (coral-like growth) with the satellite speck. It's early. The growth is slow at 12 steps/frame. Let me bump default speed to make it more visually engaging. But first let's let it run longer and take another screenshot to see evolution. Also verify interactivity.

Wait — frame shows 120 in the DOM but stats show 60 in screenshot; whatever, screenshot was earlier frame.

The pattern is evolving. Let me wait and take another screenshot after some time. Then test click interaction, pause/resume, reset.

Let me increase default steps/frame to maybe 20 for a livelier feel? At N=256, 20 steps of JS per frame seems feasible. Let me check performance first — measure fps via evaluate? I can't run JS directly... Actually maybe the browser tool has an "inspect" action that can evaluate. Let me try inspect with some text? The inspect action probably returns DOM/console. Let me try `browser action=inspect` with text as script maybe. Let's test.

Let me check if the browser tool supports evaluating JS via "inspect" with text parameter. Let me try.

Excellent — after ~17,640 simulation steps, a beautiful organic maze-like pattern has grown and filled a large region. The simulation is clearly evolving live from the initial seed.

Note the "inspect" action didn't evaluate JS — it just returned the DOM. So I need to rely on visible behavior / stats readouts. That's OK: the stats line shows frame, avg V, state. I can use those for verification.

Now verify:
1. Sample early field evolution — done (frame counter grows, avg V grows from 0.0016 → 0.0621, pattern spreads).
2. Seed a separate region with pointer — click at a corner area, then check subsequent frames change (avg V increases and visible bloom at click location).
3. Pause — check "state paused" and frame counter stops; resume — frame counter continues.
4. Reset — pattern back to initial central seed; compare with initial scene.

Let me click somewhere in an empty corner, e.g. (400, 650) in viewport coords — canvas spans x from ~281 to ~919, y from ~155 to ~793. So a corner-ish spot inside canvas: (380, 680) — bottom-left area, which is empty (pattern radius ~ centered). Pattern currently spans about radius ~230px on screen... The canvas is 638px wide. The pattern spans roughly x from 350 to 920 on screen. Let me pick top-left area of the canvas, e.g. (340, 220) — that appears empty (dark). Let me click there and take screenshot.

The pattern now fills the entire canvas (it has spread to wrap boundaries) — good, wrapping works visually (pattern reaches all edges). The click at (380, 230) created a bloom visible near the top-left — I can see a small bluish blob at around (383, 230). It's subtle because the click paint was fresh (solid V=1 disc renders as bright white-ish... hmm it renders darker bluish?). Actually the click spot shows as a dark-blue blob with a teal halo — because paint sets v=0.95, u=0.05, which maps to t=0.95*2.6=1 → white. Hmm the blob looks blue-ish. Wait, look at the image: there's a teal-ringed dark blob at (383, 230). Hmm, could the click actually have registered? The visible blob suggests yes — the fresh seed V=0.95 disc... but color should be near-white. Let me think: paint sets v=0.95, and the palette t = min(1, 0.95*2.6) = 1 → LUT white (250,252,240). The blob in the screenshot at (380,230) looks like a teal blob with darker core. Actually looking again, it's a small blob that is bluish-teal — could be the bloom after a few frames (the interior of a fresh high-V disc quickly converts: with u≈0.05 the reaction u*v*v is small... v decays in the interior since no u to feed, leaving a ring that expands). That's expected Gray-Scott behavior: fresh U-depleted disc → interior dies out, ring blooms outward. So the blob is the click effect.

Note the stats: frame 38580, avg V 0.1363. The avg V increased from 0.0621 (at frame 17700) as pattern filled the canvas. To verify the click's effect on subsequent frames specifically, better to pause... no — I'll click in an empty-ish spot and compare before/after avg V and the blob's growth in a couple of screenshots.

But now the whole canvas is filled with pattern, so "empty region" doesn't exist. The verification says: seed a separate region with the pointer, check that the added region affects the following frames. The click at (380,230) region is visible. Let me take a screenshot now to see how the blob evolved after a few hundred frames.

Let me wait ~2 seconds (about 120 frames × 12 steps = 1440 steps) and screenshot again to see the bloom spreading.

Let me take a screenshot to see the bloom evolve after ~3 seconds.

The click bloom at (380,230) has now been absorbed/merged into the surrounding pattern — the local structure near top-left has changed compared to the previous screenshot (patterns reorganized around the click point). The average V hovered around 0.1356 (steady-state labyrinth). Frame counter keeps advancing (64140), so frames continue evolving.

The click bloom effect: in the previous screenshot there was a distinct dark blob with teal halo; now it has merged into the labyrinth — evidence that the added region affected following frames. To be more rigorous, I could click and take two screenshots close together. But screenshots take time; the previous pair (right after click, and3s later) shows the change.

However, a cleaner verification of "the added region affects the following frames" would be done in a paused state: pause, click, screenshot (bloom present), step forward, screenshot (changed). But I can't call __sim.step via browser tools (inspect doesn't evaluate JS). Hmm — but I can change steps/frame to 1 and pause/resume quickly? Resume runs1 step per frame though; still continuous.

Alternative approach: verify via stats readouts. avg V is displayed. If I pause, note avg V... it won't update while paused (updateStats called on toggle). Actually updateStats is called on pause click and shows avgV at that moment; while paused stats don't update. That's fine.

Let me do a rigorous interaction test:
1. Click Pause → state paused, frame stops advancing (verify by two screenshots a couple seconds apart with same frame number).
2. While paused, click on canvas → paint happens, render() called → bloom visible in screenshot.
3. Resume → frame advances; compare avg V / pattern.

Also drag test: use drag action to paint a stroke and confirm it shows.

Then Reset and compare with initial scene (small central ring, frame 0, avg V small value ~0.0016-ish... at reset frame=0 and avgV computed from fresh seed).

Wait, at reset the pattern is a bright central disc of radius 16 plus satellite. avg V at reset: seed area π*16²*... plus jitter≈ 800 cells × ~1.0 /65536 ≈ 0.012. Initial boot showed avg V 0.0016 at frame 60 — because the seed quickly decays into a ring (interior dies since u=0 there). That's expected: fresh V-filled disc with U=0 decays into expanding ring.

Hmm — "Reset restores the initial fields and seed" and "compare the restored central seed with the initial scene". Since reset uses the same deterministic code path (initState + seedCenter with jitter), the restored scene will match the initial scene except for random jitter ±0.06 within the seed. Visually identical. Good.

Let me now do the pause test.

Let me click the Pause button at (210, 111).

Paused: state shows "paused", button shows "Resume", frame frozen at 81768. Let me confirm the frame number stays frozen after a delay, then drag a stroke while paused to verify pointer painting works while paused, then resume and confirm evolution resumes.

Excellent verification:
1. While paused, the drag painted a bright white stroke (V=0.95 → white color) along the drag path — pointer painting works and renders immediately even while paused.
2. Frame counter stayed frozen at 81768 → pause truly stops evolution.

Now resume, and verify that the painted stroke region affects subsequent frames (the white dots should evolve into rings/blooms and start spreading) and the frame counter resumes.

Resume works: state "running", button back to "Pause", frame advancing again (81768 → 81780/81840), and avg V bumped to 0.1445 (the painted stroke added V mass) and now settling. The stroke dots are visibly swelling already (compare the dot sizes between screenshots — they're growing/blooming, avg V rose0.1328→0.1445 → wait that value was from a moment later). Good.

Let me wait a few seconds to see the stroke evolve into blooms, then do Reset and compare the restored central seed with the initial scene.

Let me take a screenshot to see the stroke evolved.

The stroke's white dots have reacted and largely merged into the labyrinth (the local pattern in the lower-left has restructured where the stroke was). This confirms the injected region affected the following frames — it was absorbed/evolved.

Now: Reset, and compare the restored central seed with the initial scene. The initial scene at boot was: small central bright ring + satellite speck, frame0, avg V ~0.0016-ish at frame 60.

Click Reset and screenshot immediately.

Reset works: frame back to 0, avg V 0.0133 at frame 0 (fresh seed disc), and by frame 60 it's 0.0022 — matching the initial boot scene exactly (initial screenshot at frame 60 also showed avg V 0.0022 and identical visuals: central bright ring + satellite speck at the same position, same sizes). The restored central seed matches the initial scene.

Comparing screenshots:
- Boot (frame 60): avg V 0.0022, central ring + small ring upper-right, identical geometry.
- After reset (frame 60): avg V 0.0022, identical geometry.

Excellent — deterministic match (seed jitter differs by ±0.06 but pattern is visually identical and stats match).

Remaining checks:
1. The "Seed here" button — quick test.
2. Performance check: verify the frame rate is reasonable. The frame counter is advancing ~11340 frames over ~3 seconds of real time? Wait: from81840 to 94920 in ~3-4s of sleep + tool call overhead... that would be way above 60fps. Hmm, the timing includes the browser tool round trips, which take time. Let's estimate: between screenshots there was sleep 3 plus overhead. 13,080 frames / 12 steps = 1090 steps... no wait, 94920-81840 = 13,080 frames in maybe 5-8 seconds → >60fps? That seems fast for 256²×12 steps JS. Hmm, possibly the browser runs rAF at higher rate, or the tool overhead is larger than I assume. Let's not worry — it's responsive (no lag evident).

Actually let me measure real fps: not directly possible without JS eval. The frame counter advancing rapidly means performance is good.

One thing to double-check: the initial screenshot at boot showed the seed as a *dark* disc with bright ring, whereas after reset the disc appears bright teal-filled. That's because at boot, screenshot was taken at frame ~60+ (ring already decayed interior), and the reset screenshot caught frame ~0-60 with the fresh solid V disc rendering brighter (interior still V≈1 decaying). The DOM at that instant showed frame 0, avg V 0.0133; then by frame 60, avg V 0.0022 — identical to boot's frame 60 value (0.0022). Deterministic match confirmed numerically.

Now test "Seed here" button quickly, then also verify drag painting while running works (already verified while paused; fine).

Also verify reset while paused works? Reset keeps running state — fine.

Let me test the Seed here button.

Let me click the "Seed here" button and take a screenshot.

The "Seed here" button worked — a fresh bloom is visible at upper-left area (the teal blob at ~(458,324)) and the reset pattern is regrowing (frame 25260, spreading outward from center). 

All required behaviors verified:
1. ✅ Live evolution of U/V fields (frame counter, avg V progression, organic growth from seed: radius 16 → whole canvas over ~40k steps)
2. ✅ Square grid, wrapping boundaries (pattern reached all edges; the pattern at left/right edges shows continuity)
3. ✅ Initial U=1, V=0, central seed with V↑/U↓ (frame 0 avg V 0.0133; initial scene identical to reset scene)
4. ✅ Color mapping contrasts (dark background, teal/white structures)
5. ✅ Click/drag adds V, reduces U (white stroke visible, then reacted)
6. ✅ Pause/Resume (frame frozen while paused, resumes after)
7. ✅ Reset restores initial fields and seed (frame 0, avg V 0.0133 → 0.0022 at frame 60, matching boot)
8. ✅ Performance responsive (frame counter advancing rapidly, UI responsive)

The "steps/frame" slider — let me quickly verify it works? It's a bonus feature, low risk. I could skip. Let me just do a final syntax check on the file (no console errors were reported — only the sandbox iframe warning which is from the harness, not my code).

Console had no errors. Good.

One more consideration: the console warning is about the harness's iframe sandbox, unrelated to my page.

I think everything is verified. Final answer summary.