Reaction-diffusion · deepseek-v4.1-flash

Let me build this. Gray-Scott simulation on canvas with Canvas 2D. Let me write a self-contained index.html.

Let me design:
- Grid size N x N, e.g., 128x128 or 160. Render via ImageData scaled up.
- Fields U, V as Float32Array.
- Parameters Du=0.16, Dv=0.08, feed=0.035, kill=0.062. Time step dt=1.0, spatial step dx=1.0. That's standard and stable with these diffusion rates (Laplacian 9-point or 5-point).

Actually classic parameters: Du=0.16, Dv=0.08, f=0.035, k=0.062, dt=1.0. Stable.

Laplacian 5-point: (U[i-1]+U[i+1]+U[j-1]+U[j+1]-4U)/dx^2. With dx=1. dt=1, D*dt=0.16 < 0.25 for 2D 5-point stability, ok.

Update:
u = u + (Du*lapU - u*v*v + feed*(1-u))*dt
v = v + (Dv*lapV + u*v*v - (feed+kill)*v)*dt

Wrap indices.

Seed central region: for points within radius r of center, U=0.5, V=0.25.

Color mapping: map V to color. Contrasting. e.g., background dark, V high -> bright. Use v concentration. Maybe color = something like base plus V.

Render at grid resolution into ImageData, then drawImage scaled to canvas with imageSmoothingEnabled maybe false.

Interaction: pointer to grid coords, add V and reduce U within brush radius.

Pause/Resume, Reset buttons. Also maybe speed control. Keep it responsive.

Let me write the file. Then use browser tools.

Let me build with N=160 maybe. Canvas display 600x600. Grid 160 => each cell ~3.75px. Performance: 160*160=25600 cells, fine.

Let me do multiple simulation steps per frame maybe 8 to make it evolve faster. But work per frame bounded.

Color mapping: use palette. something like:
r = clamp(U*255) ... hmm. Better map based on V. Let me make background near-black blue, V regions cyan/white.

A common mapping: 
val = V; color gradient from dark (0,0,20) -> (0,80,160) -> (0,200,220) -> (255,255,255).
Also incorporate U? Fine.

Let me just do:
t = clamp((v - 0.05)/0.35, 0, 1)
Use palette via interpolation.

Actually to get organic visible patterns use v directly with some scaling.

Let me write functions.

Buffer swapping: use Float32Array u, v, u2, v2. To avoid allocation per frame, precompute laplacian.

Implementation of step:

for y in 0..N-1:
  ym = (y-1+N)%N, yp=(y+1)%N
  for x...
    xm, xp
    idx = y*N+x
    uC=u[idx], vC=v[idx]
    lapU = u[yN*N+xm]+u[yN*N+xp]+u[ym*N+x]+u[yp*N+x]-4*uC
    ... 5-point
    uvv = uC*vC*vC
    u2[idx]=uC+(Du*lapU - uvv + feed*(1-uC))*dt
    v2[idx]=vC+(Dv*lapV + uvv - (feed+kill)*vC)*dt

Swap.

Use dx^2=1.

Let me also precompute index offsets for wrapping? modulo is okay.

For rendering: build Uint8ClampedArray imageData once. Each render, map.

Add controls with HTML buttons. Add pointer events on canvas.

Let me write it now.

I'll also include a small info overlay and maybe display step count.

Let me write the file.

I have a typo: the last `</style>` should be `</script>`. Let me fix.

Let me look at the end of file. Actually the write ended with `</style>`. Let me read the tail. Also there's a bug in the frame loop: `if (n < 1 && perFrame > 0) n = 1;` when perFrame=0 this would make n=0. Good. But when perFrame>0 and acc<n, we still run at least 1. Fine. Actually with perFrame=8, acc increments to 8, n=8. Good.

Let me just grep tail.

Good, no `</style>` at end. I misread; the write content ended with `})();\n</script>\n</body>`. Fine. Let me reload and inspect.

The central seed is visible and evolving. Let me wait a bit and screenshot to see pattern growth. Let me inspect steps and sample field values via browser? The browser tool can't run arbitrary JS directly except through actions. It has no evaluate. But `inspect` shows DOM/console. I can use the console? Not directly. Let me just visually verify.

Let me screenshot again after motion frames. Use motion action perhaps. Let me check the seed evolves. Let me click somewhere to add V.

Actually let me measure field evolution by evaluating JS - maybe I can add a temporary console.log. But simpler: I can use browser inspect . The tool doesn't provide eval. Let me rely on screenshots.

Let me wait and screenshot.

The pattern evolves from filled blob to a ring (worm-like) with slight wobble, which is characteristic Gray-Scott. Good.

Now let me test pointer seeding. Click at a separate region, e.g., (250, 250) in canvas coordinates. The canvas is at some position on screen. Canvas starts around x=300, y=85 with size 600. So a point at canvas internal (200,200) -> screen ~ (500,285). Let me click at screen (450,250) to be in upper-left of canvas. Then screenshot to see added region and its evolution.

Let me click and then motion.

The click injected a new V region (white blob upper-left) while the central pattern has grown into a branched organic form. Good. Let me now test pause: click Pause button, record step, wait, verify step unchanged. Button at approx screen (388,731). Then click resume. Then reset and compare central seed.

Let me click Pause.

Paused at step 5344, state "paused". The two seeded regions have merged into a complex organic pattern - beautiful Gray-Scott. Let me verify step doesn't advance while paused. Take another inspect/motion.

Paused holds at step 5344 across 4 frames — pause works. Now resume and check steps advance, then reset and compare central seed.

Click Resume button at (388,731). Then wait a moment, then reset. Let me do resume.

Resumed, step advanced to 5400/5368. Now click Reset at (478,731).

Reset restored to step 32 and the central seed only, matching the initial scene. Wait, initial scene at reload showed central blob at step 48. Same. Good. Reset toggled to running.

There's one subtle issue: after clicking a control button, pointerdown on canvas? No, buttons are separate. Fine.

Now let me double check stability: the concentrations clamp to [0,1] which is fine and doesn't distort.

One concern: the `acc` logic. `acc += perFrame; if (acc > perFrame) acc = perFrame;` This always sets acc to perFrame (since acc was <1 leftover). So n = perFrame, acc=0. If perFrame=0, acc=0, n=0, then `if (n < 1 && perFrame > 0)` false. Good. At speed 0 it pauses simulation but still renders. Reasonable.

Everything verified. Let me also verify drag painting works (pointerdown + pointermove). Can I do drag action? The browser tool has "drag". Let me test a drag to create a line. This is a representative check. Let me drag across lower area.

Actually the requirement is clicking or dragging adds V. I verified click. Let me test drag quickly.

Drag works — it painted a horizontal elongated V region at the bottom that evolved. All required behaviors verified:

1. Fields U/V evolve with Gray-Scott ✓
2. Square grid, wrapping boundaries ✓ (wrap function used in diffusion indexing)
3. Parameters correct ✓
4. Initial U=1,V=0 with central seed ✓
5. Contrasting colors ✓
6. Click/drag inject ✓
7. Pause/Resume ✓
8. Reset restores initial ✓
9. Canvas 2D, bounded resolution 160x160 ✓

Note: seed center and paint wrap only for pointer; diffusion uses modulo wrapping. Good.

One issue: in reset(), I call seedCenter but don't reset the img/render? render() is called. Good.

Everything works. Also note the HUD shows running while perFrame > 0. Good.

I should double-check there are no console errors besides the sandbox warning. Console only had the warning. Good.

Final. Let me give a brief report.