Fluid simulation · grok-build-0.1

Create a real-time fluid simulation on a full-screen canvas where dragging the mouse pushes swirling colored dye through the fluid.

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user

Create a real-time fluid simulation on a full-screen canvas where dragging the mouse pushes swirling colored dye through the fluid.

assistant

thinking

The task is: "Create a real-time fluid simulation on a full-screen canvas where dragging the mouse pushes swirling colored dye through the fluid." And "Build a single-page web app and write it ALL int...First, the task is to create a single self-contained index.html file that runs a real-time fluid simulation on a full-screen canvas. Dragging the mouse pushes swirling colored dye through the fluid. No external resources, fully sandboxed.

I need to implement this in pure JS, with CSS and JS inline.

Key elements 1. Full-screen canvas: Use <canvas> with width/height = window.innerWidth/Height, handle resize.

2. Fluid sim: Use a grid-based approach like Jos Stam's method, but simplified for JS performance.

- Use a 2D grid for density (color) and velocity (u,v).

 - For color, use a density array per channel or one with RGBA.

- Mouse interaction: On drag, add force to velocity field in a circle or line, with swirl (tangential force).

- Simulation steps: Add forces, diffuse, advect, project.

For simplicity and performance in browser JS, use a 128x128 grid, update in RAF loop.

I recall a standard implementation has about 200-300 lines.

Let's outline code:

- HTML: <!DOCTYPE html><html><head><style>/*CSS*/</style></head><body><canvas id="c"></canvas><script>/*JS*/</script </body></html>

- CSS: html,body{margin:0;padding:0;overflow:hidden;height:100%} canvas{display:block;width:100%;height:100%}

- JS: Get canvas, ctx.

- Variables: let N = 128; // grid size

- density = new Array(N*N). fill(0) but use 2D or 1D.

Use 1D arrays for speed: size = (N+2)*(N+2)

Implement functions: add_source, diffuse, advect, project, set_bnd.

For swirl: when adding force, add perpendicular direction for rotation.

For color: use density for gray, but to color, use separate red,green,blue density fields, or one field with color.

Simple: use one density for amount, but color based on position or time.

For colored: use HSV, add hue based on mouse or fixed.

Let's make dye color change: when mouse drags, inject dye with varying hue.

But for simplicity, use random color or cycle.

Better: use a color field, but to keep simple, particles for color.

I decide on grid for vel and density (gray), but to color, use multiple densities or particles.

To make it colored, I'll use particles for the dye, and grid for velocity only.

This is efficient.

Code sketch:

const canvas = document.getElementById('c');

const ctx = canvas.getContext('2d');

let width, height;

function resize() {

  width = canvas.width = window.innerWidth;

  height = canvas.height = window innerHeight;

}

resize();

window.addEventListener('resize', resize);

let mouseX = 0, mouseY = 0, prevMouseX = 0, prevMouseY = 0, dragging = false;

canvas.addEventListener('mousedown', e => {

  dragging = true;

  mouseX = e.clientX;

  mouseY = e.clientY;

  prevMouseX = mouseX;

  prevMouseY = mouseY;

});

canvas.addEventListener('mousemove', e => {

  mouseX = e.clientX;

  mouseY = e.clientY;

  if (dragging) {

    // add force

  }

});

canvas.addEventListener('mouseup', () => dragging = false);

 // touch support optional: add touch events similar.

const NX = 60; // small grid for perf

const NY = NX; // square

const particles = [];

const MAX_PARTICLES = 10000;

const forceStrength = 0.2;

const viscosity = 0.1;

const dt = 0.016; // approx 60fps

let u = new Float32Array(NX * NY);

let v = new Float32Array(NX * NY);

let u_prev = new Float32Array(NX * NY);

let v_prev = new Float32Array(NX * NY);

function idx(i,j) { return j * NX + i; }

function getVelAt(x, y) { // x,y in pixels

  let gx = Math.max(0, Math.min(NX-1, x / width * NX));

  let gy = Math.max(0, Math.min(NY-1, y / height * NY));

  let x0 = Math.floor(gx), y0 = Math.floor(gy);

  let x1 = Math.min(NX-1, x0+1);

  let y1 = Math.min(NY-1, y0+1);

  let s = gx - x0, t = gy - y0;

  let u00 = u[idx(x0,y0)], u01 = u[idx(x0,y1)], u10 = u[idx(x1,y0)], u11 = u[idx(x1,y1)];

  let u_val = (1-s)*(1-t)*u00 + s*(1-t)*u10 + (1-s)*t*u01 + s*t*u11;

  // similar for v

  // ... implement bilinear for v too

  return {u: u , v: v};

}

 // implement diffuse, advect for u,v

function diffuse() {

  // copy u to u_prev

  u_prev.set(u);

  // for 5-10 iters

  for(let k=0; k<5; k++) {

    for(let j=1 ;j<NY-1;j++) for(let i=1;i<NX-1;i++) {

      let idx = idx(i,j);

      u[idx] = (u_prev[idx-1] + u_prev[idx+1] + u_prev[idx-NX] + u_prev[idx+NX] + u *4 ) / 5 ; wait adjust

      // better use average

      u[idx] = 0.25 * (u_prev[idx-1] + u_prev[idx+1] + u_prev[idx-NX] + u_prev[idx+NX]);

      // this is pure average, for diffusion need 0.2 * lap + self

      // let's use:

      u[idx] = u_prev[idx] * 0.8 + 0.2 * 0.25 * (sum neigh);

    }

  }

}

 // similar for v

function advect() {

  u_prev.set(u);

  // for each cell

  for(let j=0;j<NY;j++) for(let i=0;i<NX;i++) {

    let idx = idx(i,j);

    let x = i / NX * width;

    let y = j / NY * height;

    let vx = u_prev[idx]; wait no, use current u,v for back

    let bx = x - u[idx] * dt * width / NX ; wait scale

    // careful with units: u is velocity in grid units per frame

    // better normalize velocity to world speed.

    // assume u is in pixels per frame

    // then gx = i , but scale.

    // To simplify, let's set velocity scale accordingly.

  }

}

 // then in loop:

function update() {

  // if dragging

  if(dragging) {

    let dx = mouseX - prevMouseX;

    let dy = mouseY - prevMouseY;

 prevMouseX = mouseX;

  prevMouseY = mouseY;

    // add force to grid around mouse

    let mx = mouseX / width * NX;

    let my = mouseY / height * NY;

    let radius = 5;

    for(let dy=-radius; dy<radius; dy++) for(dx=-radius;dx<radius;dx++) {

      let dist2 = dx*dx + dy*dy;

      if(dist2 > radius*radius) continue;

      let weight = 1 - dist2 / (radius*radius);

      let i = Math.floor(mx + dx);

      let j = Math.floor(my + dy);

      if(i<0 || i>=NX || j<0 || j>=NY) continue;

      let id = idx(i,j);

      // add force tangential for swirl: perpendicular to drag

      let force = (dx * -dy + dy * dx wait

 // force direction: mouse drag direction for push, perpendicular for swirl

  let forceX = dx * forceStrength * weight;

  let forceY = dy * forceStrength * weight;

  // for swirl, add perpendicular: forceX += -dy * forceStrength *0.5 , forceY += dx * 0.5 * forceStrength

  u[id] += forceX * weight;

  v[id] += forceY * weight;

  // swirl: u[id] += -forceY * 0.5;

  v[id] += forceX * 0.5;

  }

  // spawn particles

 for(let k=0;k<20;k++) {

    if(particles.length > MAX_PARTICLES) particles.shift();

    let p = {

      x: mouseX + (Math.random()-0.5)*10,

      y: mouseY + (Math.random()-0.5)*10,

      vx: 0,

      vy: 0,

      hue: (Date.now() % 360) + Math.random()*60

    };

    particles.

→ bash {"command":"ls -la /tmp/ws"}

toolResult

total 0 drwxr-sr-x. 2 node node 6 Aug 1 19:59 . drwxrwsrwx. 3 root node 16 Aug 1 19:59 ..

assistant

thinking

The task is: "Build a single-page web app and write it ALL into one self-contained file named index.html in the current directory: CSS in a <style> tag, JS in a <script> tag, inline — do not create se...The task is to build a single-page web app in one index.html file with CSS in <style>, JS in <script>, no externals. It should be a real-time fluid simulation on full-screen canvas where mouse drag pushes swirling colored dye.

I need to implement this in pure JS using Canvas.

I recall Jos Stam's paper "Real-Time Fluid Dynamics for Games" which has a method using MAC grid, projection, etc., implementable in JS.

For a minimal version, there's a popular gist or code for 2D fluid sim in JS.

I need to write it myself.

Let's plan the code.

- Canvas full screen 100vw x 100vh.

- Use requestAnimationFrame for loop.

- Grid: let’s use N=64 for speed, but 128 better.

For JS perf, N=100 maybe.

Use 2D arrays or 1D flattened.

Use Float32Array.

Fields: velocity_x, velocity_y (N+2)^2

density (for amount), but for color: let's use one density field, and when adding, add to a color array or use HSV.

Simple: simulate density (grayscale), and add color by injecting RGB at mouse, but advect all.

To make it colored swirling: inject 3 densities r,g,b separately, but cost *3.

Since JS is fast enough for N=128, 3* (130^2 ~17000) * few arrays ~ ok.

Let's do: have dens_r, dens_g, dens_b as separate density fields, advect and diffuse each.

But to save, perhaps one density for total, and one for hue or something, but hue not advected linearly.

Best: use particles for the dye colors, and fluid grid for velocity only (with density for opacity? but particles handle).

I think particles + velocity field is good for "colored dye".

Let's go with that -- fluid velocity grid with simple diffusion and projection, particles for dye.

Code structure:

- HTML: doctype, html, head with title, style: body{margin:0; overflow:hidden; background:black;} canvas{display:block;} 

- script:

- const canvas = document.getElementById('c');

- canvas = document.body.appendChild or just use it.

- function resize() { canvas.width = innerWidth; canvas.height = innerHeight; W=width, H=height; }

- addEventListener resize, and init.

- Then mouse: let mouseX, mouseY, dragging=false;

- canvas.addEventListener 'mousedown' start drag, 'mousemove' if drag update, 'mouseup' end.

- Also touch for mobile: touchstart etc.

- Then params: const N = 128; // grid res

- const SCALE = Math.min(W,H)/N; // cell size

- function getGridPos(x,y screen) { return {i: Math.floor(x / SCALE), j: floor(y/scale)} }

- Then arrays:

let u = new Float32Array((N+2)*(N+2));

let v = new Float32Array((N+2)*(N+2));

let u_prev = new Float32 32Array same size;

let v_prev = same;

let p = new Float32Array((N+2)*(N+2)); // pressure

let div = new Float32Array((N+2)*(N+2)); // divergence

let visc = 0.1; // viscosity

let dt =  0.016; // fixed time step ~60fps

- Then function IX(i,j) { return i + (N+2)*j; }

- function set_bnd(b, arr) {

  for(let j=1; j<=N; j++) {

    arr[IX(0,j)] = b ? -arr[IX(1,j)] : arr[IX(1,j)]; // for vel x=0 left wall

    arr[IX(N+1,j)] = b ? -arr[IX(N,j)] : arr[IX(N,j)];

  }

  for(let i=1; i <=N; i++) {

    arr[IX(i,0)] = b ? -arr[IX(i,1)] : arr[IX(i,1)]; // y=0

    arr[IX(i,N+1)] = b ? -arr[IX(i,N)] : arr[IX(i,N)];

 }

  arr[IX(0,0)] = 0.5*(arr[IX(1,0)]+arr[IX(0,1)]);

  // similar for other corners

  arr[IX(0,N+1)] = 0.5*(arr[IX(1,N+ 1)] + arr[IX(0,N)]);

  arr[IX(N+1,0)] = 0.5*(arr[IX(N,0)] + arr[IX(N+1,1)]);

  arr[IX(N+1,N+1)] = 0.5*(arr[ IX(N,N+1)] + arr[IX(N+1,N)]);

}

- Then diffuse function:

function diffuse(b, x, x0, diff, dt) {

  let a = dt * diff * N*N;

  for(let k=0; k<20; k++) { // num it 20

    for(let j=1; j<=N; j++) for(let i=1; i<=N; i++) {

      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)])) / (1 + 4*a);

    }

    set_bnd(b, x);

  }

}

- advect function:

function advect(b, d, d0, u, v, dt) {

 let dt0 = dt * N;

  for(let j=1; j<=N; j++) for(let i=1; i<=N; i++) {

    let x = i - dt0 * u[IX(i,j)];

    let y = j - dt0 * v[IX(i,j)];

 x = Math.max(0.5, Math.min(N+0.5, x));

  y = Math.max(0.5, Math.min(N+0.5, y));

  let i0 = Math.floor(x), i1 = i0+1;

  let j0 = Math.floor(y ), j1 = j0+1;

  let s1 = x - i0, s0 = 1-s1;

  let 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)]);

  }

  set_bnd(b, d);

}

- project:

function project(u, v, p, div) {

  let h = 1.0 / N;

  for(let j=1; j<=N; j++) for(let i=1; i<=N; i++) {

    div[IX(i,j)] = -0.5 * h * (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;

  }

  set_bnd(0, div);

  set_bnd(0, p);

  for 20 iters:

    for i j p[IX(i,j)] = (div[IX(i,j)] + p[IX(i-1,j)] +p[IX(i+1,j)] +p[IX(i,j-1)] +p[IX(i,j+1)])/4 ;

    set_b 0 p

  then for i j :

    u[IX(i,j)] -= 0.5 * (p[IX(i+1,j)] - p[IX(i-1,j)]) / h;

    v[IX(i,j)] -= 0.5 * (p[IX(i,j+1 )] - p[IX(i,j-1)]) / h;

  set_bnd(1,u);

  set_bnd(2,v);

}

- Then vel_step function:

function vel_step(u, v, u0, v0, dt) {

  addSource(u, u0, dt);

  addSource(v, v0, dt);

  diffuse(1, u0, u, visc, dt);

  diffuse(2, v0, v, visc, dt);

  project(u0, v0, u, v);

  advect(1, u, u0, u0, v 0, dt);

  advect(2, v, v0, u0, v0, dt);

  project(u, v, u0, v0);

}

- addSource(x, s, dt) { for all i x[i] += dt * s[i]; }

- Then in main loop 60fps or rAF:

  // get mouse

  // if dragging:

  let dx = mouseX - prevX;

  let dy = mouseY - prevY;

  prevX = mouseX; prevY = mouseY;

  addForce(mouseX, mouseY, dx, dy);

  // 0 the u0 v0

  u0.fill(0);

  v0.fill(0);

  // then vel_step(u,v,u0,v0,dt);

  // then update particles

  // draw

  function addForce(x,y,dx,dy) {

    let i = Math.floor(x * N / W ) +1;

    let j = Math.floor(y * N / H ) +1;

    if(i<1 || i>N || j<1 || j>N) return;

    let rad = 1.5;

    for(let ii = i-rad; ii<=i+rad; ii++) for(jj =j-rad; jj<=j+rad; jj++) if valid {

      let dist = Math.hypot(ii-i, jj-j);

      let weight = 1 - dist/rad;

      u0[IX(ii,jj)] += dx * weight * 200; // multiplier tune 100-500

      v0[IX(ii,jj)] += dy * weight * 200;

    }

  }

  // then for particles:

  // have particles array [{x,y,hue,alpha}]

  // in loop:

  for each particle:

    let gx = p.x * N / W +0.5; gy = p.y * N / H +0.5;

    let vx = u[IX(Math.floor(gx),Math.floor(gy))];

    let vy = v[IX(..., )];

    p.x += vx * dt * (W/N) * 1.5 // scale

    p.y += vy * dt * (H/N) * 1.5

    p.x += (Math.random()-0.5)*0.5; // jitter

    p.y += (Math.random()-0.5)*0.5;

    p.alpha -= 0.01 // tune

    if out or alpha<0 remove

  // draw:

  ctx.fillStyle = 'rgba(0,0,0,0.1)'; // fade

  ctx.fillRect(0,0,W,H);

  for p:

    ctx.fillStyle = `hsl(${p.hue}, 80%, 60%)`; // fixed hue or shift

    ctx.beginPath();

    ctx.arc(p.x, p.y, 2,0,Math.PI*2);

    ctx.fill();

  // hue shift: let hue += 0.5; hue %=360; when spawn use current hue

  let hue = 0; global, increment when spawn

  // also for instructions: ctx.fillText('Drag to add dye', 10,20); but use div overlay.

  // use <div id="info" style="position:fixed; top:10px; left:10px; color:white; opacity:0.7; font-size:14px;">Drag mouse to push swirling dye</div>

  // and for clear: key 'c' : particles = []; u.fill(0); etc.

  // to make swirl, visc low 0.05, dt 0.

→ write /tmp/ws/index.html (10568 bytes)

toolResult

Successfully wrote 10568 bytes to /tmp/ws/index.html

assistant

thinking

The file has been created. I should verify that it exists and is complete.

→ bash

{"command":"ls -la /tmp/ws/index.html && head -c 300 /tmp/ws/index.html && echo \"...\" && tail -c 200 /tmp/ws/index.html"}

toolResult

-rw-r--r--. 1 node node 10572 Aug 1 20:03 /tmp/ws/index.html <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title>Fluid Dye</title> <style> * { margin: 0; padding: 0; box-sizing: border-box; } html, body { width: 100%; height: 100%; overflow: hidden; backgr... (Math.random() * 360), alpha: 0.18 + Math.random() * 0.32 }); } } }); // Start animate(); } init(); </script> </body> </html>

assistant

thinking

The file is written and present. It's a complete, self-contained single HTML file with a real-time fluid simulation using a stable fluid solver (Navier-Stokes inspired) on a grid, with dye particles a...

→ bash

{"command":"cd /tmp/ws && node -e \"\nconst fs = require('fs');\nconst html = fs.readFileSync('index.html', 'utf8');\n// Basic syntax check

toolResult

JS syntax: OK File size: 10568 bytes

assistant

thinking

The file is complete and self-contained. No external resources. Full-screen canvas. Real-time fluid simulation using a stable fluid solver (Jos Stam style) with dye particles that follow the velocity ...

Created `/tmp/ws/index.html` — a fully self-contained, sandboxed real-time fluid simulation. **Features:** - Stable Navier–Stokes grid solver (diffusion + advection + projection) running in real time - Mouse/touch drag adds localized forces that swirl the fluid - Colored dye particles are injected on drag and advected by the velocity field with natural dissipation - Soft glowing trails and continuously shifting hues - Gentle initial vorticity for immediate visual interest - **C** clears everything, **R** reseeds dye - Runs completely offline, no external assets or network calls Open `index.html` in any browser to interact.

TAKE IT TO CODE

A single self-contained HTML file — copy it and open in any browser, or reuse the prompt with your own pi-agent run.

RUN

modelgrok-build-0.1

vendorxAI · Grok

harnesspi-agent

generated2026-08-01

EVALUATION

★★★★★ 2/5 partial

Initial burst of colored streaks fades to black quickly; only drag produces a faint blob, other inputs do nothing.

Vision grade · anthropic/claude-sonnet-5

MEASUREMENTS

Raw readings from the capture, not a verdict — the grade above is the only judgement. Percentages are how much of the screen changed; the measure under-reports sparse motion on a dark background.

idle motion6.3%

on click0.0%

on drag0.3%

on wheel0.2%

on enter + space0.0%

on arrow keys0.0%

on w/a/s/d0.0%

frame spread8.5 / 255

console errors0

js errors none

METRICS

runtime227.4s

tokens in4.2k

tokens out29k

cached16k

cost / run$0.0657