Particle System

Drive many small elements with simple per-particle rules to get emergent, organic motion. Use 2D canvas for hundreds, GPU Points for thousands.

When to use

• Particle/constellation backgrounds and ambient motion.
• Celebratory bursts: confetti, sparks. Weather: snow, rain. Volumetric: smoke.
• Flow-field / curl-noise swirls and data-driven point clouds.
• Connected-dot networks (lines between nearby particles).

Core loop: integrate per particle

Each particle holds state and is advanced every frame: accumulate forces into acceleration, integrate velocity and position, age it, respawn when dead. Scale by dt for frame-rate independence.

class Particle {
  constructor() { this.reset(); }
  reset() {
    this.x = Math.random() * W; this.y = Math.random() * H;
    this.vx = 0; this.vy = 0;
    this.life = 1; this.size = 1 + Math.random() * 2;
  }
  step(dt, forces) {
    let ax = 0, ay = 0;
    for (const f of forces) { const [fx, fy] = f(this); ax += fx; ay += fy; }
    this.vx += ax * dt; this.vy += ay * dt;
    this.vx *= 0.99; this.vy *= 0.99;            // drag
    this.x += this.vx * dt; this.y += this.vy * dt;
    this.life -= dt * 0.2;
    if (this.life <= 0) this.reset();
  }
}

Prefer semi-implicit Euler (update velocity first, then position with the new velocity, as above) — it is stable for the spring/drag forces particles use. Use a fixed or clamped dt (Math.min(dt, 1/30)) so a stalled tab does not explode the simulation.

Forces

A force is a function returning an acceleration [fx, fy]. Compose a list.

const gravity = () => [0, 400];                  // constant downward
const drag = (p) => [-p.vx * 0.5, -p.vy * 0.5];  // proportional resistance
function attract(tx, ty, strength) {             // pull toward a point (e.g. mouse)
  return (p) => {
    const dx = tx - p.x, dy = ty - p.y;
    const d2 = dx*dx + dy*dy + 100;              // +100 softens the singularity
    const f = strength / d2;
    return [dx * f, dy * f];
  };
}

Repulsion is attract with negative strength. Springs toward a home position give "settle back" effects.

Flow fields / curl noise (organic swirl)

Sample a noise field to derive a velocity direction per particle. Use the noise value as an angle:

// `noise2D` from a library (e.g. simplex-noise's createNoise2D), range -1..1
function flowField(noise2D, scale = 0.002, speed = 60) {
  return (p) => {
    const angle = noise2D(p.x * scale, p.y * scale) * Math.PI * 2;
    return [Math.cos(angle) * speed - p.vx, Math.sin(angle) * speed - p.vy];
  };
}

True curl noise is divergence-free (no sources/sinks → fluid-like). Compute the curl of a potential by finite differences:

function curl(noise2D, x, y, eps = 1e-2) {
  const n1 = noise2D(x, y + eps), n2 = noise2D(x, y - eps);
  const n3 = noise2D(x + eps, y), n4 = noise2D(x - eps, y);
  return [ (n1 - n2) / (2*eps), -(n3 - n4) / (2*eps) ];  // (dN/dy, -dN/dx)
}

Add time to the noise input (noise2D(x*scale, y*scale + t)) to make the field evolve.

Emission: burst vs continuous

• Burst (confetti, sparks): spawn N particles at once at a point with randomized angle/speed within a cone, then let gravity + drag take over. No respawn — remove when dead.
• Continuous (snow, smoke): spawn a steady rate; respawn dead particles at the top/source.

Randomize within a range for natural spread: angle = base + (Math.random()-0.5)*spread; speed = min + Math.random()*(max-min).

function burst(x, y, n = 120) {
  const out = [];
  for (let i = 0; i < n; i++) {
    const a = Math.random() * Math.PI * 2;
    const s = 200 + Math.random() * 400;
    out.push({ x, y, vx: Math.cos(a)*s, vy: Math.sin(a)*s - 200,  // upward bias
               life: 1, size: 4 + Math.random()*4,
               color: `hsl(${Math.random()*360},90%,60%)`,
               rot: Math.random()*6.28, vr: (Math.random()-0.5)*10 });
  }
  return out;
}

Confetti reads as confetti because of rotation + flat rectangles + gravity + air drag, not round dots. Snow reads as snow from slow fall + gentle horizontal sine sway + size-varied depth.

Connected-dot network without O(n²)

Naively checking every pair is O(n²) and dies past ~300 particles. Use a uniform spatial grid: bin particles by cell, only compare against the 8 neighboring cells.

function connect(ctx, parts, radius) {
  const cell = radius, cols = Math.ceil(W / cell);
  const grid = new Map();
  const key = (cx, cy) => cx + cy * cols;
  for (const p of parts) {
    const cx = (p.x / cell) | 0, cy = (p.y / cell) | 0;
    (grid.get(key(cx, cy)) ?? grid.set(key(cx, cy), []).get(key(cx, cy))).push(p);
  }
  for (const p of parts) {
    const cx = (p.x / cell) | 0, cy = (p.y / cell) | 0;
    for (let oy = -1; oy <= 1; oy++) for (let ox = -1; ox <= 1; ox++) {
      const bucket = grid.get(key(cx+ox, cy+oy)); if (!bucket) continue;
      for (const q of bucket) {
        if (q === p) continue;
        const dx = p.x - q.x, dy = p.y - q.y, d = Math.hypot(dx, dy);
        if (d < radius) {
          ctx.globalAlpha = 1 - d / radius;     // fade line with distance
          ctx.beginPath(); ctx.moveTo(p.x, p.y); ctx.lineTo(q.x, q.y); ctx.stroke();
        }
      }
    }
  }
  ctx.globalAlpha = 1;
}

This is O(n) for evenly distributed particles. Each pair is found twice; halve work by only checking forward neighbors if needed.

GPU particles: Three.js Points + shader

For thousands+, push all positions into a BufferGeometry and render as Points. Animate in the vertex shader for true GPU scale.

const N = 50000;
const pos = new Float32Array(N * 3);
for (let i = 0; i < N * 3; i++) pos[i] = (Math.random() - 0.5) * 20;
const geo = new THREE.BufferGeometry();
geo.setAttribute('position', new THREE.BufferAttribute(pos, 3));
const mat = new THREE.ShaderMaterial({
  uniforms: { u_time: { value: 0 }, u_size: { value: 6 } },
  transparent: true, depthWrite: false, blending: THREE.AdditiveBlending,
  vertexShader: `
    uniform float u_time, u_size;
    void main(){
      vec3 p = position;
      p.y += sin(u_time + position.x) * 0.5;          // animate on GPU
      vec4 mv = modelViewMatrix * vec4(p, 1.0);
      gl_PointSize = u_size * (10.0 / -mv.z);          // perspective size
      gl_Position = projectionMatrix * mv;
    }`,
  fragmentShader: `
    void main(){
      float d = length(gl_PointCoord - 0.5);
      if (d > 0.5) discard;                            // round, soft points
      gl_FragColor = vec4(1.0, 0.8, 0.4, smoothstep(0.5, 0.0, d));
    }`,
});
scene.add(new THREE.Points(geo, mat));
// loop: mat.uniforms.u_time.value = clock.getElapsedTime();

AdditiveBlending + depthWrite: false gives the glowing-particle look. discard on gl_PointCoord distance makes square points round. For per-particle data (life, seed), add custom attributes and read them in the shader.

Deliver & verify (standalone HTML)

Packaged helper (scripts/): scripts/seek-shot.sh anim.html 0 1.5 3 freezes the ?t=N harness and screenshots each moment; scripts/contact-sheet.sh sheet.png frame-*.png tiles them for one-glance review. See scripts/README.md.

For a self-contained particle effect (constellation background, confetti burst, flow field, GPU points) the deliverable is one HTML file that opens directly in a browser — canvas 2D inline, or Three.js from a CDN via an importmap for GPU Points, one render loop, no build step. A single file is the right tier; don't reach for a bundler when one file does the job.

Output contract:

• One .html: for canvas, the simulation + 2D draw loop in one inline <script>; for GPU points, importmap pins three to a CDN with the Points setup inline.
• Drive the sim from one accumulated time (sum of clamped dt, or clock.getElapsedTime() / u_time for GPU). No Date.now() scattered per particle.
• Seed the RNG — replace bare Math.random() with a seeded PRNG (e.g. mulberry32) so spawn positions, angles, and bursts reproduce frame-for-frame.

Seek/freeze harness — advance to a fixed time, render ONE frame for screenshots. ?t=N re-seeds, steps the sim deterministically to N seconds with a fixed timestep, renders once, and stops the loop.

<script>
  let rng = mulberry32(1234);                 // fixed seed → reproducible
  const particles = spawn(() => rng());
  function render() { /* draw particles to canvas / renderer.render(...) */ }
  const t = new URLSearchParams(location.search).get("t");
  if (t !== null) {
    const step = 1 / 60, end = parseFloat(t);
    for (let s = 0; s < end; s += step) update(step);  // fixed-step to t
    render();                                  // one frozen frame
    window.__ready = true;
  } else {
    let prev = performance.now();
    (function loop(now){ update(Math.min((now-prev)/1000, 1/30)); prev = now;
      render(); requestAnimationFrame(loop); })(prev);
  }
</script>

Verify loop — render → freeze → screenshot → check: open at three instants — start, mid, settle (?t=0, ?t=<mid>, ?t=<end>; for a burst, t≈0 spawn / t≈0.5 spread / t≈1.5 settle) — screenshot each, and check both fidelity (matches the brief) and artifacts: a blank canvas = parse/init error (check the console), particles escaping the frame (clamp/wrap missing), NaN positions (everything vanishes), all particles bunched at the origin (RNG not wired). For GPU points, WebGL needs a GPU context; Playwright/Chromium supplies one (swiftshader) headless.

npx playwright screenshot --wait-for-timeout=600 "file://$PWD/particles.html?t=1.0" frame-mid.png

Before you finish:

1. Canvas renders particles — not blank, no console/WebGL errors, no CDN 404s.
2. ?t=N freezes a reproducible frame (seeded RNG + fixed timestep → same N → same pixels).
3. Screenshotted at start / mid / settle — matches the brief, no escaped/NaN/origin-bunched particles.
4. Disposed and leak-free if embedded in an SPA (cancel the rAF loop; for GPU, dispose geometry/material/renderer).
5. prefers-reduced-motion honored — fewer particles or a static field where motion is decorative.

Quick reference

Reference files

• references/particle-recipes.md — Complete canvas confetti, snow, and smoke systems; mouse attraction/repulsion; full simplex flow-field and curl-noise field with a rendered streaming look; the spatial-grid connected-dot background end to end; and a GPU Points system with per-particle life/seed attributes, additive glow, and respawn in the shader.