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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Double Pendulum — Particles</title>
<meta name="description" content="65,536 double pendulums with slightly different initial conditions. Chaotic divergence creates swirling particle patterns.">
<meta name="author" content="Alexandru DAN">
<meta name="theme-color" content="#050505">
<link rel="canonical" href="https://particles.alexandrudan.com/double-pendulum.html">
<link rel="icon" type="image/svg+xml" href="favicon.svg">
<!-- Open Graph -->
<meta property="og:type" content="website">
<meta property="og:url" content="https://particles.alexandrudan.com/double-pendulum.html">
<meta property="og:title" content="Double Pendulum — Particles">
<meta property="og:description" content="65,536 double pendulums with slightly different initial conditions. Chaotic divergence creates swirling particle patterns.">
<meta property="og:image" content="https://particles.alexandrudan.com/og-image.svg">
<meta property="og:site_name" content="Particles">
<!-- Twitter -->
<meta name="twitter:card" content="summary_large_image">
<meta name="twitter:title" content="Double Pendulum — Particles">
<meta name="twitter:description" content="65,536 double pendulums with slightly different initial conditions. Chaotic divergence creates swirling particle patterns.">
<meta name="twitter:image" content="https://particles.alexandrudan.com/og-image.svg">
<style>
* { margin: 0; padding: 0; box-sizing: border-box; }
body { background: #000; overflow: hidden; font-family: 'Courier New', monospace; }
canvas { display: block; }
#controls {
position: fixed;
bottom: 24px;
left: 50%;
transform: translateX(-50%);
display: flex;
gap: 20px;
background: rgba(0,0,0,0.6);
backdrop-filter: blur(12px);
border: 1px solid rgba(255,255,255,0.08);
border-radius: 12px;
padding: 14px 28px;
z-index: 10;
align-items: center;
}
.ctrl-group {
display: flex; flex-direction: column; align-items: center; gap: 4px;
}
.ctrl-group label {
color: rgba(255,255,255,0.4); font-size: 9px;
text-transform: uppercase; letter-spacing: 1.5px;
}
.ctrl-group input[type="range"] {
-webkit-appearance: none; width: 100px; height: 3px;
background: rgba(255,255,255,0.15); border-radius: 2px; outline: none;
}
.ctrl-group input[type="range"]::-webkit-slider-thumb {
-webkit-appearance: none; width: 12px; height: 12px;
border-radius: 50%; background: #fff; cursor: pointer;
}
#info {
position: fixed; top: 24px; left: 28px; z-index: 10;
}
#info h1 {
color: rgba(255,255,255,0.7); font-size: 14px; font-weight: 400;
letter-spacing: 3px; text-transform: uppercase;
}
#info p {
color: rgba(255,255,255,0.25); font-size: 10px;
margin-top: 6px; letter-spacing: 1px;
}
#fps {
position: fixed; top: 24px; right: 28px;
color: rgba(255,255,255,0.2); font-size: 10px;
letter-spacing: 1px; z-index: 10;
}
#back {
position: fixed; top: 24px; left: 50%; transform: translateX(-50%);
z-index: 10;
}
#back a {
color: rgba(255,255,255,0.2); font-size: 9px; text-decoration: none;
letter-spacing: 2px; text-transform: uppercase;
transition: color 0.3s;
}
#back a:hover { color: rgba(255,255,255,0.5); }
.zoom-btn {
width: 32px; height: 32px; border-radius: 50%;
background: rgba(255,255,255,0.06); border: 1px solid rgba(255,255,255,0.12);
color: rgba(255,255,255,0.5); font-size: 18px; cursor: pointer;
display: flex; align-items: center; justify-content: center;
transition: background 0.2s;
font-family: monospace;
}
.zoom-btn:hover { background: rgba(255,255,255,0.12); }
</style>
</head>
<body>
<div id="info">
<h1>Double Pendulum</h1>
<p id="particle-count"></p>
</div>
<div id="fps"></div>
<div id="back"><a href="index.html">Gallery</a></div>
<div id="controls">
<div class="ctrl-group">
<input type="range" id="speed" min="0.1" max="5" step="0.1" value="1">
<label>Speed</label>
</div>
<div class="ctrl-group">
<input type="range" id="bloom" min="0" max="3" step="0.1" value="0.4">
<label>Bloom</label>
</div>
<div class="ctrl-group">
<input type="range" id="size" min="0.5" max="4" step="0.1" value="1.0">
<label>Size</label>
</div>
<div class="ctrl-group">
<input type="range" id="hueShift" min="0" max="1" step="0.01" value="0">
<label>Hue</label>
</div>
<button class="zoom-btn" id="zoomOut">−</button>
<button class="zoom-btn" id="zoomIn">+</button>
</div>
<script type="importmap">
{
"imports": {
"three": "https://cdn.jsdelivr.net/npm/three@0.160.0/build/three.module.js",
"three/addons/": "https://cdn.jsdelivr.net/npm/three@0.160.0/examples/jsm/"
}
}
</script>
<script type="module">
import * as THREE from 'three';
import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
import { EffectComposer } from 'three/addons/postprocessing/EffectComposer.js';
import { RenderPass } from 'three/addons/postprocessing/RenderPass.js';
import { UnrealBloomPass } from 'three/addons/postprocessing/UnrealBloomPass.js';
import { GPUComputationRenderer } from 'three/addons/misc/GPUComputationRenderer.js';
const WIDTH = 256;
const PARTICLE_COUNT = WIDTH * WIDTH;
// Scene
const scene = new THREE.Scene();
const camera = new THREE.PerspectiveCamera(60, innerWidth / innerHeight, 0.1, 2000);
camera.position.set(0, 0, 22);
const renderer = new THREE.WebGLRenderer({ antialias: false, powerPreference: 'high-performance' });
renderer.setSize(innerWidth, innerHeight);
renderer.setPixelRatio(1);
document.body.appendChild(renderer.domElement);
const orbitControls = new OrbitControls(camera, renderer.domElement);
orbitControls.enableDamping = true;
orbitControls.dampingFactor = 0.05;
orbitControls.autoRotate = true;
orbitControls.autoRotateSpeed = 0.5;
// Post-processing
const composer = new EffectComposer(renderer);
composer.addPass(new RenderPass(scene, camera));
const bloomPass = new UnrealBloomPass(
new THREE.Vector2(innerWidth / 2, innerHeight / 2),
0.4, 0.3, 0.85
);
composer.addPass(bloomPass);
// GPU Computation
const gpuCompute = new GPUComputationRenderer(WIDTH, WIDTH, renderer);
const posTex0 = gpuCompute.createTexture();
function seedTexture(tex) {
const data = tex.image.data;
for (let i = 0; i < PARTICLE_COUNT; i++) {
const idx = i * 4;
// theta1 near PI (upright), theta2 near PI, slight variation
data[idx] = Math.PI + (Math.random() - 0.5) * 0.01; // theta1
data[idx + 1] = Math.PI + (Math.random() - 0.5) * 0.01; // theta2
data[idx + 2] = (Math.random() - 0.5) * 0.001; // omega1
data[idx + 3] = (Math.random() - 0.5) * 0.001; // omega2
}
}
seedTexture(posTex0);
const positionShader = `
uniform float uDt;
uniform float uSpeed;
uniform float uFrame;
float hash(vec2 p) {
vec3 p3 = fract(vec3(p.xyx) * 0.1031);
p3 += dot(p3, p3.yzx + 33.33);
return fract((p3.x + p3.y) * p3.z);
}
void main() {
vec2 uv = gl_FragCoord.xy / resolution.xy;
vec4 state = texture2D(texturePosition, uv);
// State: x=theta1, y=theta2, z=omega1, w=omega2
float t1 = state.x;
float t2 = state.y;
float w1 = state.z;
float w2 = state.w;
float g = 9.81;
float L1 = 3.0, L2 = 3.0;
float m1 = 1.0, m2 = 1.0;
float dt = uDt * uSpeed;
// Double pendulum equations of motion
float delta = t1 - t2;
float den = 2.0 * m1 + m2 - m2 * cos(2.0 * delta);
float alpha1 = (-g * (2.0*m1 + m2) * sin(t1) - m2*g*sin(t1 - 2.0*t2)
- 2.0*sin(delta)*m2*(w2*w2*L2 + w1*w1*L1*cos(delta))) / (L1 * den);
float alpha2 = (2.0*sin(delta)*(w1*w1*L1*(m1+m2) + g*(m1+m2)*cos(t1)
+ w2*w2*L2*m2*cos(delta))) / (L2 * den);
// Simple Euler integration (adequate for visual chaos)
w1 += alpha1 * dt;
w2 += alpha2 * dt;
t1 += w1 * dt;
t2 += w2 * dt;
// Light damping to prevent energy blow-up
w1 *= 0.9999;
w2 *= 0.9999;
// Output state (NOT position — vertex shader will compute position)
gl_FragColor = vec4(t1, t2, w1, w2);
}
`;
const posVar = gpuCompute.addVariable('texturePosition', positionShader, posTex0);
gpuCompute.setVariableDependencies(posVar, [posVar]);
posVar.material.uniforms.uDt = { value: 0.015 };
posVar.material.uniforms.uSpeed = { value: 1.0 };
posVar.material.uniforms.uFrame = { value: 0.0 };
posVar.wrapS = THREE.RepeatWrapping;
posVar.wrapT = THREE.RepeatWrapping;
const err = gpuCompute.init();
if (err !== null) console.error('GPU Computation init error:', err);
// Particle Rendering
const vertexShader = `
uniform sampler2D uPositionTexture;
uniform float uHueShift;
uniform float uPointSize;
uniform float uScale;
attribute vec2 aTexCoord;
varying vec3 vColor;
vec3 hsl2rgb(float h, float s, float l) {
float c = (1.0 - abs(2.0 * l - 1.0)) * s;
float h6 = h * 6.0;
float x = c * (1.0 - abs(mod(h6, 2.0) - 1.0));
float m = l - c * 0.5;
vec3 rgb;
if (h6 < 1.0) rgb = vec3(c, x, 0.0);
else if (h6 < 2.0) rgb = vec3(x, c, 0.0);
else if (h6 < 3.0) rgb = vec3(0.0, c, x);
else if (h6 < 4.0) rgb = vec3(0.0, x, c);
else if (h6 < 5.0) rgb = vec3(x, 0.0, c);
else rgb = vec3(c, 0.0, x);
return rgb + m;
}
void main() {
vec4 posData = texture2D(uPositionTexture, aTexCoord);
float t1 = posData.x;
float t2 = posData.y;
float speed = length(posData.zw); // angular velocities
float L1 = 3.0, L2 = 3.0;
// Tip of second pendulum
float x = L1 * sin(t1) + L2 * sin(t2);
float y = -L1 * cos(t1) - L2 * cos(t2);
float z = sin(aTexCoord.x * 6.28318 + aTexCoord.y * 3.0) * 0.5;
vec3 pos = vec3(x, y, z) * uScale;
// Color: angular velocity magnitude -> hue (slow=cool, fast=warm), speed -> lightness
float hue = fract(speed * 0.05 + uHueShift);
float saturation = 0.85;
float lightness = 0.12 + min(speed * 0.02, 0.25);
vColor = hsl2rgb(hue, saturation, lightness);
vec4 mvPosition = modelViewMatrix * vec4(pos, 1.0);
gl_PointSize = uPointSize * (55.0 / -mvPosition.z);
gl_PointSize = max(gl_PointSize, 0.3);
gl_Position = projectionMatrix * mvPosition;
}
`;
const fragmentShader = `
varying vec3 vColor;
void main() {
float d = length(gl_PointCoord - 0.5) * 2.0;
if (d > 1.0) discard;
// Soft gaussian falloff with bright core
float glow = exp(-d * d * 3.0);
float core = exp(-d * d * 12.0);
float alpha = (glow * 0.15 + core * 0.3);
// Slight color boost at core (hotter center)
vec3 col = vColor + core * 0.15;
gl_FragColor = vec4(col, alpha);
}
`;
const geometry = new THREE.BufferGeometry();
const texCoords = new Float32Array(PARTICLE_COUNT * 2);
for (let j = 0; j < WIDTH; j++) {
for (let i = 0; i < WIDTH; i++) {
const idx = (j * WIDTH + i) * 2;
texCoords[idx] = (i + 0.5) / WIDTH;
texCoords[idx + 1] = (j + 0.5) / WIDTH;
}
}
const dummyPositions = new Float32Array(PARTICLE_COUNT * 3);
geometry.setAttribute('position', new THREE.BufferAttribute(dummyPositions, 3));
geometry.setAttribute('aTexCoord', new THREE.BufferAttribute(texCoords, 2));
const material = new THREE.ShaderMaterial({
vertexShader,
fragmentShader,
uniforms: {
uPositionTexture: { value: null },
uHueShift: { value: 0.0 },
uPointSize: { value: 1.5 },
uScale: { value: 1.2 },
},
transparent: true,
blending: THREE.AdditiveBlending,
depthWrite: false,
});
const points = new THREE.Points(geometry, material);
const pivot = new THREE.Group(); pivot.add(points); scene.add(pivot);
// UI
document.getElementById('particle-count').textContent =
`${PARTICLE_COUNT.toLocaleString()} particles — fully GPU computed`;
const speedSlider = document.getElementById('speed');
const bloomSlider = document.getElementById('bloom');
const sizeSlider = document.getElementById('size');
const hueSlider = document.getElementById('hueShift');
const fpsEl = document.getElementById('fps');
document.getElementById('zoomIn').addEventListener('click', () => {
material.uniforms.uScale.value *= 1.15;
});
document.getElementById('zoomOut').addEventListener('click', () => {
material.uniforms.uScale.value *= 0.85;
});
// Animation Loop
let lastTime = performance.now();
let frameCount = 0;
function animate(now) {
requestAnimationFrame(animate);
frameCount++;
if (now - lastTime >= 1000) {
fpsEl.textContent = `${frameCount} FPS`;
frameCount = 0;
lastTime = now;
}
posVar.material.uniforms.uSpeed.value = parseFloat(speedSlider.value);
posVar.material.uniforms.uFrame.value += 1.0;
bloomPass.strength = parseFloat(bloomSlider.value);
material.uniforms.uHueShift.value = parseFloat(hueSlider.value);
material.uniforms.uPointSize.value = parseFloat(sizeSlider.value);
gpuCompute.compute();
material.uniforms.uPositionTexture.value =
gpuCompute.getCurrentRenderTarget(posVar).texture;
pivot.rotation.x += 0.0008;
orbitControls.update();
composer.render();
}
animate(performance.now());
// Resize
window.addEventListener('resize', () => {
camera.aspect = innerWidth / innerHeight;
camera.updateProjectionMatrix();
renderer.setSize(innerWidth, innerHeight);
composer.setSize(innerWidth, innerHeight);
});
</script>
<script src="shared-ui.js"></script>
</body>
</html>