Custom Code Experiment •
Klein Bottle
Source Code View HTML / CSS / JavaScript
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Klein Bottle</title>
<style>
* {
margin: 0;
padding: 0;
box-sizing: border-box;
}
body {
background: linear-gradient(135deg, #1a0033, #000011, #330011);
overflow: hidden;
font-family: 'Courier New', monospace;
touch-action: manipulation;
}
#canvas {
display: block;
background: transparent;
cursor: crosshair;
image-rendering: pixelated;
}
#canvas:active {
cursor: grabbing;
}
.control-panel {
position: fixed;
top: 10px;
right: 10px;
background: rgba(0, 0, 0, 0.95);
border: 2px solid #ffffff;
box-shadow: 0 0 10px rgba(255, 255, 255, 0.3);
padding: 12px;
color: #ffffff;
font-size: 11px;
width: 250px;
z-index: 1000;
text-transform: uppercase;
letter-spacing: 1px;
transition: transform 0.3s ease, opacity 0.3s ease;
border-radius: 8px;
}
.menu-toggle {
position: fixed;
top: 10px;
right: 10px;
width: 50px;
height: 50px;
background: rgba(0, 0, 0, 0.95);
border: 2px solid #ffffff;
color: #ffffff;
font-size: 24px;
cursor: pointer;
z-index: 1001;
border-radius: 8px;
display: none;
justify-content: center;
align-items: center;
box-shadow: 0 0 10px rgba(255, 255, 255, 0.3);
}
.menu-toggle:hover {
background: rgba(255, 255, 255, 0.1);
}
.menu-toggle:active {
background: #ffffff;
color: #000000;
}
.control-group {
margin-bottom: 10px;
}
.control-group:last-child {
margin-bottom: 0;
}
label {
display: block;
margin-bottom: 4px;
font-weight: bold;
color: #ffffff;
text-shadow: 1px 1px 1px rgba(0, 0, 0, 0.8);
}
label::before {
content: "▶";
margin-right: 6px;
color: #ffffff;
}
input[type="range"] {
width: 100%;
height: 8px;
background: linear-gradient(90deg, #666666, #999999, #cccccc, #ffffff);
outline: none;
-webkit-appearance: none;
appearance: none;
border: 1px solid #ffffff;
border-radius: 4px;
}
input[type="range"]::-webkit-slider-thumb {
appearance: none;
width: 16px;
height: 16px;
background: #ffffff;
cursor: pointer;
border: 2px solid #000000;
border-radius: 50%;
}
input[type="range"]::-moz-range-thumb {
width: 16px;
height: 16px;
background: #ffffff;
cursor: pointer;
border: 2px solid #000000;
border-radius: 50%;
}
.button-group {
display: flex;
gap: 6px;
flex-wrap: wrap;
}
button {
flex: 1;
min-width: 50px;
padding: 6px 8px;
border: 2px solid #ffffff;
background: rgba(0, 0, 0, 0.8);
color: #ffffff;
font-weight: bold;
cursor: pointer;
transition: all 0.2s ease;
font-size: 9px;
text-transform: uppercase;
font-family: 'Courier New', monospace;
border-radius: 4px;
}
button:hover {
background: rgba(255, 255, 255, 0.2);
box-shadow: 0 0 8px rgba(255, 255, 255, 0.5);
}
button:active {
background: #ffffff;
color: #000000;
}
.value-display {
font-size: 9px;
color: #ffffff;
text-align: right;
margin-top: 2px;
font-family: 'Courier New', monospace;
text-shadow: 1px 1px 1px rgba(0, 0, 0, 0.8);
}
.value-display::before {
content: "[";
color: #ffffff;
margin-right: 2px;
}
.value-display::after {
content: "]";
color: #ffffff;
margin-left: 2px;
}
@media (min-width: 769px) {
.control-panel {
display: block !important;
opacity: 1 !important;
visibility: visible !important;
transform: none !important;
pointer-events: all !important;
}
.menu-toggle {
display: none !important;
}
}
@media (max-width: 768px) {
.menu-toggle {
display: flex !important;
}
.control-panel {
top: 70px;
right: 10px;
left: 10px;
width: auto;
max-width: none;
padding: 15px;
font-size: 10px;
background: rgba(0, 0, 0, 0.98);
border: 2px solid #ffffff;
transform: translateY(-20px);
opacity: 0;
visibility: hidden;
pointer-events: none;
transition: all 0.3s ease;
border-radius: 8px;
max-height: calc(100vh - 90px);
overflow-y: auto;
}
.control-panel.mobile-visible {
transform: translateY(0);
opacity: 1;
visibility: visible;
pointer-events: all;
}
button {
font-size: 10px;
padding: 8px 10px;
min-height: 36px;
}
input[type="range"] {
height: 10px;
}
input[type="range"]::-webkit-slider-thumb {
width: 20px;
height: 20px;
}
input[type="range"]::-moz-range-thumb {
width: 20px;
height: 20px;
}
.value-display {
font-size: 10px;
}
#canvas {
touch-action: pan-x pan-y;
}
}
@media (max-width: 480px) {
.control-panel {
padding: 12px;
top: 65px;
}
.menu-toggle {
width: 45px;
height: 45px;
font-size: 20px;
}
button {
font-size: 9px;
padding: 6px 8px;
min-height: 32px;
}
.button-group {
flex-direction: column;
}
.button-group button {
width: 100%;
}
}
</style>
</head>
<body>
<canvas id="canvas"></canvas>
<div class="menu-toggle" id="menuToggle">☰</div>
<div class="control-panel" id="controlPanel">
<div class="control-group">
<label>Rotation Speed</label>
<input type="range" id="rotationSpeed" min="0.1" max="3" value="1" step="0.1">
<div class="value-display" id="rotationValue">1.0</div>
</div>
<div class="control-group">
<label>Sphere Detail</label>
<input type="range" id="sphereDetail" min="4" max="12" value="6" step="1">
<div class="value-display" id="sphereValue">6</div>
</div>
<div class="control-group">
<label>Trail Length</label>
<input type="range" id="trailLength" min="0.5" max="0.9" value="0.7" step="0.05">
<div class="value-display" id="trailValue">0.70</div>
</div>
<div class="control-group">
<div class="button-group">
<button onclick="resetRotation()">Reset</button>
<button onclick="toggleGrid()">Grid</button>
<button onclick="togglePause()">Pause</button>
</div>
</div>
</div>
<script>
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
const menuToggle = document.getElementById('menuToggle');
const controlPanel = document.getElementById('controlPanel');
let isMenuVisible = false;
let isDragging = false;
let lastTouchX = 0;
let lastTouchY = 0;
let animationId;
let isPaused = false;
let time = 0;
let rotationSpeed = 1;
let sphereDetail = 6;
let trailLength = 0.7;
let showGrid = true;
let gridDensity = 80;
let gridBursts = new Map();
const burstDuration = 40;
let rotXY = 0, rotXZ = 0, rotXW = 0, rotYZ = 0, rotYW = 0, rotZW = 0;
let colorOffset = 0;
const pixelColors = [
'#ff0080', '#ff8000', '#ffff00', '#80ff00', '#00ff80',
'#00ffff', '#0080ff', '#8000ff', '#ff00ff', '#ff4040',
'#40ff40', '#4040ff'
];
function toggleMobileMenu() {
isMenuVisible = !isMenuVisible;
if (isMenuVisible) {
controlPanel.classList.add('mobile-visible');
menuToggle.textContent = '✕';
menuToggle.style.borderColor = '#ffffff';
menuToggle.style.boxShadow = '0 0 10px rgba(255, 255, 255, 0.5)';
} else {
controlPanel.classList.remove('mobile-visible');
menuToggle.textContent = '☰';
menuToggle.style.borderColor = '#ffffff';
menuToggle.style.boxShadow = '0 0 10px rgba(255, 255, 255, 0.3)';
}
}
function handleClickOutside(event) {
if (window.innerWidth <= 768 && isMenuVisible) {
if (!controlPanel.contains(event.target) && !menuToggle.contains(event.target)) {
toggleMobileMenu();
}
}
}
function handleResize() {
if (window.innerWidth > 768) {
menuToggle.style.display = 'none';
controlPanel.classList.add('mobile-visible');
isMenuVisible = false;
} else {
menuToggle.style.display = 'flex';
controlPanel.classList.remove('mobile-visible');
isMenuVisible = false;
menuToggle.textContent = '☰';
menuToggle.style.borderColor = '#ffffff';
menuToggle.style.boxShadow = '0 0 10px rgba(255, 255, 255, 0.3)';
}
}
function initMobileMenu() {
if (window.innerWidth <= 768) {
menuToggle.style.display = 'flex';
controlPanel.classList.remove('mobile-visible');
isMenuVisible = false;
} else {
menuToggle.style.display = 'none';
controlPanel.classList.add('mobile-visible');
isMenuVisible = true;
}
}
menuToggle.addEventListener('click', toggleMobileMenu);
document.addEventListener('click', handleClickOutside);
window.addEventListener('resize', handleResize);
function resizeCanvas() {
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
ctx.imageSmoothingEnabled = false;
ctx.webkitImageSmoothingEnabled = false;
ctx.mozImageSmoothingEnabled = false;
ctx.msImageSmoothingEnabled = false;
}
function point4D(x, y, z, w) {
return { x, y, z, w };
}
function rotateXY(p, angle) {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
return point4D(
cos * p.x - sin * p.y,
sin * p.x + cos * p.y,
p.z, p.w
);
}
function rotateXZ(p, angle) {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
return point4D(
cos * p.x - sin * p.z,
p.y,
sin * p.x + cos * p.z,
p.w
);
}
function rotateXW(p, angle) {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
return point4D(
cos * p.x - sin * p.w,
p.y, p.z,
sin * p.x + cos * p.w
);
}
function project4Dto3D(p) {
const distance = 4;
const w = 1 / (distance - p.w);
return {
x: p.x * w,
y: p.y * w,
z: p.z * w
};
}
function project3Dto2D(p) {
const distance = 0.5;
const scale = Math.min(canvas.width, canvas.height) * 1.8;
const z = 1 / (distance - p.z);
return {
x: canvas.width/2 + p.x * scale * z,
y: canvas.height/2 + p.y * scale * z,
depth: p.z
};
}
function drawNonagon(x, y, size) {
ctx.beginPath();
for (let i = 0; i < 9; i++) {
const angle = (i * 2 * Math.PI) / 9;
const px = x + Math.cos(angle) * size;
const py = y + Math.sin(angle) * size;
if (i === 0) {
ctx.moveTo(px, py);
} else {
ctx.lineTo(px, py);
}
}
ctx.closePath();
}
function getNonagonGridPosition(row, col) {
const nonWidth = gridDensity;
const nonHeight = gridDensity * 0.866;
const x = col * nonWidth * 0.8;
const y = row * nonHeight + (col % 2) * nonHeight / 2;
return { x, y };
}
function getNearestNonagonNode(x, y) {
const nonWidth = gridDensity;
const nonHeight = gridDensity * 0.866;
const col = Math.round(x / (nonWidth * 0.8));
const row = Math.round((y - (col % 2) * nonHeight / 2) / nonHeight);
const nonPos = getNonagonGridPosition(row, col);
let closestDist = Infinity;
let closestPos = nonPos;
for (let dr = -1; dr <= 1; dr++) {
for (let dc = -1; dc <= 1; dc++) {
const testPos = getNonagonGridPosition(row + dr, col + dc);
const dist = Math.sqrt((x - testPos.x) ** 2 + (y - testPos.y) ** 2);
if (dist < closestDist) {
closestDist = dist;
closestPos = testPos;
}
}
}
return { pos: closestPos, distance: closestDist };
}
function checkNodeCollision(x, y) {
const nonResult = getNearestNonagonNode(x, y);
const distance = nonResult.distance;
if (distance < gridDensity * 0.5) {
const nodeKey = `${nonResult.pos.x.toFixed(0)},${nonResult.pos.y.toFixed(0)}`;
if (!gridBursts.has(nodeKey)) {
gridBursts.set(nodeKey, {
x: nonResult.pos.x,
y: nonResult.pos.y,
frame: 0,
intensity: 1,
color: getPixelColor(Math.random() * pixelColors.length)
});
}
}
}
function updateBursts() {
for (let [key, burst] of gridBursts) {
burst.frame++;
burst.intensity = Math.max(0, 1 - (burst.frame / burstDuration));
if (burst.frame >= burstDuration) {
gridBursts.delete(key);
}
}
}
function drawBursts() {
for (let [key, burst] of gridBursts) {
const size = 10 + (1 - burst.intensity) * 20;
const alpha = burst.intensity;
ctx.strokeStyle = `${burst.color}${Math.floor(alpha * 255).toString(16).padStart(2, '0')}`;
ctx.lineWidth = 3;
drawNonagon(burst.x, burst.y, size);
ctx.stroke();
ctx.fillStyle = `#ffffff${Math.floor(alpha * 255).toString(16).padStart(2, '0')}`;
ctx.fillRect(burst.x - 2, burst.y - 2, 4, 4);
}
}
function getPixelColor(index) {
const colorIndex = Math.floor((index + colorOffset) % pixelColors.length);
return pixelColors[colorIndex];
}
function createKleinBottlePoints() {
const points = [];
const a = 2;
for (let i = 0; i < sphereDetail; i++) {
for (let j = 0; j < sphereDetail * 2; j++) {
const u = (i / sphereDetail) * Math.PI * 2;
const v = (j / (sphereDetail * 2)) * Math.PI * 2;
let x, y, z, w;
if (u < Math.PI) {
x = (a + Math.cos(u/2) * Math.sin(v) - Math.sin(u/2) * Math.sin(2*v)) * Math.cos(u);
y = (a + Math.cos(u/2) * Math.sin(v) - Math.sin(u/2) * Math.sin(2*v)) * Math.sin(u);
z = Math.sin(u/2) * Math.sin(v) + Math.cos(u/2) * Math.sin(2*v);
w = Math.cos(v) * 0.5;
} else {
x = (a + Math.cos(u/2) * Math.sin(v) + Math.sin(u/2) * Math.sin(2*v)) * Math.cos(u);
y = (a + Math.cos(u/2) * Math.sin(v) + Math.sin(u/2) * Math.sin(2*v)) * Math.sin(u);
z = Math.sin(u/2) * Math.sin(v) - Math.cos(u/2) * Math.sin(2*v);
w = Math.cos(v) * 0.5;
}
points.push(point4D(x * 0.15, y * 0.15, z * 0.15, w * 0.15));
}
}
return points;
}
function drawGrid() {
if (!showGrid) return;
const nonSize = gridDensity * 0.2;
const nonWidth = gridDensity;
const nonHeight = gridDensity * 0.866;
ctx.strokeStyle = '#330066';
ctx.lineWidth = 1;
const cols = Math.ceil(canvas.width / (nonWidth * 0.8)) + 2;
const rows = Math.ceil(canvas.height / nonHeight) + 2;
for (let row = -1; row < rows; row++) {
for (let col = -1; col < cols; col++) {
const pos = getNonagonGridPosition(row, col);
if (pos.x > -nonWidth && pos.x < canvas.width + nonWidth &&
pos.y > -nonHeight && pos.y < canvas.height + nonHeight) {
drawNonagon(pos.x, pos.y, nonSize);
ctx.stroke();
}
}
}
const nodeSize = 3;
let nodeIndex = 0;
for (let row = -1; row < rows; row++) {
for (let col = -1; col < cols; col++) {
const pos = getNonagonGridPosition(row, col);
if (pos.x > -nonWidth && pos.x < canvas.width + nonWidth &&
pos.y > -nonHeight && pos.y < canvas.height + nonHeight) {
const color = getPixelColor(nodeIndex + time);
ctx.fillStyle = color;
ctx.fillRect(pos.x - nodeSize/2, pos.y - nodeSize/2, nodeSize, nodeSize);
nodeIndex++;
}
}
}
}
function animate() {
if (isPaused) {
animationId = requestAnimationFrame(animate);
return;
}
time += 0.02 * rotationSpeed;
colorOffset += 0.1 * rotationSpeed;
rotXY += 0.006 * rotationSpeed;
rotXZ += 0.008 * rotationSpeed;
rotXW += 0.004 * rotationSpeed;
rotYZ += 0.007 * rotationSpeed;
rotYW += 0.005 * rotationSpeed;
rotZW += 0.009 * rotationSpeed;
ctx.fillStyle = `rgba(26, 0, 51, ${1 - trailLength})`;
ctx.fillRect(0, 0, canvas.width, canvas.height);
updateBursts();
drawGrid();
drawBursts();
const kleinPoints = createKleinBottlePoints();
const transformedPoints = kleinPoints.map((p, index) => {
let point = p;
point = rotateXY(point, rotXY);
point = rotateXZ(point, rotXZ);
point = rotateXW(point, rotXW);
const p3d = project4Dto3D(point);
const p2d = project3Dto2D(p3d);
return { ...p2d, originalIndex: index };
});
transformedPoints.sort((a, b) => a.depth - b.depth);
ctx.strokeStyle = 'rgba(255, 255, 255, 0.3)';
ctx.lineWidth = 1;
for (let i = 0; i < transformedPoints.length; i++) {
const nextI = (i + 1) % transformedPoints.length;
const nextRow = (i + sphereDetail * 2) % transformedPoints.length;
if (i % (sphereDetail * 2) !== (sphereDetail * 2 - 1)) {
const p1 = transformedPoints[i];
const p2 = transformedPoints[nextI];
const distance = Math.sqrt((p1.x - p2.x) ** 2 + (p1.y - p2.y) ** 2);
if (distance < 150) {
const alpha = Math.max(0, 1 - distance / 150) * 0.25;
const color = getPixelColor(i * 0.1);
ctx.strokeStyle = `${color}${Math.floor(alpha * 255).toString(16).padStart(2, '0')}`;
ctx.beginPath();
ctx.moveTo(p1.x, p1.y);
ctx.lineTo(p2.x, p2.y);
ctx.stroke();
}
}
if (i < transformedPoints.length - sphereDetail * 2) {
const p1 = transformedPoints[i];
const p2 = transformedPoints[nextRow];
const distance = Math.sqrt((p1.x - p2.x) ** 2 + (p1.y - p2.y) ** 2);
if (distance < 150) {
const alpha = Math.max(0, 1 - distance / 150) * 0.25;
const color = getPixelColor(i * 0.1 + 3);
ctx.strokeStyle = `${color}${Math.floor(alpha * 255).toString(16).padStart(2, '0')}`;
ctx.beginPath();
ctx.moveTo(p1.x, p1.y);
ctx.lineTo(p2.x, p2.y);
ctx.stroke();
}
}
}
transformedPoints.forEach(point => {
checkNodeCollision(point.x, point.y);
const size = 4 + (1 - point.depth) * 2;
const color = getPixelColor(point.originalIndex + time * 2);
ctx.fillStyle = color;
ctx.fillRect(point.x - size/2, point.y - size/2, size, size);
ctx.fillStyle = '#ffffff';
ctx.fillRect(point.x - size/2, point.y - size/2, 1, 1);
});
animationId = requestAnimationFrame(animate);
}
document.getElementById('rotationSpeed').addEventListener('input', (e) => {
rotationSpeed = parseFloat(e.target.value);
document.getElementById('rotationValue').textContent = rotationSpeed.toFixed(1);
});
document.getElementById('sphereDetail').addEventListener('input', (e) => {
sphereDetail = parseInt(e.target.value);
document.getElementById('sphereValue').textContent = sphereDetail;
});
document.getElementById('trailLength').addEventListener('input', (e) => {
trailLength = parseFloat(e.target.value);
document.getElementById('trailValue').textContent = trailLength.toFixed(2);
});
function resetRotation() {
rotXY = rotXZ = rotXW = rotYZ = rotYW = rotZW = 0;
time = 0;
}
function toggleGrid() {
showGrid = !showGrid;
const gridButton = document.querySelector('button[onclick="toggleGrid()"]');
gridButton.textContent = showGrid ? 'Grid On' : 'Grid Off';
gridButton.style.borderColor = showGrid ? '#ffffff' : '#666666';
}
function togglePause() {
isPaused = !isPaused;
const pauseButton = document.querySelector('button[onclick="togglePause()"]');
pauseButton.textContent = isPaused ? 'Play' : 'Pause';
pauseButton.style.borderColor = isPaused ? '#666666' : '#ffffff';
}
canvas.addEventListener('touchstart', (e) => {
e.preventDefault();
isDragging = true;
const touch = e.touches[0];
lastTouchX = touch.clientX;
lastTouchY = touch.clientY;
if (isMenuVisible && window.innerWidth <= 768) {
toggleMobileMenu();
}
});
canvas.addEventListener('touchmove', (e) => {
e.preventDefault();
if (!isDragging) return;
const touch = e.touches[0];
const deltaX = (touch.clientX - lastTouchX) * 0.01;
const deltaY = (touch.clientY - lastTouchY) * 0.01;
rotXY += deltaX;
rotXZ += deltaY;
lastTouchX = touch.clientX;
lastTouchY = touch.clientY;
});
canvas.addEventListener('touchend', (e) => {
e.preventDefault();
isDragging = false;
});
canvas.addEventListener('mousedown', (e) => {
isDragging = true;
lastTouchX = e.clientX;
lastTouchY = e.clientY;
});
canvas.addEventListener('mousemove', (e) => {
if (!isDragging) return;
const deltaX = (e.clientX - lastTouchX) * 0.01;
const deltaY = (e.clientY - lastTouchY) * 0.01;
rotXY += deltaX;
rotXZ += deltaY;
lastTouchX = e.clientX;
lastTouchY = e.clientY;
});
canvas.addEventListener('mouseup', () => {
isDragging = false;
});
canvas.addEventListener('click', (e) => {
const rect = canvas.getBoundingClientRect();
const x = e.clientX - rect.left;
const y = e.clientY - rect.top;
const nodeKey = `${x.toFixed(0)},${y.toFixed(0)}`;
if (!gridBursts.has(nodeKey)) {
gridBursts.set(nodeKey, {
x: x,
y: y,
frame: 0,
intensity: 1,
color: getPixelColor(Math.random() * pixelColors.length)
});
}
});
window.addEventListener('resize', () => {
resizeCanvas();
handleResize();
});
resizeCanvas();
initMobileMenu();
animate();
</script>
</body>
</html>