Visualization of a solution of the Lorentz attractor plotted in the x-z plane.
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March 7, 2023 21:59
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Lorenz System
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height: 600 | |
license: MIT |
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<!DOCTYPE html> | |
<meta charset="utf-8"> | |
<style> | |
.circle { | |
opacity: 0.5; | |
fill: #ccc; | |
stroke: steelblue; | |
r: 3px; | |
} | |
.track { | |
fill: none; | |
stroke: url("#line-gradient"); | |
} | |
</style> | |
<body></body> | |
<script src="https://d3js.org/d3.v4.min.js"></script> | |
<script> | |
var margin = {top: 10, right: 10, bottom: 10, left: 10}, | |
width = 600 - margin.left - margin.right, | |
height = 600 - margin.top - margin.bottom; | |
var rho = 28.0, | |
sigma = 10.0, | |
beta = 8.0 / 3.0, | |
x = 0, | |
y = z = 1, | |
t = 0.01, | |
iter = 0, | |
max_iter = 10000, | |
data = []; | |
var svg = d3.select("body").append("svg") | |
.attr("width", width + margin.left + margin.right) | |
.attr("height", height + margin.top + margin.bottom) | |
.append("g") | |
.attr("class", "g-lorentz") | |
.attr("transform", "translate(" + margin.left + "," + margin.top + ")"); | |
var colorScale = d3.scaleLinear() | |
.domain([0, 40]) | |
.range([0, 1]); | |
var circle = svg.append("circle") | |
.attr("class", "circle"); | |
var line = d3.line() | |
.curve(d3.curveCardinal) | |
.x(function(d) { return d[0]; }) | |
.y(function(d) { return d[1]; }); | |
var track = svg.append("path") | |
.attr("class", "track"); | |
// set the gradient | |
svg.append("linearGradient") | |
.attr("id", "line-gradient") | |
.attr("x1", "10%").attr("x1", "90%") | |
.attr("y1", "10%").attr("y2", "90%") | |
.selectAll("stop") | |
.data([ | |
{offset: "0%", color: "#b2182b"}, | |
{offset: "100%", color: "#2166ac"} | |
]) | |
.enter().append("stop") | |
.attr("offset", function(d) { return d.offset; }) | |
.attr("stop-color", function(d) { return d.color; }); | |
function lorentz(callback) { | |
callback( | |
x += t * (sigma * (y - x)), | |
y += t * (x * (rho - z) - y), | |
z += t * (x * y - beta * z) | |
); | |
} | |
function draw(x, y, z) { | |
data.push([(width / 2 + 10 * x), (height + 10 * -z)]); | |
track.attr("d", line(data)).attr("stroke", "url(#line-gradient)"); | |
circle.attr("transform", function(d) { return "translate(" + data[data.length - 1] + ")"; }); | |
} | |
var interval = setInterval(function() { | |
iter++; | |
if (iter >= max_iter) | |
clearInterval(interval); | |
lorentz(draw); | |
}, 10); | |
</script> |
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{ | |
"name": "lorentz attractor", | |
"version": "0.0.1", | |
"description": "Visualization of a Lorentz attractor", | |
"keywords": [ | |
"math", | |
"visualization", | |
"chaos theory", | |
"d3.js", | |
"oscillator" | |
], | |
"author": "Hugo Janssen <nl-hugo@hugojanssen.nl>", | |
"private": true, | |
"license": "MIT" | |
} |
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