Lorenz interactive
File: lorenz_interactive.html (click for a live demo)
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>math.js | Lorenz Attractor</title>
<script src="https://unpkg.com/mathjs@14.0.1/lib/browser/math.js"></script>
<script src="https://cdn.plot.ly/plotly-2.28.0.min.js" charset="utf-8"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.js"
integrity="sha512-LQNxIMR5rXv7o+b1l8+N1EZMfhG7iFZ9HhnbJkTp4zjNr5Wvst75AqUeFDxeRUa7l5vEDyUiAip//r+EFLLCyA=="
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<style>
body,
html {
width: 100%;
height: 100vh;
padding: 0;
margin: 0;
}
body {
display: flex;
flex-direction: column;
}
#LorenzGraph {
flex: 1;
}
#inputsDiv {
z-index: 1;
position: absolute;
background: white;
}
</style>
</head>
<body>
<div id="LorenzGraph"></div>
<div id="inputsDiv">
<fieldset name="inputs" id="inputs">
<legend for="inputs">Inputs:</legend>
<table>
<tr>
<td>
<label for="sigma" id="sigmaLabel">sigma</label>
</td>
<td>
<input type="range" id="sigma" name="sigma" value=10 min=9 max=11 step=0.01>
</td>
<td>
<label for="beta" id="betaLabel">beta</label>
</td>
<td>
<input type="range" id="beta" name="beta" value=8/3 min=2 max=4 step=0.01>
</td>
<td>
<label for="rho" id="rhoLabel">rho</label>
</td>
<td>
<input type="range" id="rho" name="rho" value=28 min=20 max=30 step=0.01>
</td>
</tr>
<tr>
<td>
<label for="x0" id="x0Label">x0</label>
</td>
<td>
<input type="range" id="x0" name="x0" value=1 min=-5 max=5 step=0.01>
</td>
<td>
<label for="y0" id="y0Label">y0</label>
</td>
<td>
<input type="range" id="y0" name="y0" value=1 min=-5 max=5 step=0.01>
</td>
<td>
<label for="z0" id="z0Label">z0</label>
</td>
<td>
<input type="range" id="z0" name="z0" value=0 min=-5 max=5 step=0.01>
</td>
</tr>
<tr>
<td>
<label for="epsilon" id="epsilonLabel">epsilon</label>
</td>
<td>
<input type="range" id="epsilon" name="epsilon" value=0.01 min=0.0001 max=0.1 step=0.0001>
</td>
</tr>
</table>
</fieldset>
</div>
</body>
<script defer>
katex.render(String.raw`\sigma`, document.querySelector("#sigmaLabel"))
katex.render(String.raw`\beta`, document.querySelector("#betaLabel"))
katex.render(String.raw`\rho`, document.querySelector("#rhoLabel"))
katex.render(String.raw`x_0`, document.querySelector("#x0Label"))
katex.render(String.raw`y_0`, document.querySelector("#y0Label"))
katex.render(String.raw`z_0`, document.querySelector("#z0Label"))
katex.render(String.raw`\epsilon`, document.querySelector("#epsilonLabel"))
const inputs = document.querySelector("#inputs")
// define the constants for the Lorenz attractor
const sigma = document.querySelector("#sigma")
const beta = document.querySelector("#beta")
const rho = document.querySelector("#rho")
// define the initial location
const x0 = document.querySelector('#x0')
const y0 = document.querySelector('#y0')
const z0 = document.querySelector('#z0')
// define the tolerance for the solution
const epsilon = document.querySelector('#epsilon')
const layout = {
interactive: true,
title: 'Lorenz Attractor',
uirevision: 'true',
sliders: [{
name: 'sigma',
currentvalue: {
xanchor: 'right',
prefix: 'color: ',
font: {
color: '#888',
size: 20
}
},
steps: [{ label: 'g', method: "updateSolution" }, { label: 'f' }]
}]
}
const t_span = [0, 100]
inputs.addEventListener("change", updateSolution)
let trace
// solve the Lorenz attractor with the initial values
updateSolution()
// crates a trace in the format needed for plotly
function createTrace(sol) {
// make colors that represents time differences in the solution
const diff = math.diff(sol.t)
const color = [diff[0], ...diff]
const trace = [{
x: sol.y.map(u => u[0]),
y: sol.y.map(u => u[1]),
z: sol.y.map(u => u[2]),
line: {
color,
colorscale: 'Jet'
},
type: "scatter3d",
mode: "lines"
}]
return trace
}
function createLorenz(sigma, rho, beta) {
// define the lorenz attractor as a function of t and u in the format needed for solveODE
return function lorenz(t, u) {
const [x, y, z] = u
// return x', y', z'
return [
sigma * (y - x),
x * (rho - z) - y,
x * y - beta * z
]
}
}
function updateSolution() {
const y_0 = [x0.value, y0.value, z0.value]
const sol = math.solveODE(createLorenz(sigma.value, rho.value, beta.value), t_span, y_0, { tol: epsilon.value })
trace = createTrace(sol)
// reactively render the plot on update
Plotly.react('LorenzGraph', trace, layout)
}
</script>
</html>