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feat: Interactive lorenz example (#3151)
* Interactive lorenz * Separate Interactive Lorenz * Cleanup * Bigger graphs * Full screen examples --------- Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
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| Original file line number | Diff line number | Diff line change |
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| <!DOCTYPE html> | ||
| <html lang="en"> | ||
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| <head> | ||
| <meta charset="UTF-8"> | ||
| <title>math.js | Lorenz Attractor</title> | ||
| <script src="../../lib/browser/math.js"></script> | ||
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| <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==" | ||
| crossorigin="anonymous" referrerpolicy="no-referrer"></script> | ||
| <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.9/katex.min.css" | ||
| integrity="sha512-fHwaWebuwA7NSF5Qg/af4UeDx9XqUpYpOGgubo3yWu+b2IQR4UeQwbb42Ti7gVAjNtVoI/I9TEoYeu9omwcC6g==" | ||
| crossorigin="anonymous" referrerpolicy="no-referrer" /> | ||
| <style> | ||
| body, | ||
| html { | ||
| width: 100%; | ||
| height: 100vh; | ||
| padding: 0; | ||
| margin: 0; | ||
| } | ||
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| body { | ||
| display: flex; | ||
| flex-direction: column; | ||
| } | ||
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| #LorenzGraph { | ||
| flex: 1; | ||
| } | ||
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| #inputsDiv { | ||
| z-index: 1; | ||
| position: absolute; | ||
| } | ||
| </style> | ||
| </head> | ||
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| <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> | ||
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| </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")) | ||
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| const inputs = document.querySelector("#inputs") | ||
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| // define the constants for the Lorenz attractor | ||
| const sigma = document.querySelector("#sigma") | ||
| const beta = document.querySelector("#beta") | ||
| const rho = document.querySelector("#rho") | ||
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| // define the initial location | ||
| const x0 = document.querySelector('#x0') | ||
| const y0 = document.querySelector('#y0') | ||
| const z0 = document.querySelector('#z0') | ||
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| // define the tolerance for the solution | ||
| const epsilon = document.querySelector('#epsilon') | ||
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| 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' }] | ||
| }] | ||
| } | ||
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| const t_span = [0, 100] | ||
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| inputs.addEventListener("change", updateSolution) | ||
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| let trace | ||
| // solve the Lorenz attractor with the initial values | ||
| updateSolution() | ||
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| // 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 | ||
| } | ||
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| 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 | ||
| ] | ||
| } | ||
| } | ||
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| 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) | ||
| } | ||
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| </script> | ||
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| </html> |