PORTAL_Dynamical_system

## Images <figure class="wt-gifplate"> <img src="https://commons.wikimedia.org/wiki/Special:FilePath/Lorenz_attractor.gif" alt="Attractor Dynamics" loading="lazy" decoding="async"> <figcaption><strong>Attractor Dynamics</strong> — Watch a trajectory trace a butterfly-shaped path. This is the Lorenz attractor—how deterministic rules generate endlessly complex, bounded motion.<br> <span class="wt-credit">Wikimedia Commons · <strong>licence pending verification</strong> (run <code>g17_gif_verify.py</code> on a networked lane) · <a href="https://commons.wikimedia.org/wiki/File:Lorenz_attractor.gif">Details</a></span></figcaption> </figure> *Room plate for [[Dynamical_system]]. The interactive builds live below; this is the room's one still-motion establishing shot.*  The canonical spine of [[Dynamical_system]]: its full tree-verified child structure, publishable to Obsidian as the scaffold for route objects (microsims, songs, semiotics, cardsets, games, streams, transcripts) keyed to this hub.  ## Play every microsim on this page <p class="microsim-gallery-note">Every microsim linked from this portal, embedded live. <strong>65 players</strong> — 32 threejs · 33 p5js. 7 are staged but not yet deployed and show as placeholders.</p> <ul class="microsim-gallery"> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Attractor.html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Attractor — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Attractor">Attractor</a></div><div class="ms-sub">threejs · <a 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Class</a></div></div> </li> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Geodesic_microsim.html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Geodesic — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Geodesic">Geodesic</a></div><div class="ms-sub">threejs · <a href="https://wikitube-3d-microsims.netlify.app/Geodesic_microsim.html" target="_blank" rel="noopener">open full-screen</a></div></div> </li> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Hamiltonian_mechanics.html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Hamiltonian mechanics — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Hamiltonian_mechanics">Hamiltonian mechanics</a></div><div class="ms-sub">threejs · <a 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allow-same-origin" title="Langtons ant 3D — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Langton's_ant">Langtons ant 3D</a></div><div class="ms-sub">threejs · <a href="https://wikitube-3d-microsims.netlify.app/Langtons_ant_3D.html" target="_blank" rel="noopener">open full-screen</a> · on <a href="https://en.wikitube.io/wiki/Langton's_ant">Langton's ant</a></div></div> </li> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Liouville's_theorem_(Hamiltonian).html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Liouville's theorem (Hamiltonian) — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Liouville's_theorem_(Hamiltonian)">Liouville's theorem (Hamiltonian)</a></div><div class="ms-sub">threejs · <a 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automaton</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/90jeLsBsW" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Acoustic wave — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/WT!P5_js_Microsim_Master_Class">Acoustic wave</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/90jeLsBsW" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/WT!P5_js_Microsim_Master_Class">p5.js Microsim Master Class</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/tHGSVAofH" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Aliasing — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a 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href="https://en.wikitube.io/wiki/Force">Force</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/mWeE8qoAB" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/ed_W_W-NO" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Functional analysis (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Functional_analysis">Functional analysis (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/ed_W_W-NO" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Functional_analysis">Functional analysis</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/Q1lzsnapy" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Graph theory (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Graph_theory">Graph theory (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/Q1lzsnapy" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Graph_theory">Graph theory</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/HVNGd9nMv" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Histogram — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/WT!P5_js_Microsim_Master_Class">Histogram</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/HVNGd9nMv" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/WT!P5_js_Microsim_Master_Class">p5.js Microsim Master Class</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/byCRgwg34" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Information theory — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Information_theory">Information theory</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/byCRgwg34" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/MFFPM7AEH" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Information theory (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Information_theory">Information theory (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/MFFPM7AEH" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Information_theory">Information theory</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/Y0VWcco23" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Johannes Kepler — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Johannes_Kepler">Johannes Kepler</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/Y0VWcco23" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/NLo0EVO0C" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Lie group (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Lie_group">Lie group (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/NLo0EVO0C" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Lie_group">Lie group</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/ONl3-NO3g" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Newton's laws of motion — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Newton's_laws_of_motion">Newton's laws of motion</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/ONl3-NO3g" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/1_JVzl6L5" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Nonlinear system (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Nonlinear_system">Nonlinear system (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/1_JVzl6L5" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Nonlinear_system">Nonlinear system</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/Q21EyK7NF" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Oscillation — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Oscillation">Oscillation</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/Q21EyK7NF" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/vtdlSNRup" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Pendulum — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Pendulum">Pendulum</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/vtdlSNRup" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/I72z0hVuk" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Phase transition — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Phase_transition">Phase transition</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/I72z0hVuk" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/IOMm0e1Kk" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Probability (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Probability">Probability (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/IOMm0e1Kk" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Probability">Probability</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/o1ATfTxiG" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Probability density function (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Probability_density_function">Probability density function (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/o1ATfTxiG" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Probability_density_function">Probability density function</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/A_73AMciC" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Quantum mechanics — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Quantum_mechanics">Quantum mechanics</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/A_73AMciC" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/QPai0xNyx" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Recurrence relation (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Recurrence_relation">Recurrence relation (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/QPai0xNyx" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Recurrence_relation">Recurrence relation</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/iLnN6bFev" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Sequence — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Sequence">Sequence</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/iLnN6bFev" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/VG2lh_GDS" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="System dynamics — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/System_dynamics">System dynamics</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/VG2lh_GDS" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/O50GeFp7y" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Velocity — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Velocity">Velocity</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/O50GeFp7y" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/ZBxM-wEIe" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Wayback Machine — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Wayback_Machine">Wayback Machine</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/ZBxM-wEIe" target="_blank" rel="noopener">open in the p5 editor</a></div></div> </li> <li class="microsim-card" data-lib="p5js"> <iframe src="https://editor.p5js.org/sciencenibber/full/GOfgvZX-X" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Weather forecasting (p5.js) — p5js microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Weather_forecasting">Weather forecasting (p5.js)</a></div><div class="ms-sub">p5js · <a href="https://editor.p5js.org/sciencenibber/full/GOfgvZX-X" target="_blank" rel="noopener">open in the p5 editor</a> · on <a href="https://en.wikitube.io/wiki/Weather_forecasting">Weather forecasting</a></div></div> </li> <li class="microsim-card is-pending" data-lib="threejs"> <div class="ms-placeholder">Staged, not yet deployed — <code>Configuration_space_%28physics%29.html</code></div> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Configuration_space_(physics)">Configuration space (physics)</a></div><div class="ms-sub">threejs · awaiting CDN deploy</div></div> </li> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Weather_forecasting.html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Controls -> what each maps to — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Weather_forecasting">Controls -> what each maps to</a></div><div class="ms-sub">threejs · <a href="https://wikitube-3d-microsims.netlify.app/Weather_forecasting.html" target="_blank" rel="noopener">open full-screen</a> · on <a href="https://en.wikitube.io/wiki/Weather_forecasting">Weather forecasting</a></div></div> </li> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Lie_group.html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Controls → what each maps to — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Lie_group">Controls → what each maps to</a></div><div class="ms-sub">threejs · <a href="https://wikitube-3d-microsims.netlify.app/Lie_group.html" target="_blank" rel="noopener">open full-screen</a> · on <a href="https://en.wikitube.io/wiki/Lie_group">Lie group</a></div></div> </li> <li class="microsim-card is-pending" data-lib="threejs"> <div class="ms-placeholder">Staged, not yet deployed — <code>Ellipse.html</code></div> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Ellipse">Ellipse</a></div><div class="ms-sub">threejs · awaiting CDN deploy</div></div> </li> <li class="microsim-card is-pending" data-lib="threejs"> <div class="ms-placeholder">Staged, not yet deployed — <code>Expected_value.html</code></div> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Expected_value">Expected value</a></div><div class="ms-sub">threejs · awaiting CDN deploy</div></div> </li> <li class="microsim-card is-pending" data-lib="threejs"> <div class="ms-placeholder">Staged, not yet deployed — <code>Fibonacci_sequence.html</code></div> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Fibonacci_sequence">Fibonacci sequence</a></div><div class="ms-sub">threejs · awaiting CDN deploy</div></div> </li> <li class="microsim-card is-pending" data-lib="threejs"> <div class="ms-placeholder">Staged, not yet deployed — <code>Finite-state_machine.html</code></div> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Finite-state_machine">Finite-state machine</a></div><div class="ms-sub">threejs · awaiting CDN deploy</div></div> </li> <li class="microsim-card is-pending" data-lib="threejs"> <div class="ms-placeholder">Staged, not yet deployed — <code>Graph_of_a_function.html</code></div> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Graph_of_a_function">Graph of a function</a></div><div class="ms-sub">threejs · awaiting CDN deploy</div></div> </li> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Lyapunov_stability.html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Lyapunov stability — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Lyapunov_stability">Lyapunov stability</a></div><div class="ms-sub">threejs · <a href="https://wikitube-3d-microsims.netlify.app/Lyapunov_stability.html" target="_blank" rel="noopener">open full-screen</a></div></div> </li> <li class="microsim-card" data-lib="threejs"> <iframe src="https://wikitube-3d-microsims.netlify.app/Numerical_integration.html" loading="lazy" frameborder="0" sandbox="allow-scripts allow-same-origin" title="Numerical integration — threejs microsim"></iframe> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Numerical_integration">Numerical integration</a></div><div class="ms-sub">threejs · <a href="https://wikitube-3d-microsims.netlify.app/Numerical_integration.html" target="_blank" rel="noopener">open full-screen</a></div></div> </li> <li class="microsim-card is-pending" data-lib="threejs"> <div class="ms-placeholder">Staged, not yet deployed — <code>Projective_geometry.html</code></div> <div class="ms-meta"><div class="ms-title"><a href="https://en.wikitube.io/wiki/Projective_geometry">Projective geometry</a></div><div class="ms-sub">threejs · awaiting CDN deploy</div></div> </li> </ul>   **Craft standard:** Both craft standards apply here — [[WT!Three_js_Microsim_Master_Class|three.js]] and [[WT!P5_js_Microsim_Master_Class|p5.js]].   *Microsims from the articles linked below:* <div class="wt-simrow"> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/solar/Solar_System.html?obj=Ceres&embed=1" data-title="Ceres in the Solar System explorer"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Drag_(physics).html" data-title="Drag (physics)"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Fluid_dynamics.html" data-title="Fluid dynamics"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Kármán_vortex_street.html" data-title="Kármán vortex street"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Newton's_laws_of_motion.html" data-title="Newton's laws of motion"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/solar/Solar_System.html?view=orbits&embed=1" data-title="The orbits (Solar System explorer)"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/acoustics/Oscillation.html" data-title="Oscillation"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Pendulum.html" data-title="Pendulum"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Rayleigh–Bénard_convection.html" data-title="Rayleigh–Bénard convection"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/solar/Solar_System.html?obj=Saturn&scale=true&embed=1" data-title="Saturn in the Solar System explorer"></div> <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Turbulence.html" data-title="Turbulence"></div> </div>   ## Canonical link structure — 500 tree-verified children Hub article: [[Dynamical_system]] · tree harvested 2026-07-29T22:46:18Z · every entry below is in this hub's harvested child tree (v09-gated). Unbuilt links are intentional forward-refs: the populate scaffold. **A** — [[Abelian_sandpile_model]] · [[Abstract_algebra]] · [[Accumulation_point]] · [[Affine_geometry]] · [[Affine_transformation]] · [[Aircraft]] · [[Aleksandr_Lyapunov]] · [[Alexandroff_extension]] · [[Algebraic_curve]] · [[Algebraic_geometry]] · [[Algebraic_group]] · [[Algebraic_number_field]] · [[Algebraic_quantum_field_theory]] · [[Algebraic_variety]] · [[Ali_H._Nayfeh]] · [[American_Mathematical_Society]] · [[Amie_Wilkinson]] · [[Analytic_function]] · [[Anosov_diffeomorphism]] · [[Apollonius_of_Perga]] · [[Applied_mathematics]] · [[Arithmetic_dynamics]] · [[Arnold's_cat_map]] · [[Arnold_tongue]] · [[ArXiv]] · [[Associative_property]] · [[Astronomer]] · [[Attenuation]] · [[Attractor]] · [[Audrey_Terras]] · [[Automorphism_group]] · [[Autonomous_system_(mathematics)]] · [[Axiom_A]] **B** — [[Baker's_map]] · [[Banach_fixed-point_theorem]] · [[Banach_space]] · [[Behavioral_modeling]] · [[Benoit_Mandelbrot]] · [[Bernard_Koopman]] · [[Bernoulli_scheme]] · [[Bibcode]] · [[Bifurcation_diagram]] · [[Bifurcation_theory]] · [[Biology]] · [[Borel_set]] · [[Bouncing_ball]] · [[Boundary_value_problem]] · [[Boundedness]] · [[Bridge]] · [[Brosl_Hasslacher]] · [[Brownian_motion]] · [[Bryna_Kra]] · [[Building]] · [[Butterfly_effect]] **C** — `C*-algebra` · [[Canonical_transformation]] · [[Caroline_Series]] · [[Category_theory]] · [[Cauchy_sequence]] · [[Celestial_mechanics]] · [[Cellular_automaton]] · [[Celso_Grebogi]] · [[Central_limit_theorem]] · [[Ceres_(dwarf_planet)]] · `Chaos:_Making_a_New_Science` · [[Chaos_theory]] · [[Chemistry]] · [[Chen_Guanrong]] · [[Chua's_circuit]] · [[Classical_mechanics]] · [[Cliodynamics]] · [[Cognitive_model]] · [[Compactification]] · [[Compact_operator]] · [[Compact_space]] · [[Complexity]] · [[Complex_dynamics]] · [[Complex_dynamic_systems_theory]] · [[Complex_number]] · [[Complex_quadratic_polynomial]] · [[Computational_fluid_dynamics]] · [[Computer]] · [[Computer_(occupation)]] · [[Configuration_space_(physics)]] · [[Conformal_map]] · [[Conjugacy_class]] · [[Conley's_fundamental_theorem_of_dynamical_systems]] · [[Conservation_law]] · [[Conservative_system]] · [[Constant_of_motion]] · [[Contact_geometry]] · [[Continuous_function]] · [[Control_of_chaos]] · [[Control_theory]] · [[Coordinate_system]] · [[Correlation_dimension]] · [[Countable_set]] · [[Coupled_map_lattice]] · [[Coxeter_group]] · [[Crane_(machine)]] · [[Critical_phenomena]] **D** — [[David_Ruelle]] · [[Degrees_of_freedom]] · [[Dense_set]] · [[Determinism]] · [[Deterministic_system]] · [[Diffeomorphism]] · [[Differentiable_function]] · [[Differentiable_manifold]] · [[Differential_equation]] · [[Diffusion_model]] · [[Digital_image_processing]] · [[Digital_object_identifier]] · [[Dimension]] · [[Dirac_delta_function]] · [[Discrete_mathematics]] · [[Discrete_space]] · [[Discrete_time_and_continuous_time]] · [[Discretization_of_Navier–Stokes_equations]] · [[Dissipation]] · [[Dissipative_system]] · [[Distribution_(mathematical_analysis)]] · [[Double_pendulum]] · [[Drag_(physics)]] · [[Duffing_equation]] · [[Duffing_map]] · [[Dyadic_transformation]] · [[Dynamical_billiards]] · [[Dynamical_systems_theory]] · [[Dynamics]] · [[Dynamics_(mechanics)]] **E** — [[Economics]] · [[Edge_of_chaos]] · [[Edward_Norton_Lorenz]] · [[Edward_Ott]] · [[Eigenvalues_and_eigenvectors]] · [[Elastic_pendulum]] · [[Ellipse]] · [[Emergence]] · [[Empty_set]] · [[Endomorphism]] · [[Engineering]] · [[Ensemble_(mathematical_physics)]] · [[Equilibrium_point_(mathematics)]] · [[Equivalence_class]] · [[Equivalence_relation]] · [[Ergodicity]] · [[Ergodic_hypothesis]] · [[Ergodic_theory]] · [[Ernst_Zermelo]] · [[ETH_Zurich]] · [[Expected_value]] · [[Exponential_function]] · [[Exponential_map_(discrete_dynamical_systems)]] **F** — [[False_nearest_neighbor_algorithm]] · [[Feedback_passivation]] · [[Fermi–Pasta–Ulam–Tsingou_problem]] · [[Fibonacci_sequence]] · [[Field_(mathematics)]] · [[Finite-state_machine]] · [[Finite_difference]] · [[Finite_field]] · [[Finite_geometry]] · [[Finite_group]] · [[Finite_mathematics]] · [[Fixed_point_(mathematics)]] · [[Florin_Diacu]] · [[Floris_Takens]] · [[Flow_(mathematics)]] · [[Fluid_dynamics]] · [[Force]] · [[Fractal]] · [[Frame_of_reference]] · [[Franklin_Institute]] · [[Franklin_Institute_Awards]] · [[Functional_(mathematics)]] · [[Functional_analysis]] · [[Functional_equation]] · [[Function_(mathematics)]] · [[Fundamental_theorem_of_arithmetic]] **G** — [[Galois_theory]] · [[Gauss_iterated_map]] · [[General_relativity]] · [[General_topology]] · [[Geodesic]] · [[Geometry]] · [[George_David_Birkhoff]] · [[Gerald_Teschl]] · [[Giancarlo_Gandolfo]] · [[Gingerbreadman_map]] · [[Global_analysis]] · [[Glossary_of_dance_moves]] · [[Gradient_descent]] · [[Graph_(discrete_mathematics)]] · [[Graph_dynamical_system]] · [[Graph_of_a_function]] · [[Graph_theory]] · [[Group_action]] · [[Group_representation]] **H** — [[Hahn–Banach_theorem]] · [[Hamiltonian_mechanics]] · [[Hamiltonian_system]] · [[Handle_System]] · [[Hartman–Grobman_theorem]] · [[Hausdorff_dimension]] · [[Hausdorff_space]] · [[Hee_Oh]] · [[Henri_Poincaré]] · [[Heuristic]] · [[Hilbert_space]] · [[Holonomic_constraints]] · [[Homeomorphism]] · [[Homomorphism]] · [[Horseshoe_map]] · [[Hyperbolic_equilibrium_point]] · [[Hyperion_(moon)]] · [[Hénon_map]] · [[Hénon–Heiles_system]] **I** — [[Identity_(mathematics)]] · [[Ikeda_map]] · [[Image_(mathematics)]] · [[Induced_representation]] · [[Infinite_compositions_of_analytic_functions]] · [[Information_theory]] · [[Initial_condition]] · [[Initial_value_problem]] · [[Integer]] · [[Integer_lattice]] · [[Integrable_system]] · [[Interval_(mathematics)]] · [[Interval_exchange_transformation]] · [[Invariant_measure]] · [[Irrational_number]] · [[Irrational_rotation]] · [[Irreducible_representation]] · [[ISBN]] · [[Isomorphism]] · [[ISSN]] · [[Itamar_Procaccia]] · [[Iterated_function]] · [[Ivar_Ekeland]] **J** — [[Jacob_Palis]] · [[James_A._Yorke]] · [[James_Gleick]] · [[Jerrold_E._Marsden]] · [[Jet_engine]] · [[Johannes_Kepler]] · [[Jump_process]] **K** — [[Kaplan–Yorke_map]] · [[Kicked_rotator]] · [[Kolmogorov–Arnold–Moser_theorem]] · [[Koopman–von_Neumann_classical_mechanics]] · [[Korteweg–De_Vries_equation]] · [[Krylov–Bogolyubov_theorem]] · [[Kármán_vortex_street]] **L** — [[Lagrange's_theorem_(group_theory)]] · [[Lagrangian_mechanics]] · [[Lagrangian_system]] · [[Lai-Sang_Young]] · [[Landau_theory]] · [[Langevin_equation]] · [[Langton's_ant]] · [[Lattice_(group)]] · [[Lattice_model_(physics)]] · [[Lebesgue_measure]] · [[Leon_O._Chua]] · [[Lewis_Fry_Richardson]] · [[Lie_group]] · [[Limit_set]] · [[Linearity]] · [[Linear_dynamical_system]] · [[Liouville's_theorem_(Hamiltonian)]] · [[Lipschitz_continuity]] · [[List_of_chaotic_maps]] · [[List_of_dynamical_systems_and_differential_equations_topics]] · [[List_of_people_in_systems_and_control]] · [[Locally_compact_space]] · [[Logistic_map]] · [[Lorenz_system]] · [[Lotka–Volterra_equations]] · [[Ludwig_Boltzmann]] · [[Lyapunov_exponent]] · [[Lyapunov_stability]] **M** — [[Machine]] · [[Machine_learning]] · [[Mackey–Glass_equations]] · [[Manifold]] · [[Map_(mathematics)]] · [[Marcelo_Viana]] · [[Martin_Gutzwiller]] · [[Mary_Cartwright]] · [[Mary_Rees]] · [[Mary_Tsingou]] · [[Mathematical_model]] · [[Mathematics]] · [[Matrix_difference_equation]] · [[Matrix_exponential]] · [[Maupertuis's_principle]] · [[Measurable_function]] · [[Measurable_space]] · [[Measure-preserving_dynamical_system]] · [[Measure_(mathematics)]] · [[Measure_space]] · [[Mechanics]] · [[Medicine]] · [[Meteorology]] · [[Metric_tensor]] · [[Michael_Berry_(physicist)]] · [[Michel_Hénon]] · [[Microstate]] · [[Microstate_(statistical_mechanics)]] · [[Minkowski–Bouligand_dimension]] · [[Mitchell_Feigenbaum]] · [[Mixing_(mathematics)]] · [[Modulo]] · [[Monoid]] · [[Morris_Hirsch]] · [[Moving_average]] · [[Multidimensional_system]] · [[Multiscroll_attractor]] · [[Multivalued_function]] **N** — [[Network_theory]] · [[Neural_network_(machine_learning)]] · [[Newton's_laws_of_motion]] · [[Nina_Snaith]] · [[Noether's_theorem]] · [[Nondeterministic_Turing_machine]] · [[Nonholonomic_system]] · [[Nonlinear_system]] · [[Number_line]] · [[Number_theory]] · [[Numerical_integration]] **O** — [[Observable]] · [[Oleksandr_Sharkovsky]] · [[Open_set]] · [[Operator_(mathematics)]] · [[Operator_algebra]] · [[Orbit]] · [[Orbital_resonance]] · [[Orbit_(dynamics)]] · [[Order_and_disorder]] · [[Ordinary_differential_equation]] · [[Oscillation]] · [[Otto_Rössler]] · [[Outer_billiards]] **P** — [[PageRank]] · [[Parabola]] · [[Partial_differential_equation]] · [[Pendulum]] · [[Percolation]] · [[Period-doubling_bifurcation]] · [[Periodic_point]] · [[Permutation]] · [[Peter_Grassberger]] · [[Phase_space]] · [[Phase_transition]] · [[Philip_Holmes]] · [[Physics]] · [[Picard–Lindelöf_theorem]] · [[Piecewise_linear_function]] · [[Planet]] · [[Poincaré_map]] · [[Poincaré_recurrence_theorem]] · [[Poincaré–Bendixson_theorem]] · [[Poincaré–Birkhoff_theorem]] · [[Poisson_manifold]] · [[Pomeau–Manneville_scenario]] · [[Poncelet_map]] · [[Population_dynamics]] · [[Potential_flow]] · [[Predictability]] · [[Prime_number]] · [[Principle_of_maximum_caliber]] · [[Probability]] · [[Probability_density_function]] · [[Probability_measure]] · [[Probability_space]] · [[Projection_(set_theory)]] · [[Projective_geometry]] · [[Providence,_Rhode_Island]] · [[PubMed]] · [[PubMed_Central]] **Q** — [[Quantum_chaos]] · [[Quantum_electrodynamics]] · [[Quantum_mechanics]] · [[Quantum_state]] · [[Quantum_state_space]] · [[Quantum_systems]] **R** — [[Rabinovich–Fabrikant_equations]] · [[Ralph_Abraham_(mathematician)]] · [[Random_dynamical_system]] · [[Rational_mapping]] · [[Rational_number]] · [[Rayleigh–Bénard_convection]] · [[Real_number]] · [[Recurrence_plot]] · [[Recurrence_relation]] · [[Recursion]] · [[Recursive_neural_network]] · [[Renormalization_group]] · [[Representation_theory]] · [[Riemannian_manifold]] · [[Rings_of_Saturn]] · [[Robert_L._Devaney]] · [[Robert_Shaw_(physicist)]] · [[Robotic_arm]] · [[Rocket_engine]] · [[Rudolphine_Tables]] · [[Rufus_Bowen]] · [[Rössler_attractor]] **S** — [[Santa_Fe_Institute]] · [[Scholarpedia]] · [[Self-assembly]] · [[Self-organization]] · [[Self-organized_criticality]] · [[Semigroup]] · [[Semigroup_action]] · [[Sequence]] · [[Set_(mathematics)]] · [[Share_price]] · [[Sharkovskii's_theorem]] · [[Ship]] · [[Simply_connected_space]] · [[Sinai–Ruelle–Bowen_measure]] · [[Singularity_(mathematics)]] · [[Singular_measure]] · [[Skyscraper]] · [[Smoothness]] · [[Smooth_dynamics]] · [[Solar_System]] · [[Soliton]] · [[Spacecraft]] · [[Stability_theory]] · [[Stable_manifold]] · [[Stable_manifold_theorem]] · [[Standard_map]] · [[State-space_representation]] · [[State_space_(computer_science)]] · [[Statistical_mechanics]] · [[Statistics]] · [[Steady_state]] · [[Stephen_Smale]] · [[Steven_Strogatz]] · [[Stochastic]] · [[Stochastic_differential_equation]] · [[Stochastic_process]] · [[Stone–Čech_compactification]] · [[Structural_stability]] · [[Structure]] · [[Superposition_principle]] · [[Svetlana_Jitomirskaya]] · [[Swinging_Atwood's_machine]] · [[Symbolic_dynamics]] · [[Symmetry]] · [[Symplectic_geometry]] · [[Symplectic_manifold]] · [[Synchronization_of_chaos]] · [[Systems_engineering]] · [[Systems_theory]] · [[System_dynamics]] **T** — [[Takens's_theorem]] · [[Tangent_bundle]] · [[Tangent_space]] · [[Tent_map]] · [[Thermodynamic_state]] · [[Thermohaline_circulation]] · [[Three-body_problem]] · [[Tick_size]] · [[Tilt-A-Whirl]] · [[Time]] · [[Time-scale_calculus]] · [[Time-translation_symmetry]] · [[Time_evolution]] · [[Tinkerbell_map]] · [[Topological_conjugacy]] · [[Topological_dynamics]] · [[Topological_group]] · [[Topological_space]] · [[Topology]] · [[Torus]] · [[Trajectory]] · [[Transfer_operator]] · [[Tuple]] · [[Turbulence]] · [[Turing_machine]] · [[Tycho_Brahe]] **U** — [[Unbounded_operator]] **V** — [[Van_der_Pol_oscillator]] · [[Variational_principle]] · [[Vector_field]] · [[Vector_space]] · [[Velocity]] · [[Vladimir_Arnold]] · [[Volume]] **W** — [[Wayback_Machine]] · [[Weather_forecasting]] · [[Welington_de_Melo]] **Y** — [[Yakov_Sinai]] **Z** — [[Zaslavskii_map]] **#** — [[Σ-algebra]] ## Route objects (§10.3 stubs — placeholders declared in `_registry/firebase/`) - **microsim** — `microsim/{library}/Dynamical_system__{YYYYMMDD}T{HHMM}Z/` - **songs** — `songs/{Band_name}/{Song_name}/Dynamical_system/` - **semiotics** — `semiotics/{authorizer}/{set}/{Song_name}/{audio_video_id}/Dynamical_system/` - **cardset** — `cardset/{authorizer}/{set}/Dynamical_system/` - **games** — `games/quizzes/Dynamical_system/` - **channel_stream** — `channel_stream/Dynamical_system/` - **transcripts** — `transcripts/{audio_video_id}/Dynamical_system/` Hub + children route keys are pre-declared in `_registry/firebase/expansion_matches.csv` (54,000 Related Wikipedia Matches). Minting any leaf passes §10.1 registration.  --- *Repopulated 2026-09-19 · append-only · source: _tools/generate/g34_portal_section_sims.py@36068b13 (players of the linked articles, each URL 200-checked) · 1 added · 0 deletions*