# Chaos theory
<!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside -->
## Microsims — p5.js
### Chaos theory (p5.js) · `sensitive x₀`
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/Q97Yq6fHC" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Chaos theory — p5.js microsim"></iframe>
</div>
*Deterministic systems so sensitive to initial conditions they look random — order and unpredictability entwined.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/Q97Yq6fHC) · movement *IX · Foundations & the rest of the toolbox* · library `p5js`
### Related microsims
Live sims on neighbouring articles — 5 of them inside this article's own Wikipedia link tree:
- [[Bifurcation_theory]] *(in tree)*
- [[Functional_analysis]] *(in tree)*
- [[Information_theory]] *(in tree)*
- [[Nonlinear_system]] *(in tree)*
- [[Weather_forecasting]] *(in tree)*
- [[Analog_signal]]
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
<!-- MICROSIMGEN:END -->
## MicroSim spec
- **Recommended sim type:** phase-space plot
- **Microsimmability score:** 96/100
- **Layout:** phase-space (x vs x') plot on the canvas; sliders below.
### Parameters (tunable controls)
- `Control parameter`
- `Initial condition`
- `Time step dt`
### What animates
A trajectory traces through [[Phase_space|phase space]], revealing fixed points, limit cycles, or a strange attractor as the control parameter is tuned.
### Learning objective
Show how a control parameter reshapes a system's long-term behavior in phase space.
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Chaos_theory.json (2026-07-30T02:09:12Z) -->
`Adolf_Zeising` · `Aftershock` · `Airplane` · `Alan_Turing` · `Albert_J._Libchaber` · `Aleksandr_Lyapunov` · `Almost_all` · `American_Association_for_the_Advancement_of_Science` · `American_Mathematical_Society` · `Amie_Wilkinson` · `Amplitude_death` · `Annales_Henri_Poincaré` · `Anosov_diffeomorphism` · `Anthropology` · `Aristid_Lindenmayer` · `Arnold's_cat_map` · `Arnold_tongue` · `Astrophysics` · `Asymptotic_analysis` · [[Attractor]] · `Audrey_Terras` · `Axiom_A` · `BEAM_robotics` · `Baker's_map` · `Barnsley_fern` · `Benoit_Mandelbrot` · `Bernardo_Huberman` · `Bifurcation_diagram` · [[Bifurcation_theory]] · `Biology` · `Boris_Chirikov` · `Brazil` · `Brosl_Hasslacher` · `Bryna_Kra` · `Butterfly_effect` · `Butterfly_effect_in_popular_culture` · `Camouflage` · `Canada_lynx` · `Cantor_set` · `Cardiac_cycle` · `Cardiotocography` · `Caroline_Series` · [[Catastrophe_theory]] · `Causality` · `Celestial_mechanics` · [[Cellular_automaton]] · `Celso_Grebogi` · `Chaos:_Making_a_New_Science` · `Chaos_game` · `Chaos_machine` · `Chaotic_cryptology` · `Chaotic_mixing` · `Chaotic_scattering` · `Chen_Guanrong` · `Chirikov_criterion` · [[Christiaan_Huygens]] · `Chua's_circuit` · `Clifford_A._Pickover` · `Cliodynamics` · `Complete_metric_space` · [[Complex_adaptive_system]] · `Complex_quadratic_polynomial` · [[Complexity]] · `Computational_Statistics_&_Data_Analysis` · `Computational_neuroscience` · [[Computer_science]] · `Conservative_system` · `Continuous_function` · `Contour_advection` · `Control_of_chaos` · `Conus_textile` · `Correlation_dimension` · [[Coupled_map_lattice]] · `Crisis_management` · `Crop` · `Cryptographic_primitive` · `Cryptographically_secure_pseudorandom_number_generator` · `Cryptography` · `Crystal` · [[Crystal_structure]] · `D'Arcy_Wentworth_Thompson` · `David_Malone_(independent_filmmaker)` · `David_Ruelle` · `Dense_set` · `Derek_Muller` · `Determinism` · `Deterministic_system` · `Dietmar_Saupe` · [[Differential_equation]] · `Digital_watermarking` · `Dimension` · `Dimension_(vector_space)` · `Discrete_mathematics` · `Double_pendulum` · `Duffing_equation` · `Duffing_map` · `Dune` · `Dyadic_transformation` · `Dye` · `Dynamical_billiards` · [[Dynamical_system]] · `Earthquake` · [[Ecology]] · `Economic_bubble` · `Economics` · `Econophysics` · `Edge_of_chaos` · [[Edward_Norton_Lorenz]] · `Edward_Ott` · `Elastic_pendulum` · [[Electrical_engineering]] · `Ellen_Fetter` · [[Emergence]] · `Empedocles` · `Encyclopedia_of_Mathematics` · [[Engineering]] · `Environmental_science` · `Epidemic` · `Ergodic_theory` · `Ergodicity` · `Ernst_Haeckel` · `European_Journal_of_Obstetrics_&_Gynecology_and_Reproductive_Biology` · `Exponential_growth` · `Exponential_map_(discrete_dynamical_systems)` · `Eye_movement` · `Fermi–Pasta–Ulam–Tsingou_problem` · `Fibonacci` · `Finance` · `Financial_market` · `Floral_symmetry` · `Florence` · `Floris_Takens` · [[Fluid_dynamics]] · `Foam` · [[Fractal]] · `Fractal_dimension` · `Fracture` · `Free_content` · [[Functional_analysis]] · `Gauss_iterated_map` · `Geology` · `George_David_Birkhoff` · `Gerald_Teschl` · `Gingerbreadman_map` · `Greg_Sams` · `Group_development` · `Gutenberg–Richter_law` · `Halting_problem` · `Hausdorff_dimension` · `Hee_Oh` · `Heinz-Otto_Peitgen` · `Henri_Poincaré` · `Hill_differential_equation` · `Horseshoe_map` · `Hydrology` · `Hénon_map` · `Hénon–Heiles_system` · `Ian_Stewart_(mathematician)` · `Ikeda_map` · [[Ilya_Prigogine]] · `Infinitesimal` · [[Information_theory]] · `Initial_condition` · `Interval_(mathematics)` · `Interval_exchange_transformation` · `Intrauterine_hypoxia` · `Invariant_measure` · `Irrational_rotation` · `Isabelle_Stengers` · `Italy` · `Itamar_Procaccia` · `Iterated_function_system` · `Iteration` · `Ivar_Ekeland` · `Ivars_Peterson` · `J._Doyne_Farmer` · `Jacques_Hadamard` · `James_A._Yorke` · `James_Clerk_Maxwell` · `James_Gleick` · `James_P._Crutchfield` · `Jean-Pierre_Eckmann` · `Jean_Bellissard` · `John_Briggs_(author)` · `John_Edensor_Littlewood` · `John_Guckenheimer` · `Joseph_Plateau` · `Journal_of_Hydrology` · `Julia_set` · `Jump_process` · `Kaplan–Yorke_map` · `Kicked_rotator` · `Kolmogorov_automorphism` · `Kolmogorov–Arnold–Moser_theorem` · `Krylov–Bogolyubov_theorem` · `Kuramoto_model` · `Kurt_Wiesenfeld` · `Kármán_vortex_street` · `LGP-30` · `Lai-Sang_Young` · `Landslide` · `Langton's_ant` · `Leon_Glass` · `Leon_O._Chua` · `Lev_Landau` · `Liber_Abaci` · `Limit_cycle` · `Limit_set` · `Linear_system` · `Liouville's_theorem_(Hamiltonian)` · `List_of_chaotic_maps` · [[Logarithmic_spiral]] · `Logistic_map` · `Lorenz_system` · `Lotka–Volterra_equations` · `Lyapunov_exponent` · [[Lyapunov_stability]] · `Lyapunov_time` · `Mackey–Glass_equations` · `Mandelbrot_set` · `Map_(mathematics)` · `Marcelo_Viana` · `Margaret_Hamilton_(software_engineer)` · `Martin_Gutzwiller` · [[Mary_Cartwright]] · `Mary_Rees` · `Mary_Tsingou` · [[Mathematical_model]] · `Mathematics` · `Mathematics_and_art` · `Meander` · `Measure-preserving_dynamical_system` · `Measure_(mathematics)` · `Menger_sponge` · `Meteorology` · `Metric_space` · `Michael_Berry_(physicist)` · `Michel_Hénon` · `Mimicry` · `Mitchell_Feigenbaum` · `Mixing_(mathematics)` · `Moons_of_Pluto` · `Multiscroll_attractor` · `National_Institute_of_Mental_Health` · `Natural_selection` · `Neuron` · `New_York_Academy_of_Sciences` · `Niles_Eldredge` · `Nina_Snaith` · `Non-Euclidean_geometry` · [[Nonlinear_system]] · `Norman_Packard` · `Numerical_analysis` · `Office_of_Naval_Research` · `On_Growth_and_Form` · `Open_set` · `Orbit_(dynamics)` · `Otto_Rössler` · `Outer_billiards` · `Pandemic` · `Paradigm_shift` · `Parameter` · `Parastichy` · [[Particle_swarm_optimization]] · `Passive_dynamics` · `Pathogen` · [[Pattern_formation]] · `Pattern_recognition_(psychology)` · `Patterns_in_nature` · `Per_Bak` · `Period-doubling_bifurcation` · `Periodic_point` · `Peter_Grassberger` · [[Phase_space]] · [[Phase_transition]] · `Philip_Holmes` · `Philosophy` · `Phyllotaxis` · `Physical_Review_Letters` · [[Physics]] · `Physiology` · `Pierre_Hohenberg` · `Plane_(mathematics)` · `Plasma_confinement` · `Plateau's_laws` · `Plato` · `Poincaré_map` · `Poincaré_recurrence_theorem` · `Poincaré–Bendixson_theorem` · `Politics` · [[Population_dynamics]] · [[Population_model]] · [[Predictability]] · `Predictive_modelling` · `Predrag_Cvitanović` · `Princeton_University_Press` · `ProQuest` · `Providence,_Rhode_Island` · `Pseudorandom_noise` · `Punctuated_equilibrium` · `Pythagoras` · `Quantum_chaos` · `Quantum_field_theory` · [[Quantum_mechanics]] · `Quantum_turbulence` · [[Quasicrystal]] · `Quasiperiodicity` · `Rabinovich–Fabrikant_equations` · `Ralph_Abraham_(mathematician)` · `Randomness` · `Rayleigh–Bénard_convection` · `Recurrence_plot` · `Recurrence_quantification_analysis` · `Robert_L._Devaney` · `Robert_May,_Baron_May_of_Oxford` · `Robert_Shaw_(physicist)` · `Rufus_Bowen` · `Rule_30` · `Rössler_attractor` · `Santa_Fe_Institute` · `Scale_invariance` · `Schizophrenia` · [[Schrödinger_equation]] · `Scientific_American` · `Scientific_method` · `Second-countable_space` · `Self-assembly` · [[Self-organization]] · [[Self-organized_criticality]] · `Self-similarity` · `Sexual_selection` · `Shadowing_lemma` · `Sharkovskii's_theorem` · `Smoothness` · `Soap_bubble` · `Sociology` · `Solar_flare` · `Spontaneous_symmetry_breaking` · `Stability_theory` · `Stable_manifold` · `Stable_manifold_theorem` · `Standard_map` · `Statistical_population` · `Steganography` · `Stephen_Jay_Gould` · `Stephen_Smale` · `Steven_Strogatz` · `Stochastic` · `Stochastic_differential_equation` · `Stock_market` · `Supersymmetric_theory_of_stochastic_dynamics` · `Svetlana_Jitomirskaya` · `Swinging_Atwood's_machine` · `Symmetry` · `Symmetry_in_biology` · `Synchronization_of_chaos` · `Takens's_theorem` · `Team_building` · `Telephone` · `Tent_map` · [[Tessellation]] · `Texas` · `The_Chemical_Basis_of_Morphogenesis` · `The_Fractal_Geometry_of_Nature` · `The_Structure_of_Scientific_Revolutions` · [[Theoretical_ecology]] · `Thomas_Kuhn` · `Three-body_problem` · `Tilt-A-Whirl` · [[Time_series]] · `Tinkerbell_map` · `Topological_conjugacy` · `Topological_quantum_field_theory` · `Topology` · `Tornado` · `Trajectory` · `Turbulence` · `Turing_machine` · `Universality_(dynamical_systems)` · `University_of_Nottingham` · `Van_der_Pol_oscillator` · [[Viscosity]] · `War` · `Water_cycle` · [[Wave]] · [[Wayback_Machine]] · [[Weather_forecasting]] · `Widmanstätten_pattern` · `Wiktionary` · `Wilson_Bentley` · `Wingtip_vortices` · `Wolf_Prize_in_Physics` · `Yakov_Sinai` · `Zaslavskii_map` · `Étienne_Ghys`
<!-- GIFPLATE:BEGIN v1.0 g16 — Commons hotlink; do not hand-edit inside -->
## Images
<figure class="wt-gifplate">
<img src="https://commons.wikimedia.org/wiki/Special:FilePath/Demonstrating_Chaos_with_a_Double_Pendulum.gif" alt="Chaos & Sensitivity" loading="lazy" decoding="async">
<figcaption><strong>Chaos & Sensitivity</strong> — Demonstrate sensitive dependence on initial conditions in chaotic systems.<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:Demonstrating_Chaos_with_a_Double_Pendulum.gif">Details</a></span></figcaption>
</figure>
*Still companion to the 1 live microsim above: the sim is the instrument, the plate is the glance. §15 keeps the player first; this sits in the image slot on [[Chaos_theory]].*
<!-- GIFPLATE:END -->
## From the vault media library
!Chaos theory thumb.png
*Chaos Theory — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.*
<!-- LOCAL-MEDIA-PASS:END -->
> p5.js MicroSim stub · part of [[System]] · [Wikipedia source](https://en.wikipedia.org/wiki/Chaos_theory)
> Relation: subfield of System.
## Concept summary
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions.
## Build checklist
- [ ] Claim it: set `status: in-progress` + `lease` + `leased_at`
- [ ] Write the child page explaining the concept (tie it back to system)
- [ ] Finalize parameter ranges and defaults
- [ ] Implement the p5.js sketch (drawing + control regions)
- [ ] Add caption + the learning objective on the page
- [ ] Set `status: done`
## p5.js sketch
```javascript
// MicroSim: Chaos theory
let controls = {};
function setup() {
// createCanvas(...); create sliders for the parameters above.
}
function draw() {
// background(...); read controls; render phase-space plot; respond live.
}
```
---
Back to [[System]] · Wikipedia: [Chaos theory](https://en.wikipedia.org/wiki/Chaos_theory)
---
<!-- SEMIOTIC-PROFILE:START -->
## Semiotic profile
> *The semiotic universals this article invokes, machine-derived from the crossref — **unverified** (born so). Populated 2026-07-06 for the Systems room.*
**Universals (6):** 🟢 attractor chaos (25) · 🟡 system (20) · 🟡 science (5) · 🟢 bifurcation (3) · 🟢 iteration (3) · 🟢 cycle (1)
**Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal
<!-- SEMIOTIC-PROFILE:END -->
<!-- LOCAL-MEDIA-PASS:START -->
<!-- CRAFT-LINK:START g12 -->
*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Chaos_theory) : [Wikitube](https://en.wikitube.io/wiki/Chaos_theory)
## Previous hub tags
Tree parents: [[Complex_system]] · [[Cybernetics]] · [[Decision_theory]] · [[Dynamical_system]] · [[Emergence]] · [[Feedback]] · [[Phase_space]] · [[Self-organization]] · [[System_dynamics]] · [[Systems_science]] · [[Systems_theory]].
Legacy hubs: none.
---
*Sources: 3 legacy notes. Minted wave 1, 2026-07-30 (v1.6 order).*