# Catastrophe theory
<!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside -->
## Microsims — three.js
### Catastrophe theory (three.js)
<div class="microsim-player">
<iframe src="https://wikitube-3d-microsims.netlify.app/Catastrophe_theory.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Catastrophe theory — three.js microsim"></iframe>
</div>
**Open it full-screen:** [Catastrophe_theory.html](https://wikitube-3d-microsims.netlify.app/Catastrophe_theory.html) · library `threejs` · route `microsim/threejs/`
### Related microsims
Live sims on neighbouring articles — 1 of them inside this article's own Wikipedia link tree:
- [[Bifurcation_theory]] *(in tree)*
- [[Attractor]]
- [[Dissipative_system]]
- [[Hierarchy]]
- [[Scale-free_network]]
- [[Synchronization]]
*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|phase space]] / [[Attractor|attractor]]
- **Microsimmability score:** 84/100
- **Layout:** drawing region (canvas) on top; control region (sliders/buttons) below.
### Parameters (tunable controls)
- `Control x`
- `Control y`
- `Slow drive`
### What animates
A state slides smoothly then jumps suddenly as the control parameters cross a fold.
### Learning objective
Show how smooth parameter changes can trigger abrupt jumps in state.
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Catastrophe_theory.json (2026-07-30T02:09:12Z) -->
`ADE_classification` · `Airy_function` · `Ak_singularity` · [[Bifurcation_theory]] · `Butterfly_effect` · `Caustic_(optics)` · [[Chaos_theory]] · `Christopher_Zeeman` · `Cloud_condensation_nuclei` · [[Complex_system]] · [[Control_theory]] · `Critical_point_(mathematics)` · `Cusp_(singularity)` · `Dark_matter` · `Diffeomorphism` · `Domino_effect` · [[Dynamical_system]] · [[Emergence]] · `Encyclopedia.com` · `Focal_surface` · [[Geometry]] · `Germ_(mathematics)` · `Hysteresis` · `Ian_Stewart_(mathematician)` · `Inflection_point` · `Landslide` · `Lyapunov_function` · `Magnitude_(mathematics)` · `Mathematics` · `Morphology_(biology)` · `Morse_theory` · `Nature_(journal)` · `Optics` · `Outer_sphere_electron_transfer` · `Parameter_space` · `Pearcey_integral` · [[Phase_transition]] · `Pitchfork_bifurcation` · `Punctuated_equilibrium` · `Quasar` · `Rainbow` · `René_Thom` · `Saddle-node_bifurcation` · `Salvador_Dalí` · `Scalar_potential` · `Scientific_American` · `Simple_Lie_group` · `Singularity_theory` · `Snowball_effect` · `Spontaneous_symmetry_breaking` · `Structural_fracture_mechanics` · `Structural_stability` · `Taylor_series` · `The_Swallow's_Tail` · `Tim_Poston` · `Umbilical_point` · `Valentin_Afraimovich` · `Vladimir_Arnold`
## From the Real GENERATIVE library
*Catastrophe theory — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Information room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Fold_bifurcation.svg).*
*Animated: Catastrophe theory — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Information room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:Fold_catastrophe_animation.gif).*
> In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. ([Wikipedia](https://en.wikipedia.org/wiki/Catastrophe_theory))
<!-- REAL-GENERATIVE-MEDIA:END -->
> p5.js MicroSim stub · part of Systems Thinking · [Wikipedia source](https://en.wikipedia.org/wiki/Catastrophe_theory)
> Relation: subfield of systems thinking.
## Concept summary
In mathematics, catastrophe theory is a branch of [[Bifurcation_theory|bifurcation theory]] in the study of dynamical systems; it is also a particular special case of more general singularity theory in [[Geometry|geometry]].
## Build checklist
- [ ] Claim it: set `status: in-progress` + `lease` + `leased_at`
- [ ] Write the child page explaining the concept (tie it back to systems thinking)
- [ ] 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: Catastrophe theory
let controls = {};
function setup() {
// createCanvas(...); create sliders for the parameters above.
}
function draw() {
// background(...); read controls; render phase space / attractor; respond live.
}
```
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Back to Systems Thinking · Wikipedia: [Catastrophe theory](https://en.wikipedia.org/wiki/Catastrophe_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 (4):** 🟡 system (7) · 🟢 attractor chaos (4) · 🟢 bifurcation (2) · 🟡 geometry (2)
**Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal
<!-- SEMIOTIC-PROFILE:END -->
<!-- REAL-GENERATIVE-MEDIA:START -->
## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Catastrophe_theory) : [Wikitube](https://en.wikitube.io/wiki/Catastrophe_theory)
## Previous hub tags
Tree parents: [[Control_theory]] · [[Cybernetics]] · [[Decision_theory]] · [[Emergence]] · [[Information_theory]] · [[Systems_theory]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*