# Chaos Studies

> Chaos Studies by Field Bureau + Werkstatt is an app that draws nine strange attractors in real-time 3D as clouds of particles, with a seven-stem spatial soundtrack that rotates with the view. It runs on iPhone, iPad and Mac ($1.99, one universal App Store purchase) and on Playdate ($2.99 in the Playdate Catalog). No score, no goal, no account, no tracking.

- Publisher: Field Bureau + Werkstatt (https://fieldbw.com). Chaos Studies is the first piece in its ET Series.
- Attractors: Lorenz, Rössler, Aizawa, Burke-Shaw, Halvorsen, Chen, Nose-Hoover, Sprott B, Dadras.
- Each particle is laid down red and cools as it ages; the coldest are recycled first.
- Controls: drag to orbit, pinch to zoom, tap to scatter the points (implode and explode), tilt parallax on iPhone, iPad and Playdate; the crank turns the attractor on Playdate.
- Sound: seven loops composed on the teenage engineering OP-XY, placed around the listener (tings above, pad below, percussion in front, cello behind, drone left, bass right, kick centre); presets Calm, Crisp, Cine, Driven, None.
- The Playdate version came first (1-bit, crank, custom C module for the point tracking).

## Buy

- [App Store: iPhone, iPad and Mac, $1.99](https://apps.apple.com/us/app/chaos-studies/id6758313363)
- [Playdate Catalog: $2.99](https://play.date/games/chaos-studies/)

## Field guide

- [All nine attractors side by side](https://chaosstudies.app/attractors): equations, parameters, divergence and origin in one table.
- [Lorenz attractor](https://chaosstudies.app/attractors/lorenz): The Lorenz attractor is the butterfly-shaped set that the Lorenz equations trace in three dimensions. A point circles one of two wings, then switches to the other at moments nobody can predict. Parameters: σ = 10, ρ = 28, β = 8/3.
- [Rössler attractor](https://chaosstudies.app/attractors/rossler): The Rössler attractor is a single chaotic band. A point spirals outward near a plane, is lifted, folds over and drops back into the middle of the spiral. Parameters: a = 0.2, b = 0.2, c = 5.7.
- [Aizawa attractor](https://chaosstudies.app/attractors/aizawa): The Aizawa attractor is a chaotic flow that winds around a sphere-like shell and threads a narrow tube along its axis. Parameters: a = 0.95, b = 0.7, c = 0.6, d = 3.5, e = 0.25, f = 0.1.
- [Burke-Shaw attractor](https://chaosstudies.app/attractors/burke-shaw): The Burke-Shaw attractor is a two-lobed chaotic system derived from the Lorenz equations, compact and tightly wound. Parameters: s = 10, v = 4.272.
- [Halvorsen attractor](https://chaosstudies.app/attractors/halvorsen): The Halvorsen attractor is a chaotic system with three identical wings arranged around the diagonal x = y = z. Parameters: a = 1.89.
- [Chen attractor](https://chaosstudies.app/attractors/chen): The Chen attractor is a two-winged chaotic system closely related to Lorenz, with wider lobes and a busier crossing between them. Parameters: a = 40, b = 3, c = 28.
- [Nose-Hoover attractor](https://chaosstudies.app/attractors/nose-hoover): The Nosé-Hoover attractor comes from a thermostat used in molecular dynamics: a spring-like oscillator coupled to a variable that nudges its energy toward a set temperature. Parameters: no free parameters.
- [Sprott B attractor](https://chaosstudies.app/attractors/sprott-b): Sprott B is one of the simplest known chaotic flows: three equations with five terms, two of them quadratic. Parameters: no free parameters.
- [Dadras attractor](https://chaosstudies.app/attractors/dadras): The Dadras attractor is a chaotic system of overlapping scrolls whose look changes a great deal with the viewing angle. Parameters: a = 3, b = 2.7, c = 1.7, d = 2, e = 9.

## Learn

- [What is a strange attractor](https://chaosstudies.app/what-is-a-strange-attractor): the definition, fixed points and limit cycles, fractal dimension, divergence, and a live simulation.
- [The butterfly effect](https://chaosstudies.app/attractors/lorenz#butterfly-effect): two Lorenz trajectories that start 0.00001 apart, separating live, with the history of the name.
- [Chaos Studies on Playdate](https://chaosstudies.app/playdate): the 1-bit original, its controls, music and how it differs from the Apple version.
- [Getting started](https://chaosstudies.app/docs/getting-started): controls, settings and music on each platform. Markdown: https://chaosstudies.app/docs/getting-started.md

## Legal

- [Privacy](https://chaosstudies.app/privacy): the app collects, stores and transmits no personal data.
- [Terms of service](https://chaosstudies.app/terms): what the app does, its system requirements (iOS and iPadOS 17.6, macOS 14.0, Playdate) and how it is licensed.