Chaos Studies

Getting started with Chaos Studies

Controls, settings and music for Chaos Studies on iPhone, iPad, Mac and Playdate.

What Chaos Studies is

Chaos Studies is a real-time 3D visualisation of chaotic dynamical systems: strange attractors drawn as animated point clouds. Nine mathematical systems, each with its own visual character, respond to your hands and play a soundtrack placed in space around you.

It runs on iPhone, iPad and Mac from one App Store purchase, and on Playdate through the Playdate Catalog, bought separately.

The attractors

Each attractor is a set of differential equations that produce deterministic but unpredictable motion. Points trace the attractor’s shape in real time, building up a cloud that shows the underlying structure.

  1. Lorenz: the classic butterfly. Two lobes connected by a narrow bridge, the system that started chaos theory.
  2. Rössler: a single-wing spiral that folds back on itself.
  3. Aizawa: intertwined loops with a dense, layered structure.
  4. Burke-Shaw: compact and tightly wound, with fine internal detail.
  5. Halvorsen: three symmetric wings around the centre.
  6. Chen: a Lorenz-like system with wider, more distinct lobes.
  7. Nose-Hoover: the default. Smooth orbital paths with deceptive complexity.
  8. Sprott B: energetic, spray-like motion in a tight pattern.
  9. Dadras: fast-moving and multi-layered, with a flowing character.

The field guide has the equations, parameters and history of each one.

iPhone, iPad and Mac

Controls

  • Drag to orbit around the attractor
  • Pinch to zoom in and out
  • Tap to trigger an explosion: the points scatter and reform
  • Tilt the device for parallax depth (iPhone and iPad, not Mac)

Release a drag and the rotation carries on with its momentum.

Settings

The menu screen has buttons in the top right for music and speed settings, help, and dark mode. On iPhone and iPad, shaking the device opens more settings:

  • Dark mode: white points on black, or black on white
  • Show grid: the geodesic wireframe overlay
  • Haptics: tactile feedback on interactions

Music

Chaos Studies has seven spatial audio stems placed around the listener. As you rotate the camera, the mix shifts: each stem pans and gets quieter or louder with its position relative to the view.

Five presets set the mix:

  • Calm: tings, pad, drone, cello. Ambient and relaxing.
  • Crisp: tings, pad, percussion. Brighter and rhythmic.
  • Cine: tings and cello only.
  • Driven: all stems.
  • None: silence. Pick your own stems in the settings.

Each stem can also be turned on or off on its own.

Playdate

On Playdate the same nine attractors are drawn in 1-bit: thousands of points on a 400 × 240 screen. The Playdate page has more on how this version differs.

  • Up and down: choose an attractor
  • A button: start the visualisation
  • Left and right: add spin
  • B button: open the instructions

Visualisation

  • Crank: rotate vertically around the attractor
  • Up and down: zoom in and out
  • Left and right: add horizontal spin with momentum
  • A button: restart, with the explosion
  • B button: back to the menu
  • Tilt: a subtle parallax depth effect

Settings

In the Playdate system menu:

  • Dark mode: invert the colours
  • Crank hint: show or hide the crank indicator when the crank is docked
  • Music: choose Calm, Crisp or None

The explosion

Tapping (iPhone, iPad and Mac) or pressing A (Playdate) starts a multi-phase animation: the points implode toward the centre, a ripple scatters them outward, then the attractor explodes into a starfield before it reforms.

Use it to reset the visualisation, or just to watch it.

Next steps