What is Chaos Studies?
Chaos Studies is a real-time 3D visualization of chaotic dynamical systems — strange attractors rendered as animated point clouds. Nine mathematical systems, each with unique visual character, come to life through interactive controls, spatial audio, and smooth animation.
Available on iOS, macOS, and Playdate.
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 reveals the underlying structure.
- Lorenz — The classic butterfly. Two lobes connected by a narrow bridge, the system that started chaos theory.
- Rossler — A single-wing spiral that folds back on itself.
- Aizawa — Complex intertwined loops with a dense, layered structure.
- Burke-Shaw — Compact and tightly wound, with intricate internal detail.
- Halvorsen — Three symmetric wings radiating from the center.
- Chen — A Lorenz-like system with wider, more distinct lobes.
- Nose-Hoover — The default. Smooth orbital paths with deceptive complexity.
- Sprott B — Energetic, spray-like motion in a tight pattern.
- Dadras — Fast-moving, multi-layered, with a flowing character.
iOS and macOS
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 (iOS only)
Release a drag to see momentum carry the rotation forward.
Settings
The menu screen has buttons in the top right for music/speed settings, help, and a dark mode toggle. On iOS, shaking the device opens additional settings:
- Dark Mode — white points on black, or black on white
- Show Grid — toggle the geodesic wireframe overlay
- Haptics — tactile feedback on interactions
Music
Chaos Studies features seven spatial audio stems positioned around the listener. As you rotate the camera, the mix shifts — stems pan and attenuate based on their position relative to the view.
Five presets control the mix:
- Calm — Tings, pad, drone, cello. Ambient and relaxing.
- Crisp — Tings, pad, percussion. Brighter and rhythmic.
- Cine — Tings and cello only. Cinematic minimalism.
- Driven — All stems active. Full immersive mix.
- None — Silence. Pick your own stems from the settings.
Each stem can also be toggled individually.
Playdate
On Playdate, the same nine attractors are rendered in strict 1-bit graphics — thousands of points on a 400x240 screen.
Controls
Menu screen:
- Up/Down — select attractor
- A Button — launch visualization
- Left/Right — add spin
- B Button — open instructions
Visualization:
- Crank — rotate vertically around the attractor
- Up/Down — zoom in and out
- Left/Right — add horizontal spin with momentum
- A Button — restart with explosion animation
- B Button — back to menu
- Tilt — subtle parallax depth effect
Settings
Access via the Playdate system menu:
- Dark Mode — toggle inverted colors
- Crank Hint — show or hide the crank indicator when docked
- Music — choose Calm, Crisp, or None
The Explosion
Tapping (iOS/macOS) or pressing A (Playdate) triggers a multi-phase animation: points implode toward the center, a ripple wave scatters outward, then the attractor explodes into a starfield before reforming. The whole sequence takes about 1.2 seconds.
Use it to reset the visualization, or just because it looks good.
Next Steps
- The Attractors — what each of the nine systems looks like and where it comes from
- Chaos Primer — an introduction to chaos theory, dynamical systems, and the mathematics behind the app