Phase Space Explorer — RageBuilder

Why this project?

Strange attractors are among the most beautiful objects in mathematics — they emerge from simple differential equations yet produce infinitely complex, never-repeating trajectories. While 3D visualizations of attractors exist online, none let you hear the chaos while simultaneously tuning the system's parameters in real time. This project bridges visual mathematics and auditory perception: your trajectory through phase space becomes both a sculpture and a soundscape.

What is it?

An interactive explorer for nonlinear dynamical systems. You select a system of ordinary differential equations (like the Lorenz or Rössler attractor), and the app integrates them in real time using 4th-order Runge-Kutta, rendering the resulting 3D trajectory on canvas. Parameters are live-tunable — change a single value and watch the entire geometry morph. Enable audio to hear the system's state mapped to pitch, timbre, and rhythm via the Web Audio API.

How does it work?

RK4 Integration: Each attractor is defined by 3 coupled ODEs. The system advances the state vector using classical Runge-Kutta (4th order) for accuracy at each frame.
3D Projection: Manual perspective projection — no WebGL or Three.js. Points are rotated by user-controlled yaw/pitch angles, then projected onto 2D canvas with depth-based sizing and opacity.
Color Trails: Each point's color is derived from its position in phase space, mapped through HSL color gradients. The trail is a ring buffer capped at the configured length.
Sonification: Three oscillators (one per state variable x, y, z) map trajectory coordinates to musical frequencies using logarithmic scaling. A low-pass filter shapes timbre based on velocity magnitude. Gain is modulated by the system's Lyapunov-like divergence rate.

How to use it

Rotate view: Click and drag on the canvas to orbit the camera around the attractor.
Zoom: Scroll wheel (or pinch on mobile) to zoom in/out.
Select system: Use the dropdown in the control panel to switch between Lorenz, Rössler, Aizawa, Thomas, Halvorsen, and Sprott attractors.
Tune parameters: Drag sliders to change system parameters in real time. Watch how small changes can dramatically alter the geometry — this is chaos.
Presets: Click preset buttons to load famous parameter combinations (e.g., Lorenz's original σ=10, ρ=28, β=8/3).
Audio: Click "Audio Off" to toggle sonification. Each state variable drives an oscillator — together they create an eerie, ever-shifting drone.
Keyboard shortcuts: R reset trajectory, Space pause/resume, A toggle audio.