Phase Space

Equations, evolved until they breathe.

A generative audio-visual installation by Joshua Borsman. Chaotic dynamical systems rendered in real-time WebGL and sonified through modal resonator synthesis. Each equation sings the shape of its own chaos.

Strange Attractors
  • Lorenz
  • Rössler
  • Thomas
  • Aizawa
  • Halvorsen
  • Chen
  • Chua's Circuit
  • Arneodo
 
  • Dadras
  • Sprott B
  • Burke-Shaw
  • Rabinovich-Fabrikant
  • Nose-Hoover
  • Newton-Leipnik
  • Finance
  • Four-Wing
Dynamical Systems
  • Gray-Scott Reaction-Diffusion
  • Double Pendulum Ensemble
  • Kuramoto Coupled Oscillators
drag orbit   scroll zoom   R toggle rotation   B toggle bloom   space pause

Sound on · Headphones recommended

Initializing · · ·
drag · scroll · [r] rotate · [b] bloom · [m] mute · [i] about · [space] pause
by Joshua Borsman
SOUND
WEB AUDIO
CV OUT

Phase Space

Equations, evolved until they breathe.

About the Work

Phase Space is a generative audio-visual installation that renders chaotic dynamical systems as both light and sound. Sixteen strange attractors and three dynamical systems unfold in real time, their trajectories sonified through modal resonator synthesis — each equation singing the shape of its own chaos.

The mathematics drive everything. Particle positions map to pitch. Velocity determines brightness. Zero-crossings and direction reversals trigger plucked-string resonances that decay into long reverberant tails. The result is an evolving soundscape that could play for hours without repetition — because chaos, by definition, never repeats.

The piece can operate in two modes: as a self-contained browser experience using Web Audio synthesis, or as a control surface for analog modular rack gear, sending control voltages to hardware synthesizers via DC-coupled audio interfaces.

Systems

Lorenz, Rössler, Thomas, Aizawa, Halvorsen, Chen, Dadras, Sprott B, Burke-Shaw, Rabinovich-Fabrikant, Nose-Hoover, Newton-Leipnik, Chua’s Circuit, Arneodo, Finance, Four-Wing — sixteen strange attractors integrated via fourth-order Runge-Kutta. Gray-Scott reaction-diffusion, double pendulum ensemble (350 near-identical initial conditions diverging into chaos), and Kuramoto coupled oscillators demonstrating spontaneous synchronization.

Technology

WebGL (Three.js) for rendering. Web Audio API for modal resonator pluck synthesis, algorithmic reverb, and multi-tap delay. DC-coupled CV output for analog modular rack gear. Single HTML file, no build step, no dependencies beyond the browser.

Artist

Joshua Borsman makes work that treats environmental and physical phenomena as collaborators rather than subjects. Trained in engineering and signal processing, he builds instruments — sculptural, sonic, kinetic — that render unseen forces into perceptible form.

joshuaborsman.com