DIRECTORY / SANDBOXES / STRANGE-ATTRACTORS.3D

STRANGE ATTRACTORS 3D

Chaotic differential equations, fractal dimensions, and orbital phase-space sonification.

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// CHAOTIC MANIFOLD SELECTOR

SIMULATION SPEED (dt) 1.0x

PARTICLE STREAM DENSITY 1200

TRAIL PERSISTENCE (PHOSPHOR) 0.92

MOUSE DRAG: 3D Orbit Rotate | SCROLL: Zoom | VELOCITY: Modulates Audio Pitch

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RESEARCH & LEARNING VAULT // Strange Attractors & Chaotic Phase Manifolds

Deterministic chaos, continuous differential flow, and Lyapunov sonification in 3D phase space.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Edward Lorenz discovered the butterfly attractor in 1963 while modeling atmospheric convection. Masaya Aizawa, René Thomas, and Otto Rössler expanded the catalog of bounded chaotic topological manifolds.

// GOVERNING EQUATIONS

\dot{x} = (z-b)x - dy, \quad \dot{y} = dx + (z-b)y, \quad \dot{z} = c + az - \frac{z^3}{3} - (x^2+y^2)(1+ez) + fz x^3

// BROWSER IMPLEMENTATION

Integrates continuous non-linear differential equations using 2nd-order Runge-Kutta (Midpoint method). Rotates in 3D orbital space and maps phase velocities directly into polyphonic WebAudio frequency modulation.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOX

1Aizawa Torus Collapse

🎯 Action:Select Aizawa Torus, set Speed to 2.0x, and rotate camera directly down the Z-axis.

✨ Observe:Observe particles funneling through the central quantum singularity before erupting into the outer toroidal shell.

// CURATED PAPERS, RFCS & RESOURCES

Deterministic Nonperiodic Flowpaper

By Edward N. Lorenz (1963)

The foundational paper on the butterfly attractor and sensitive dependence on initial conditions.