ChaosVision

Real-time 3D trajectory ribbons, Lyapunov divergence tracking, and live generative soundscapes.

ChaosVision is an interactive computational laboratory and generative art studio for non-linear dynamical systems, deterministic chaos, strange attractors, and fractal bifurcations.

Built with native ECMAScript modules, direct HTML5 Canvas projection pipelines, and the Web Audio API, ChaosVision operates with zero external build dependencies, zero framework overhead, and hardware-accelerated 60/120 FPS numerical simulation.

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Visual Exhibition Gallery

(1) 3D Continuous Attractors, (2) 2D Discrete Silk Manifolds, (3) Double Pendulum Swarm, (4) Feigenbaum Bifurcation Cascade.

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Key Features

1. High-Precision Numerical Integrators & Dynamics

• Runge-Kutta 4th-Order (RK4) Solver: High-precision numerical integration for continuous differential equations with adaptive sub-stepping (up to 64 steps/frame) and finite-number boundary recovery.
• Lagrangian Dynamics Engine: Simulates multi-pendulum mechanical systems with kinetic/potential energy monitoring and automatic rest-state re-energization when friction is adjusted.
• Visual Equation Editor & Multi-Equation AST Sandbox: Real-time visual math input with formatted LaTeX translation, 2D/3D multi-equation compiling ($x_{n+1}, y_{n+1}, z_{n+1}$), and isolated parameter scope.
• Lyapunov Divergence Tracking: Calculates Euclidean phase-space separation across parallel trajectories initialized with microscopic $10^{-4}$ offsets.
• 3D Phase-Space Feigenbaum Bifurcation Cascade: Canonical $(r, x_n, x_{n-1})$ delay-coordinate embedding combining classical 2D diagrams with 3D period-doubling spatial manifolds.
• Anti-Stall & Anti-Collapse Watchdog: Real-time velocity monitoring prevents discrete maps from collapsing into single-point equilibrium traps.

2. Unified Rendering & Camera Architecture

• Adaptive Density Accumulator: Accumulates millions of particle iterations with zoom-compensated batch scaling (up to $100,000+$ pts/frame) and adaptive point sizing to preserve luminosity.
• Unified 3D Perspective Projection Engine: Full 3-axis pitch, yaw, pan, and perspective scaling across continuous attractors, discrete maps, pendulums, and bifurcations.
• Inertial Multi-Touch Camera & Universal Auto-Rotation: Frame-rate independent constant angular velocity ($\omega = 0.15\text{ rad/s}$) across all systems with seamless drag-pause and instant resumption.
• Curated Designer Color Gradients: Bioluminescence, Cyberpunk, CRT Matrix Green, Solar Flare, Cosmic Nebula, Electric Amethyst, and Infrared.

3. Physics-Coupled Generative Zen Soundscapes (Web Audio API)

• 8-Voice Polyphonic Voice Pool: Discrete decaying singing bowl and crystal chime plucks with analog warm lowpass filtering.
• Harmonic Pentatonic Tuning: Calibrated to C Major 9 and A Minor scales ($C_4$ through $C_6$).
• 100% Deterministic Physics Alignment:
  • 3D Attractors: Orbital curvature turning cusps and $z$-elevation drive pitch and left-right panning.
  • Double Pendulum: Lagrangian kinetic energy peaks and outer bob height drive resonant singing bowls and celestial bell flips.
  • 2D Discrete Maps & Sandbox: Polar phase angle $\theta = \mathrm{atan2}(y, x)$ directly traces the fractal's geometric winding number.
  • Bifurcation Cascade: State coordinate $x$ sonifies pure harmonic intervals in periodic windows and complex shimmering chords in chaos.

4. Interactive Live Museum Tour

• Draggable Exhibit Deck: Floating, repositionable educational card synchronized with the live canvas simulation.
• Comprehensive 13-Exhibit Catalog: Covers Lorenz, Aizawa, Thomas, Rössler, Chen, Halvorsen, Clifford, De Jong, Tinkerbell, Ikeda, Gumowski-Mira, Double Pendulum Swarm, and Feigenbaum Bifurcation.
• Two-Way Control Sync: Switching systems in the control drawer updates the tour card instantly, and navigating exhibits updates the drawer.

5. Studio Exporters & State Serialization

• 4K Ultra-HD Wallpaper: Asynchronously renders a dedicated $3840 \times 2160$ offscreen PNG with supersampling off the main JS thread.
• Universal Vector SVG Export: Converts continuous 3D orbital loops, 20,000-point discrete maps, pendulums, and bifurcations into publication-ready <path> and <circle> vector artwork without artifacts.
• High-Fidelity Shareable URL State: Serializes multi-equations, math variables, camera transform, speed, decay, and color ramps with strict parameter schema isolation.

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Dynamical Systems Catalog

System Name	Type	Mathematical Formulation	Primary Parameters
Lorenz Attractor	3D Continuous	$\dot{x} = \sigma(y-x), \dot{y} = x(\rho-z)-y, \dot{z} = xy-\beta z$	$\sigma$ (Viscosity), $\rho$ (Heat), $\beta$ (Aspect)
Aizawa Attractor	3D Continuous	$\dot{x} = (z-b)x - dy, \dot{y} = dx + (z-b)y, \dot{z} = c + az - \frac{z^3}{3} - (x^2+y^2)(1+ez) + fzx^3$	$a$ (Growth), $d$ (Vortex), $e$ (Coupling)
Thomas Labyrinth	3D Continuous	$\dot{x} = \sin(y) - bx, \dot{y} = \sin(z) - by, \dot{z} = \sin(x) - bz$	$b$ (Energy Damping / Friction)
Rössler Attractor	3D Continuous	$\dot{x} = -y - z, \dot{y} = x + ay, \dot{z} = b + z(x - c)$	$a$ (Spiral), $c$ (Fold / Catapult)
Chen System	3D Continuous	$\dot{x} = a(y - x), \dot{y} = (c - a)x - xz + cy, \dot{z} = xy - bz$	$a$ (Vortex), $c$ (Cross-Scroll)
Halvorsen Attractor	3D Continuous	$\dot{x} = -ax - 4y - 4z - y^2, \dot{y} = -ay - 4z - 4x - z^2, \dot{z} = -az - 4x - 4y - x^2$	$a$ (Coupling / Dissipation)
Peter de Jong Map	2D Discrete	$x_{n+1} = \sin(ay_n) - \cos(bx_n), y_{n+1} = \sin(cx_n) - \cos(dy_n)$	$a, b, c, d$ (Interference Harmonics)
Clifford Map	2D Discrete	$x_{n+1} = \sin(ay_n) + c\cos(ax_n), y_{n+1} = \sin(bx_n) + d\cos(by_n)$	$a, b, c, d$ (Toroidal Frequencies)
Hopalong Attractor	2D Discrete	$x_{n+1} = y_n - \mathrm{sgn}(x_n)\sqrt{\vert bx_n - c \vert}, y_{n+1} = a - x_n$	$a, b, c$ (Fractal Displacement)
Ikeda Map	2D Discrete	$t = k - \frac{p}{1+x^2+y^2}, x_{n+1} = 1+u(x\cos t - y\sin t), y_{n+1} = u(x\sin t + y\cos t)$	$u$ (Reflectivity), $p$ (Refraction)
Gumowski-Mira Map	2D Discrete	$x_{n+1} = y + \alpha(1-\beta y^2)y + F(x), y_{n+1} = -x + F(x_{n+1})$	$\alpha$ (Perturbation), $\mu$ (Stability)
Tinkerbell Map	2D Discrete	$x_{n+1} = x_n^2 - y_n^2 + ax_n + by_n, y_{n+1} = 2x_n y_n + cx_n + dy_n$	$a, b, c, d$ (Quadratic Shear)
Double Pendulum	Lagrangian Mechanics	$L = T - V$ evaluated via 4th-order Runge-Kutta equations of motion	Gravity ($g$), Friction, Swarm Count
Feigenbaum Cascade	3D Delay Manifold	$x_{n+1} = r \cdot x_n(1 - x_n)$ in 3D delay embedding $(r, x_n, x_{n-1})$	Growth rate ($r$), Settle, Samples
Custom Sandbox	Multi-Equation AST	Real-time visual math inputs ($x_{n+1}, y_{n+1}, z_{n+1}$) with automatic parameter binding	User variables ($a, b, c, \dots$)

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Architecture & Codebase Structure

ChaosVision/
├── index.html              # Core application entry point and HUD layout
├── styles.css              # Glassmorphic dark design system and responsive styles
├── LICENSE                 # MIT Open Source License (c) 2026 Sheng254
├── README.md               # Technical documentation
├── assets/
│   ├── chaosvision.webp    # Animated demonstration of 3D chaotic ribbons
│   └── gallery_showcase.png# 4-tile comparative systems gallery
└── src/
    ├── main.js             # Main render loop coordinator and lifecycle manager
    ├── config/
    │   ├── palettes.js     # Curated mathematical color gradient definitions
    │   └── presets.js      # Exhibition catalog and editorial educational metadata
    ├── math/
    │   ├── rk4.js          # Runge-Kutta 4th-Order numerical integrator & swarm buffer
    │   ├── attractors.js   # Continuous and discrete mathematical system catalog
    │   ├── pendulum.js     # Lagrangian double pendulum physics solver
    │   ├── bifurcation.js  # 3D phase-space Feigenbaum bifurcation cascade engine
    │   └── parser.js       # Safe AST tokenizer and bytecode formula compiler
    ├── renderer/
    │   ├── camera.js       # Inertial orbit camera, panning, and touch pinch zoom
    │   ├── canvas2d.js     # High-density particle density accumulator & anti-stall
    │   └── webgl3d.js      # 3D trajectory ribbons and pendulum projection engine
    ├── audio/
    │   └── sonifier.js     # Generative Web Audio API Zen soundscape
    └── ui/
        ├── hud.js          # Control deck, draggable museum tour, and tooltips
        ├── exporter.js     # Asynchronous 4K wallpaper and universal vector SVG exporters
        └── urlState.js     # URL hash parameter serialization and decompression

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Keyboard Shortcuts

Shortcut	Action	Description
T	Tutorial	Toggle studio guide and navigation controls
R	Recenter	Smoothly recenter camera angle, pan offset, and zoom
M	Audio Mute / Play	Toggle generative ambient soundscape
H	Toggle Drawer	Collapse or expand the left Dynamical Controls drawer

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Getting Started

ChaosVision requires no build tools, compilers, or package managers.

Running Locally

1. Clone the repository:

   git clone https://github.com/Sheng254/ChaosVision.git
   cd ChaosVision

2. Start any local HTTP server:

   # Using Python 3
   python3 -m http.server 8080
   
   # Or using Node.js
   npx serve .

3. Open your browser and navigate to:

   http://localhost:8080
   

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License

ChaosVision is open-source software licensed under the MIT License.

Copyright (c) 2026 Sheng254.