Welcome to the Grid
Chaos Atlas is an interactive exploration platform for chaotic dynamical systems, combining mathematical rigor with vintage Tron aesthetics. It brings complex dynamical systems to life through real-time visualizations, built with Test-Driven Development and modern web standards.
Available both as a live web application and as a Python package, Chaos Atlas provides tools for studying bifurcations, attractors, and chaos across dozens of canonical systems and spatiotemporal coupled dynamics.
Source code is freely available on GitHub.
Python Package
The same numerical kernels powering the web visualizations are available as a NumPy-vectorised library. Install from PyPI:
pip install chaos-atlas
See the PyPI page for documentation and usage examples.
Core Features
π Diffusive CML
Explore spatiotemporal pattern formation through diffusive coupling. Watch Turing patterns, spiral waves, and chaotic synchronization emerge in real time.
πΊοΈ Ten Map Pages
Interactive visualizations of Logistic, Tent, HΓ©non, Standard, Ikeda, Arnold Cat, Baker's, Tinkerbell, Duffing, and Complex Quadratic maps.
π Comparative Analysis
Side-by-side comparison of chaotic systems with synchronized parameters. Bifurcation and Lyapunov comparison views are still in progress.
π¨ Tron Aesthetic
Vintage Tron-inspired visual design with neon glow effects and a dark, immersive interface.
Numerical Methods
Chaos Atlas computes Lyapunov spectra using Benettin's algorithm with Gram-Schmidt reorthonormalisation. Every spectrum is validated against the conservation identity sum(Ξ»_i) = β¨ln|det J|β©. All analytic Jacobians are verified against central finite differences.
This rigorous approach ensures that visual patterns reflect genuine dynamical properties, not numerical artifacts.
Testing & Quality
π§ͺ Comprehensive Testing
322 tests covering unit, integration, and end-to-end scenarios: 283 Jest unit tests and 39 Playwright E2E tests.
π Numerical Validation
Jacobian verification, conservation law checks, and stability tests ensure correctness of dynamical computations.
π¦ Modern Stack
Next.js 16, React 19, TypeScript, Tailwind CSS, and D3.js, with GitHub Actions CI/CD.
The Mathematics Behind
Coupled Map Lattices
Coupled Map Lattices (CMLs) are discrete-time dynamical systems where multiple identical maps are coupled together on a lattice structure.
General Form:
x_i(t+1) = (1-Ξ΅)f(x_i(t)) + Ξ΅/2 Ξ£_neighbors [f(x_j(t)) - f(x_i(t))]
Diffusive Coupling
Each site interacts with its immediate neighbors through a diffusion-like process, creating local pattern formation.
Lyapunov Exponents
Measure of sensitivity to initial conditions. Positive values indicate chaos; zero indicates bifurcation points.
Visualization Techniques
π¨ Color Mapping
Color gradients encode system dynamics: escape times, Lyapunov exponents, or density of orbits.
β‘ Real-time Rendering
Canvas-based rendering with optimized pixel updates enables parameter sweeps and interactive exploration at reasonable frame rates.
π¬ Parameter Control
Interactive sliders allow real-time parameter adjustment, enabling exploration of bifurcations and phase transitions.
π Lyapunov Spectra
Built-in tools compute and visualize the full spectrum of Lyapunov exponents to quantify multidimensional chaos.
Start Exploring Chaos
Ready to explore coupled map lattices and discrete dynamics? Experience the beauty of chaos with our interactive visualizations.