Welcome to the Grid
CML Visualizer is an interactive exploration platform for coupled map lattices and chaos theory, combining mathematical beauty with vintage Tron aesthetics. Built with Test-Driven Development and modern web standards, it brings complex dynamical systems to life through stunning visualizations.
Step into a digital world where chaos meets order, where simple mathematical rules create breathtaking patterns, and where the legacy of Tron meets modern accessibility standards.
Core Features
π Diffusive CML
Experience spatiotemporal pattern formation through diffusive coupling. Watch as Turing patterns, spiral waves, and chaotic synchronization emerge.
π Global CML
Explore synchronization phenomena in globally coupled systems. From independent chaos to complete synchronization, discover collective dynamics.
πΊοΈ Classic Maps
Interactive visualizations of Logistic, HΓ©non, and Standard maps. Experience period-doubling bifurcations and strange attractors.
π¨ Tron Theme System
Vintage Tron aesthetic with neon glow effects and modern accessibility. WCAG AA compliant with full keyboard navigation and screen reader support.
Technical Excellence
π§ͺ Test-Driven Development
140+ comprehensive tests covering unit, integration, accessibility, performance, and error handling scenarios.
β‘ Performance Optimized
60fps animations, React.memo optimization, efficient re-renders, and minimal bundle size for lightning-fast performance.
βΏ Accessibility First
WCAG AA compliant, keyboard navigation, screen reader support, reduced motion, and high contrast mode compatibility.
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.
Global Coupling
Each site couples to the global average of all sites, leading to synchronization phenomena.
Visualization Techniques
π¨ Color Mapping
Advanced color gradients map system states to visual properties, making chaos patterns instantly recognizable and beautiful.
β‘ Real-time Updates
Optimized rendering pipeline ensures smooth 60fps animations even with large lattice sizes and complex dynamics.
π¬ Parameter Control
Interactive controls allow real-time parameter adjustment, enabling exploration of bifurcations and phase transitions.
π Data Analysis
Built-in tools for measuring synchronization, calculating Lyapunov exponents, and analyzing spatial correlations.
Built With Excellence
This project demonstrates modern web development practices combined with deep understanding of complex systems and chaos theory.
π οΈ Technology Stack
- β’ Next.js 14 with React 18
- β’ TypeScript for type safety
- β’ Tailwind CSS for styling
- β’ Three.js for 3D visualizations
- β’ D3.js for data visualization
- β’ Playwright for E2E testing
- β’ Jest for unit testing
π― Development Methodology
- β’ Test-Driven Development (TDD)
- β’ GitHub Spec Kit specification
- β’ GitHub Actions CI/CD
- β’ Accessibility-first design
- β’ Performance optimization
- β’ Semantic HTML and ARIA
Start Exploring Chaos
Ready to dive into the fascinating world of coupled map lattices? Experience the beauty of chaos with our interactive visualizations.