3-Body Random Generator

A beautiful web application that generates truly random numbers using the chaotic motion of the gravitational 3-body problem combined with prime number theory.

🌟 Features

• 3-Body Physics Simulation: Real-time gravitational simulation using Runge-Kutta 4th order integration
• Prime Number Theory: Utilizes prime generation, gaps, and patterns for additional entropy
• Multiple Mixing Algorithms: XOR, modular arithmetic, hash-based, and entropy-weighted mixing
• Beautiful Visualizations:
  • Animated 3-body orbits with trails
  • Ulam prime spiral visualization
  • Real-time distribution histograms
• Statistical Analysis: Quality metrics, autocorrelation, and distribution analysis
• Pastel UI/UX: Smooth animations and calming color palette
• Export Functionality: Save generated numbers to JSON

🚀 Quick Start

# Install dependencies
npm install

# Run development server
npm run dev

# Build for production
npm run build

Open http://localhost:5173/ in your browser.

📖 How It Works

3-Body Problem

The gravitational 3-body problem is a chaotic system with extreme sensitivity to initial conditions. The simulator:

• Uses Runge-Kutta 4th order integration for accurate physics
• Extracts chaos values from positions, velocities, and inter-body distances
• Creates unpredictable patterns ideal for randomness

Prime Number Theory

Prime numbers add mathematical structure and additional entropy:

• Sieve of Eratosthenes for prime generation
• Miller-Rabin primality testing
• Prime gaps and twin primes
• Prime-based hashing functions

Mixing Algorithms

Four different methods combine chaos and primes:

1. XOR Mixing: Bitwise XOR operations for fast mixing
2. Modular Arithmetic: Uses Mersenne primes for modular reduction
3. Hash-based: String hashing with prime multiplication
4. Entropy-weighted: Dynamic weighting based on simulation entropy

🎮 Usage

Control Panel

• Generate Random Number: Create a single random number
• Generate Batch: Create multiple numbers at once
• Min/Max Values: Set the output range
• Mixing Algorithm: Choose how chaos and primes are combined
• Simulation Steps: Control how much the simulation advances (higher = more chaos)
• Reset Simulation: Start with new random initial conditions

Statistics

The output panel shows:

• Mean & Variance: Distribution metrics
• Quality Score: Chi-square test for uniformity (0-100%)
• Autocorrelation: Measures independence between consecutive numbers
• Distribution Histogram: Visual representation of number distribution

Visualizations

• 3-Body Simulation: Watch the chaotic orbits in real-time
  • Click "Clear Trails" to reset the trail visualization
• Ulam Spiral: See prime number patterns
  • Twin primes highlighted with pink outlines

Export

Click "Export Numbers" to download all generated numbers as JSON.

🛠️ Technical Details

Core Components

• ThreeBodySimulator.ts: Physics engine with RK4 integration
• PrimeGenerator.ts: Prime number utilities and tests
• RandomGenerator.ts: Mixing algorithms and statistics
• ThreeBodyCanvas.tsx: Canvas-based 3-body visualization
• PrimeVisualizer.tsx: Ulam spiral renderer
• RandomOutput.tsx: Statistics and distribution display
• ControlPanel.tsx: User controls and configuration

Performance

• Simulation runs at 60 FPS
• Batch generation up to 10,000 numbers
• Efficient prime caching
• Canvas-based rendering for smooth animations

🎨 Design

The UI features:

• Pastel color palette (purples, pinks, blues, greens)
• Smooth CSS transitions and animations
• Responsive grid layouts
• Glassmorphism effects
• Gradient backgrounds

📊 Randomness Quality

The generator provides high-quality randomness suitable for:

• Simulations and Monte Carlo methods
• Game development
• Educational demonstrations
• Art and generative design

Note: While this provides excellent randomness, it's not cryptographically secure. For cryptographic applications, use crypto.getRandomValues().

🧮 Mathematical Background

Chaos Theory

The 3-body problem has no closed-form solution and exhibits:

• Sensitive dependence on initial conditions
• Non-periodic trajectories
• Positive Lyapunov exponents

Prime Number Theory

• Prime Number Theorem for distribution estimates
• Miller-Rabin for probabilistic primality testing
• Prime gaps and irregularities add entropy

🤝 Contributing

Contributions welcome! Areas to explore:

• Additional mixing algorithms
• More visualization options
• Different chaotic systems (Lorenz attractor, double pendulum)
• Advanced statistical tests (NIST suite)
• WebGL rendering for performance

📝 License

MIT License - feel free to use in your projects!

🌟 Credits

Built with:

• React + TypeScript
• Vite
• Canvas API
• Pure mathematical chaos ✨

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Enjoy generating random numbers through the beautiful dance of gravitational chaos! 🌌