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--- |
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license: mit |
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language: |
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- en |
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library_name: chaossim |
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tags: |
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- chaos-theory |
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- mathematics |
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- simulation |
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- game-theory |
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- fibonacci |
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- bernoulli |
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- nash-equilibrium |
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- dynamical-systems |
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--- |
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# ChaosSim |
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A sophisticated chaos simulation software utilizing the Wolfram Programming Language to model randomized chaotic systems through mathematical principles. |
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## Overview |
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ChaosSim combines Bernoulli numbers, Fibonacci sequences, and game-sum theory (Nash equilibrium) to simulate and visualize complex chaotic patterns and behaviors in mathematical systems. |
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## Features |
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- **Bernoulli Number Integration**: Leverage Bernoulli numbers for probabilistic chaos modeling |
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- **Fibonacci-Based Patterns**: Generate chaotic sequences based on Fibonacci number properties |
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- **Nash Equilibrium Analysis**: Apply game theory principles to simulate equilibrium states in chaotic systems |
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- **Advanced Visualizations**: Create stunning visual representations of chaotic patterns |
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- **Customizable Parameters**: Adjust simulation parameters for different chaos scenarios |
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## Requirements |
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- Wolfram Mathematica (version 12.0 or higher recommended) |
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- Wolfram Engine or Wolfram Desktop |
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## Project Structure |
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``` |
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ChaosSim/ |
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├── README.md # Project documentation |
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├── ChaosSim.nb # Main simulation notebook |
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├── MathUtils.wl # Mathematical utility functions |
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├── Visualizations.nb # Visualization examples |
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└── Examples.nb # Sample simulations |
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``` |
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## Getting Started |
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1. Open `ChaosSim.nb` in Wolfram Mathematica |
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2. Evaluate all cells to initialize the simulation environment |
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3. Explore different chaos scenarios by adjusting parameters |
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4. Check `Examples.nb` for pre-built simulation demonstrations |
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## Usage |
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### Basic Chaos Simulation |
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```mathematica |
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(* Generate Bernoulli-based chaos *) |
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bernoullliChaos = SimulateBernoulliChaos[iterations, complexity] |
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(* Create Fibonacci pattern *) |
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fibonacciPattern = GenerateFibonacciChaos[depth, variance] |
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(* Analyze Nash equilibrium *) |
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nashState = AnalyzeNashEquilibrium[payoffMatrix, players] |
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``` |
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## Mathematical Foundation |
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### Bernoulli Numbers |
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Used for generating probabilistic distributions in chaos modeling, providing smooth transitions between chaotic states. |
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### Fibonacci Sequences |
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Creates self-similar patterns and golden ratio-based chaos structures, fundamental to natural chaotic systems. |
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### Nash Equilibrium |
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Models strategic interactions in multi-agent chaotic systems, determining stable states in game-theoretic scenarios. |
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## Examples |
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See `Examples.nb` for complete demonstrations including: |
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- Multi-dimensional chaos attractors |
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- Bernoulli-weighted random walks |
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- Fibonacci spiral chaos patterns |
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- Game-theoretic equilibrium in chaotic markets |
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## License |
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MIT License - Feel free to use and modify for your research and projects. |
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## Contributing |
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Contributions are welcome! Please feel free to submit pull requests or open issues for bugs and feature requests. |
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## Author |
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Created for advanced chaos theory research and mathematical simulation. |
