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