| | --- |
| | 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. |
