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It provides a comprehensive toolkit for generating matrices, simulating chains, and visualizing key metrics like steady-state distributions and convergence.\n\n## Features\n- **Simulate Markov Chain**: Simulates state transitions over time based on a given stochastic matrix.\n- **Generate Random Stochastic Matrix**: Creates random transition matrices, ensuring valid probability distributions where each row sums to 1.\n- **Plotting Functions**: Visualizes matrices, state transitions, and multiple chains using plots for a clearer understanding of transitions, steady-state behavior, and convergence patterns.\n- **Calculate Steady-State Distribution**: Determines the long-term distribution where the system stabilizes, representing the equilibrium probabilities.\n- **Analyze Absorption Probabilities**: Calculates the probabilities of being absorbed into certain states, crucial for systems with absorbing states.\n- **Simulate Multiple Chains**: Executes multiple independent Markov chain simulations to observe the behavior from different starting points and compare results.\n- **Analyze Convergence to Steady-State**: Monitors how quickly the system approaches its steady-state, offering insights into the stability and time evolution of the system.\n- **Compute Mean First Passage Times**: Computes the average steps required to reach a particular state from another, useful for analyzing the efficiency of state transitions.\n\n## Requirements\n- Python 3.8+\n- `numpy` for numerical computations\n- `matplotlib` and `seaborn` for plotting\n\n## Installation\n1. Clone the repository: `git clone https://github.com/yourusername/markov-chain-simulator.git`\n2. Navigate into the project directory: `cd markov-chain-simulator`\n3. Install dependencies: `pip install -r requirements.txt`\n\n## Usage\n1. Run the application: `python main.py`\n2. Follow the menu prompts to interact with the Markov chain simulator.\n\n## Contributing\nContributions are welcome! Please submit a pull request with your changes.\n\n## License\n[MIT License](https://opensource.org/licenses/MIT)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvisvav%2Fmarkov-chain-simulator-using-stochastic-matrices","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fvisvav%2Fmarkov-chain-simulator-using-stochastic-matrices","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvisvav%2Fmarkov-chain-simulator-using-stochastic-matrices/lists"}