Khaos - Chaotic System Simulator

This is a Python program that allows you to simulate and visualize various chaotic systems using a graphical user interface (GUI). The program uses the tkinter library for the GUI, matplotlib for plotting, and other libraries for sound generation and playback.

Installation

To run this program, you need to have Python installed on your system. You can download Python from the official website: python.org.

In addition, the program requires the following dependencies:

• matplotlib
• numpy
• pydub

You can install these dependencies using pip by running the following command:

pip install matplotlib numpy pydub

Usage

To run the program, execute the following command:

python Khaos.py

Upon running the program, a GUI window titled "Chaotic System Simulator" will open. The GUI provides various options and sliders to control and visualize different chaotic systems.

System Selection

The topmost dropdown menu allows you to select the system you want to simulate. The available options are:

• Logistic Map: Simulates the logistic map and displays the resulting bifurcation diagram.
• Lorenz System: Simulates the Lorenz system and displays the resulting trajectory in 3D.
• Bifurcation Diagram: Displays the bifurcation diagram for a given range of parameters.

Parameter Sliders

The parameters for each system are controlled using sliders. The sliders are dynamically generated based on the selected system. The available sliders for each system are as follows:

• Logistic Map: Sliders for r (growth rate) and x0 (initial value).
• Lorenz System: Sliders for sigma, rho, beta (system parameters), x0, y0, z0 (initial values), and dt (time step).
• Bifurcation Diagram: Sliders for r (growth rate), x0 (initial value), num_iterations (number of iterations), and skip (number of iterations to skip before plotting).

Plotting

The program displays the results of the selected system in a plot area. The plot is automatically updated whenever you change the system or adjust the parameter sliders. The type of plot depends on the selected system:

• Logistic Map: Shows the bifurcation diagram with x values plotted against r.
• Lorenz System: Shows the trajectory of the Lorenz system in 3D space.
• Bifurcation Diagram: Shows the bifurcation diagram with x values plotted against r.

Sound Generation

The program also provides a "Play Sound" button. However, the sound generation feature is currently implemented only for the Logistic Map system. Clicking the button will generate a sound based on the logistic map simulation. The pitch of the sound is determined by the x values of the logistic map, ranging from 440Hz (A4) to 1320Hz (E6).

Contributing

Contributions to this project are welcome. If you find any issues or have suggestions for improvements, please open an issue on the GitHub repository: https://github.com/Khosraw/Khaos/

License

This project is licensed under the MIT License. Feel free to use, modify, and distribute this code as permitted by the license.