Mandelbrot Set Visualization

This project provides two implementations of the Mandelbrot set visualization using Python and Pygame. The Mandelbrot set is a complex fractal, and this project allows you to zoom in and explore its intricate details interactively.

Project Structure

• .gitignore: Specifies the files and directories that should be ignored by Git, including bytecode, build directories, virtual environments, and more.
• main.py: A basic implementation of the Mandelbrot set visualization.
• main2.py: An optimized implementation that utilizes multithreading to speed up the computation.

Requirements

• Python 3.x
• Pygame
• NumPy

You can install the required packages using pip:

pip install pygame numpy

Running the Project

To run the basic Mandelbrot set visualization:

python main.py

To run the optimized version with multithreading:

python main2.py

Mandelbrot Set

The Mandelbrot set is a set of complex numbers defined by the iterative equation:

[ z_{n+1} = z_n^2 + c ]

where z0z0​ is initially zero, and cc is a complex number. The set is defined as the set of all cc values for which the sequence znzn​ does not diverge to infinity. This project visualizes the Mandelbrot set by mapping points in the complex plane to pixels on the screen and using a color gradient to represent the number of iterations required to determine if the point is in the Mandelbrot set.

Features

• Zooming: Use the left mouse button to zoom in and the right mouse button to zoom out.
• Multithreading (in main2.py): Utilizes multiple threads to accelerate the calculation of the Mandelbrot set.

Code Explanation

main.py

• mandelbrot(c, max_iter): Computes the number of iterations before the point diverges.
• draw_mandelbrot(surface, xmin, xmax, ymin, ymax, max_iter): Draws the Mandelbrot set on the Pygame surface and updates the display.
• main(): Handles user input and manages the zooming functionality.

main2.py

• mandelbrot(c, max_iter): Computes the Mandelbrot set using NumPy arrays and handles large chunks of data concurrently.
• draw_mandelbrot(surface, xmin, xmax, ymin, ymax, max_iter): Divides the computation into chunks and processes them in parallel using the concurrent.futures module.
• draw_axes(surface, xmin, xmax, ymin, ymax): Draws axes and labels on the Pygame surface.
• main(): Similar to main.py, but optimized with multithreading.

License

This project is licensed under the MIT License. See the LICENSE file for details.

Contribution

Feel free to fork this repository, open issues, and submit pull requests.

Acknowledgments

• Pygame
• NumPy