Mandelbrot Set Visualizer

This repository contains a C++ program and supporting files for visualizing the Mandelbrot set. The Mandelbrot set is a famous fractal that is known for its intricate and beautiful boundary structures that exhibit an infinite level of recursive detail.

Mandelbrot Set Algorithm

The heart of the Mandelbrot set visualization is based on the iterative algorithm. For each point c in the complex plane, the function f(z) = z^2 + c is iterated, starting with z = 0. A point is considered part of the Mandelbrot set if, under iteration of the function, it does not escape to infinity.

Structure

The repository includes the following files:

• complex_numbers.cpp and complex_numbers.h: Define a class for complex number arithmetic.
• color.cpp and color.h: Provided by my professor Prof. Dr. Selgrad, these define a function for mapping iteration counts to colors.
• mandelbrot.cpp: Contains the main program that generates images of the Mandelbrot set.
• zoom.sh: A shell script partially provided by the professor to generate a zooming video of the Mandelbrot set.
• kardioid.png, antenna_of_satellite.png, seahorse_tail.png, spiral.png: Example images from different parts of the Mandelbrot set.
• mandelbrot.mov: A 30-second video showcasing a zoom into the Mandelbrot set at a resolution of 1024x1024 pixels.
• Makefile: to compile the program easy.

Compiling the Program

To compile the Mandelbrot set visualizer, ensure you have a C++ compiler that supports C++17 and the png++ library installed on your system. The program also utilizes OpenMP for parallel computing to speed up the image generation process.

The included Makefile simplifies the compilation process. To compile the program, simply run the following command in the terminal from the root directory of this repository:

make

This command will compile the source files and create an executable named prog (or another name if specified differently in your Makefile). Ensure that the Makefile is correctly set up to include all necessary source files and linked libraries.

Generating Images

After compiling the program, you can generate an image by running:

./mandelbrot 1024 1024 output.png

Replace 1024 1024 with your desired width and height, and output.png with your desired output file name.

Generating a Zoom Video

The zoom.sh script can be used to generate a zooming video of the Mandelbrot set:

./zoom.sh

You can adjust the zooming parameters within zoom.sh to control the center point, zoom rate, and image size. The script uses ffmpeg to stitch together individual frames into a video.

Example Images and Video

The repository includes four example images and a video:

Shows the main cardioid of the Mandelbrot set.

Depicts the structure of an antenna-like protrusion from the set.

Illustrates the spiral formations known as seahorse tails.

Features a spiral pattern within the fractal.

To view the 30-second journey into the complexity of the Mandelbrot set at high resolution, I initially created a video file (mandelbrot.mov). However, due to the file size limit on GitHub (100 MB) and to ensure easy viewing directly on GitHub, I converted the video into a GIF (mandelbrot.gif). While the GIF format does not retain the same level of quality as the original .mov file, it allows for direct embedding and viewing in this README.

Acknowledgements

The color.cpp and color.h files were provided by my professor Prof. Dr. Selgrad, along with portions of the zoom.sh shell script. They play a crucial role in the visualization process by mapping the iteration counts to a color spectrum that enhances the details of the fractal.

Contributing

Contributions to the project are welcome, whether they involve refining the algorithms, enhancing the visualization, or improving the performance.

License

This project is open source and available under the MIT License.