# Mandelbrot Set Viewer

Dec, 2014

I created a small tool to visualize the
Mandelbrot set at different zoom levels in real time.
This project emerged from an assignment at the university during a nonlinear dynamics lecture.
The Mandelbrot set is defined as all complex numbers `c`

for which the function

`z`

_{n+1} = z_{n}^{2} + c

stays finite when the sequence is iterated starting from `z`

. This set can be illustrated nicely by plotting all of its points in the two dimensional complex plane, which leads to the famous fractal graph shown above. Zooming in at different parts shows the same structure of the whole set again in a sub part as the Mandelbrot set is a fractal with self-similar properties._{0}=0

To visualize the Mandelbrot set, the sequence is iterated for each pixel of the image until either a predefined maximum iteration count is reached or the iterated value exceeds a certain threshold. According to the iteration count until the threshold value is reached the pixel gets its color. The program is written in c++ and uses OpenGL to render the image. The code can be found on GitHub. The following image is created using the program.