Mandelbrot-Visualizer

This project uses the pygame library to visualize the Mandelbrot Set. This set is an extremely popular image from mathematics. The series is found by computing the function $f_c(z) = z^2 + c$. Z always begins at 0, but c can be any number in the complex plane. Here is an example for c = 1. $f_1(0) = 0^2 + 1 = 1$, then $f_1(1) = 1^2 + 1 = 2$. This value carries on to infinity, so 1 is not in the mandelbrot set. In our case, numbers in the mandelbrot set are colored white. Seeing if $f_c(f_c(f_c(...f_c(0))))$ converges or diverges and coloring that point $c$ based on that creates a fractal.

To view the fractal more clearly my program lets users zoom and move in all four directions. Zooming in and out by a large factor is controlled by g and h. Zooming in and out by a small factor is controlled by o and p. Moving is controlled by the arrow keys, and for more precise movements you can use q,w,e, and r for right,left,up, and down respectively.

Here is a picture showing a visualization from my program