Mandelbrot Set

8/28/2023

last updated 12/28/2023

The Mandelbrot set is the set of values of c in the complex plane that stay bounded (don't go to infinity) when iterating over the function

z_n+1 = z²_n + c.

In the image on the right the black portion is the set it's self and the colorful parts are outside the set.

The technique I used to render the Mandelbrot set is referred to as the escape time algorithm. Which involves iterating over z_n+1 = z²_n + c until |z| > 2. If the value of |z| grows greater than 2 then the function is never bounded.