{"id":1776,"date":"2021-04-01T06:00:00","date_gmt":"2021-04-01T11:00:00","guid":{"rendered":"http:\/\/www.jaimerios.com\/?p=1776"},"modified":"2025-12-30T23:52:48","modified_gmt":"2025-12-30T23:52:48","slug":"mandelbrot-set","status":"publish","type":"post","link":"https:\/\/jaimerios.com\/?p=1776","title":{"rendered":"Mandelbrot Set"},"content":{"rendered":"\n

I’m quite fascinated with the image that the Mandelbrot Set produces, but admittedly, I didn’t understand how to implement the function from the description on Wikipedia.<\/p>\n\n\n\n

Thankfully, there are 2 really good videos that give an overview and an in depth explanation of the function, which you can watch at:<\/p>\n\n\n\n

Mandelbrot back to basics:
https:\/\/youtu.be\/FFftmWSzgmk<\/a><\/p>\n\n\n\n

Mandelbrot Set described:
https:\/\/youtu.be\/NGMRB4O922I<\/a><\/p>\n\n\n\n

The formula, z<\/mi>n<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub>=<\/mo>z<\/mi>n<\/mi>2<\/mn><\/msubsup>+<\/mo>c<\/mi><\/mrow>z _{n+1}=z_n^2+c<\/annotation><\/semantics><\/math> , involves complex numbers, which you will see used in my implementation.<\/p>\n\n\n\n

In my implementation, we go through each x,y coordinate, checking if at that coordinate, whether or not the values returned are within the Mandelbrot Set \u2026 don’t forget to watch the above videos for what that means.<\/p>\n\n\n\n

At each x,y coordinate, we have to scale those coordinates to be within a 2×2 box, which has it’s x coordinate centered at -0.5 and it’s y coordinate centered at 0.0… to then call out to my get_number_of_iterations<\/code> function, which iterates until the complex number… ‘explodes’, then we return that iteration count back to our calling function.<\/p>\n\n\n\n

The resulting grayscale image definitely looks like a Mandelbrot:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Here is the code I created to make the above image:<\/p>\n\n\n\n

C++<\/span><\/span>