This was a quick project because Lân was bored, and so decided to create a Mandelbrot renderer in ASM. Firstly, Lân read the Wikipedia page for the Mandelbrot set to start to understand how the pattern happens, and how to write code do show the pattern. This wasnt very helpful, so Lân watched the video by Numberphile about the subject. This was much more helpful than Wikipedia, and now Lân understood the pattern and how it was created. Next, Lân researched the way that programmers test if a number is finite or not. After a short time, Lân discovered that a common technique is to test that fc(z) = z^2 + c for something like one thousand times, and if z didnt go above a certain amount AND goes to the iteration limit, the number is finite. Then, Lân used the code on Wikipedia on the page Plotting algorithms for the Mandelbrot set to see how this was done without the use of complex number libraries. Lân used the code from the segment called 'Optimized escape time algorithms', and rewrote the code in python, so she understood the cod before writing in ASM. Here are some pictures of the python code:

Now, it was time to write the code in ASM.
Firstly, Lân needed to create a system of showing points on the terminal screen. To do this, she used 'ANSI escape sequences' to change the colour of the foreground and background of the character '▄'. With this, Lân could change the foreground to change the colour of the bottom pixel, and the background to change the colour of the higher pixel. With this, you can place pixels like this over the entire screen and then place pixels of any ANSI colour anywhere on the screen. After this system worked, Lân continued to write code to render the Mandelbrot set. This was hard to do with the FPU, because of the fact that the FPU is similar to the stack. But Lân finished the code in a short time, and after some debugging, the code showed the Mandelbrot set.

As you can see, the set is shown correctly, but its in a weird place and the colours are weird too. However this was very easy to fix, because it was a very obvious bug with colours, and the position of the set was easy to fix also because you only need to change the position of the top left, and the zoom.After changing these problems, it looked like this:

Now everything was correct. Lân needed to write code to move the image and to zoom into the Mandelbrot set. Fortunately, this is easy because the zoom level was defined by a number near the start of the code, and every bit of maths uses this number. So, to change the zoom, you only needed to change that number. After finishing this, the project was finished. If you want, you can download the project from GitHub to try the code for yourself.