mandelbrot | Mandelbrot set in various languages | Runtime Evironment library

My code is as follows:

I am writing code to visualize Mandelbrot sets and other fractals. Below is a snippet of the code that is being run. The code runs perfectly fine as is, but I am trying to optimize it to make higher resolution images faster. I've tried using caching on fractal(), along with @jit and @njit from Numba. Caching resulted in a crash (from memory overflow I'm assuming) and @jit just slows down the execution of my program by a factor of 6. I am also aware of the many mathematical ways there are of making my code run faster, as I've seen on the Wikipedia page, but I would like to see if I can get one of the above methods or some alternative to work.

For creating multiple images in a row (to make a zoom animation, like this one) I've implemented multiprocessing (which seems to run 9 processes at once) but I don't know how to implement the same in the creation of a single high resolution image.

Here is my code snippet:

Background: I'm trying to create a simple bootstrap function for sampling means with replacement. I want to parallelize the function since I will eventually be deploying this on data with millions of data points and will want to have sample sizes much larger. I've ran other examples such as the Mandelbrot example. In the code below you'll see that I have a CPU version of the code, which runs fine as well.

I've read several resources to get this up and running:

Random Numbers with CUDA

Writing Kernels in CUDA

The issue: This is my first foray into CUDA programming and I believe I have everything setup correctly. I'm getting this one error that I cannot seem to figure out:

I am working on creating deep zooms into the Mandelbrot set, and as you might know OpenGL ES does not support the double data type. The highest precision that it can offer is that of a IEEE 754 float. On Googling, and after a lot of searching, I came across this blog: https://blog.cyclemap.link/2011-06-09-glsl-part2-emu/ that is totally dedicated to this topic. But, unfortunately I cannot understand the code for addition, subtraction and multiplication, presented there. Especially, I can't understand the part that deals with the error correction and carrying. It would be extremely helpful, if you could explain to me, the depth of the error checking and carrying over of bits from low parts to higher. So, far I only understand the fundamental concept of splitting the double into two floats. But, the implementation of the basic operations is unclear to me. It would be very helpful if the explanation is done using the context of binary numbers.

I've been trying to understand how bmp files work so I can render some Mandelbrot set pictures and output them as bmp files since that seems to be one of the easiest methods but for some reason when I use an aspect ratio that isn't 1:1 even though its something to the power of 4 (so no padding is needed) I get weird artifacts like these 200:100 48:100 what I'm trying to do is turning an array of pixels that has white for even numbers and black for odd numbers into a bmp, this (100:100) is what it looks like with 1:1 aspect ratio. I've tried reading through the wikipedia article to see if I can figure out what I'm doing wrong but I still don't get what I'm missing.

This is the script I've written in Lua so far:

I've tried many algorithms for the rendering of the Mandelbrot set, inclusive of the naive escape time algorithm, as well as the optimized escape time algorithm. But, are there faster algorithms that are used to produce really deep zooms efficiently like the ones we see on YouTube. Also, I would love to get some ideas on how to increase my precision beyond the C/C++ double

I'm trying to use shaders in Godot and I need a really precise calculation (more than float). Is it possible to have a double in Godot shaders? I searched the documentation but I found nothing...

Edit: I've made a Mandelbrot set explorer and with floats after some zooming the image gets all pixelated because the precision limit is reached, I think that with doubles I would be able to zoom further without losing quality. You can check out my code here btw

I am encountering an error with the following code:

I have a requirement to create an image and save it in a database. I am creating it with python Pillow and saving it as JPEG.