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So, I was talking with a colleague about this, and as I am finding it difficult to make time for working on this between other things (life getting in the way, etc.) he suggested I submit my query to grok. After some time explaining what I was trying to do, it spit out this code:

\documentclass ...

I'm unsure what the error was, but for whatever reason, it resolved when I restarted the program. Very strange. Perhaps, as you say, it inadvertently loaded another file by mistake.

I was able to find information in the PGF/TikZ documentation pertinent to what I am trying to do. https://tikz.dev/math-algorithms
Thanks for your help.

So, random tangent, but upon trying to set the following code (from here: https://pgfplots.net/strange-attractors/) in Texifier, I receive an error for a line which, to my lying eyes, is not present in the document:
\documentclass{standalone}
\usepackage{pgfplots,luacode}
\pgfplotsset{compat=1.18 ...

Great. Will post code here if/when successful.

Would you please supply the code for the example you posted on X? I would be grateful if you would please do so. I have just tried copying it off of the image, but I am getting several errors within the first few lines.

I see. That makes sense. This certainly betrays my unfamiliarity with the language. Just to be exhaustive, I have these other two examples of code that I am basing my thoughts off of. So, for starters there is this example:
\documentclass{article}
\usepackage{tikz}

\makeatletter
\newcommand ...

Thanks for the advice. Apologies for taking my time in responding. Been busy, etc. I took your advice, and have gone with a LaTeX editor, specifically Texifier. Works very well. I have looked around on the internet, and gotten several examples of code that people have used to generate Pascal's ...

I am new to using TikZ, but have been using LaTeX via LyX for several years now. While I am not the most adept user, I am somewhat confident in my understanding of how the program works, albeit unfamiliar with all of its features. I understand this is a fairly high level task to try to implement ...