wav mp3 "conversion" using filters and effects?

Heya, so I had the idea for a “visualization” of what mp3 compression does to the audio. That is, I want to “manually convert” uncompressed audio to mimic the mp3 in Audacity, using filters and effects (without export/import) I know this is very vague and I haven’t been able to make a real plan for this yet. I found out it uses psycho-acoustics, meaning it’s more than just cutting out high frequencies (for example, it also “hides” more quiet sounds when something loud is playing). Now I couldn’t find a list of specific changes needed to be done to get from wav to mp3 anywhere, and looking at the source code from converters hasn’t helped much (considering my rather insufficient understanding of programming and the fact that many of the technicalities probably aren’t relevant for what I want to do). I would like to have such a list, and then try and figure out how to do that in audacity. Although, I assume that I’m missing something as such “visualization” would probably exist otherwise.

Thanks a lot in advance! Any help or pointing me towards resources I might have missed would be greatly appreciated. Have a great day!

Ubuntu 20.04.2 LTS (64-bit)
Audacity 3.0.2 (installed from Ubuntu store)

So this article looks like a great place to start: https://en.wikipedia.org/wiki/MP3 It includes over a hundred references on MP3.

Someone beat you to it … The Ghost in the MP3