Magnifying the Micro with Moiré Patterns

Here I design circular screen patterns that can be used to magnify grid-like stuff, like the pixels on your screen or threads in a cloth via Moiré Patterns, such that you can calculate properties about them with a crude measuring tool like a ruler. At the same time, I present a mathematical formulation of what even are Moiré Patterns. It's a rather ad-hoc formulation, so if there are some things I missed do point it out.

I might write a follow up post where the patterns are printed on transparencies to be used IRL.

Some context: Most of these explorations happened back in 2018 with a friend of mine, Vernice. Me and Vernice even printed out the patterns on transparencies to slap on random things IRL. Unfortunately I don't have the original files and transparencies, neither did I document anything so here I've recreated everything and re-derived the Math and stuff.

What are Moiré Patterns?

Moiré Patterns are these trippy magnified patterns that come from overlapping repeated small screen pat