In my early teens I used to try to create something like a equirectangular projection because when drawing it, it looked cool. Obviously I had no idea that it was called this. I was trying to draw reflections of a square window onto a sphere, and then I moved on to trying to cover the sphere in a checkered pattern. This is awesome to see, thank you!

An equirectangular projection just means plotting latitude and longitude in a rectangle.

Do you mean my diagonal grid that I projected back onto the sphere? I'm not sure that has a name.