ExplosionMare

A visual update now when I can post pictures again:

This is a circle grid fitted to 8x8 pixels. The dots are the center of each pixel, and are used to select which pixels get lit (black) and which don't (white):
 

The grey circle and the anchors with numbers represent the actual circle shape. If the pixel centers (the dots) are inside the circle shape, the pixel get lit.

When the circle is expanded to cover 16x16 pixels, you can see it works exactly the same. The circle looks round. The math works. However...

A 14x14 circle starts having conflicts. The centers of the pixels are so close to the circle outline, that it is up to the artist to decide which pixels get lit. The black pixels are definitely inside the circle. But including the dark red ones I colored myself, and ignoring the orange ones I also colored (not part of the circle), the shape looks more like a round square than a circle.
The math works, but the result is ambiguous. It is symmetrical, but doesn't yield any good result.

I would choose to remove the red pixels, as well as the orange ones, to make the circle more round. I don't need to see where the pixel centers are, I just need to see if it looks good or not. It is an artistic choice!

When making video games, it is a balance between artistic choices and math. Math can cover so much, but if the game and art were all math, it wouldn't look very good.

I direct this message to @ExplosionMare and @You.

@Splashee®

Thanks for all the references!

You are welcome!