Material Pixel Limit?

Hey Everyone! I am messing around with fractals in unreal, and while Im having a lot of fun, I noticed something odd. These fractals are generated with some very simple HSLS code, and colored with a few lerps here and there. In theory, these shouldnt have a resolution, but when zoom into my fractals more than 12000 times, stuff is starting to get pretty pixelated! First I thought this was capped by the iterations of my formula, but changing it did not change the resolution. Im wondering if there is some sort of pixel limit that I’m not aware of? Is there a way to get around this?
This is obviously not for a game, and Im just messing around a bit.

I should also note that Im not physically zooming in that far, but rather scaling the fractal on a plane.