Picture zooming out from a repeating image. Eventually an entire picture takes a single pixel then multiple images per pixel. You can pick one pixel from a full image but that's going to get aliasing effects, or you can use multiple but that just means blur.
Increase the # of samples to any finite number, and you get the same problem at a higher zoom level.
The problem is that it is very difficult to filter a generic texture so that it looks perfect near the horizon. For a particular simple texture such as the checkerboard you can compute the exact rendering explicitly. But I know of no method to do it in general.