Not to dig up those squares again...but they appear as three distinct shades of gray to me. What does that mean from a perception standpoint? 
It probably means your display's calibration is not ideal. The basic mechanism behind those squares is that each pixel on your screen consists of three sub-pixels: Red, green and blue. Due to the values of colours, each sub-pixel is either on, or it is off.
Each pixel lit looks like this:
███and each pixel shut down looks like this:
███Cyan-red subpixel pattern looks like this:
████████████Broken into sub-pixels, it looks like this:
███ ██████ ███When it repeats, it looks like this:
███ ██████ ███ ███ ███ ███ ███ ███ ███ ███ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ███ ███ ███ ███ ███ ███ ███ ███ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ███ ███ ███ ███ ███ ███ ███ ███ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ███ ███ ███ ███ ███ ███ ███ ███ ███
███ ██████ ██████ ██████ ██████ ██████ ███So you can basically see that overall exactly half of the sub-pixels are lit, and half are shut down. This is effectively the exact same thing as dithering full white and full black pixels similarly; only the sub-pixel arrangement changes line by line.
This exact same distribution (with slightly varying subpixel order for each line) should repeat for all the squares, regardless of the colour of the pixels - the structure of the display renders them effectively similar to what dithered black-white checker board would be. Sub-pixel layout of your display will also effect the ordering of each lines (I used horizontal RGB layout which is I think the most common).
If your display doesn't do this, then I would look into some calibrations, specifically RGB gamma curves and possibly colour temperature, but I'm not certain what type of monitor would display the squares significantly differently...

Also, my pixels are not square.

EDIT: Here are the yellow-blue and magenta-green patterns:
███████████████ ██████ ██████ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ██████████████████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███
███ ██████ ██████ ██████ ██████ ██████ ███The last one is particularly interesting because it spreads the sub-pixel distribution evenly in an on/off pattern.