I distinctly remember that "Paintbrush" in Windows 3.1 had something very similar to this. Check it out in the Win3.1 emulator: https://archive.org/details/win3_stock -- open Paintbrush, go to Options -> Image Attributes and set "Colors" to "Black and White".

However, the dithering there is not fixed to the background but depends on your brushstroke / mouse position.