Image → Mode → Indexed. Check the box “Remove unused and duplicate colors from colormap”. For dithering I recommend you choose “Floyd-Steinberg”. Whether you want to use colors or not is up to you. After you are satisfied with the result, export as a PNG and try removing as much metadata from the image as you can to help aid in lowering the size even more.
# Using ordered dithering (less detail but smaller filesize) convert input.png -scale 600x -colorspace gray -ordered-dither o8x8 output.png # Using Floyd-Steinberg convert input.png -scale 600x -dither FloydSteinberg -remap pattern:gray50 output.png # The `-scale` flag is there to resize the image to a width of 600. You can # change the width to something bigger, or smaller (won't recommend), if you wish.
An online image dithering tool that’s easy to use. Not much else to say, try it out!