More commonly known as Spot Color printing. Still used today. Although I have not tried it, I believe you can do this with Symbols or Swatches. I think you will need to create a symbol or swatch for every color you plan to use in the art which could be a pain. This involves actually drawing the array of circles in each color and saving them as a symbol or swatch. So, when you actually draw the art, use one of swatches you made for fill color and you should get that effect.
Anyone else like to add to this?