I emailed Graham Franciose about this one, and he replied:
“The original painting was a watercolor and gouache painting on cotton paper. From there we got a high res scan of the painting and then I sent it to my friend at Sweet Relief Printing in Austin TX... The technique he used is referred to as the CMYK process. Basically he separates out the four basic colors (Cyan, Magenta, Yellow, and blacK). With these four colors you can make any color with proper layering. He then prints a layer of each color, one on top of another. The dots are there because of the nature of the screen that is being printed through. It's sort of like looking at an old tv screen up close and you see all the different little squares of color that are making up the image.”