Cut white paper into twelve 2-by-11-inch strips. Using an electric mixer, beat the confectioners sugar and egg white until thick and smooth, about 5 minutes. Divide the icing into 2 small bowls. Stir the yellow food coloring into one batch and the blue food coloring into the other. Cover the blue icing with plastic wrap.
Arrange the paper strips side by side on a work surface. Scrape the yellow icing into a small, resealable plastic bag and snip off a tiny corner. Pipe out the icing onto the paper strips in dots, about 1/3 inch apart in even rows of 3. When about a quarter of the yellow icing remains, add approximately the same amount of blue icing to the bag, stirring with a toothpick. Continue to pipe green icing dots onto each paper strip. Transfer the blue icing to another small, resealable plastic bag and continue piping. Let the dots sit at room temperature until hardened, 12 hours or overnight.