That’s TIE-dyed, as in USING A SILK TIE to dye the eggs. There’s a full tutorial here, but the gist is that you take a colorful silk tie, wrap it around the egg, tie dental floss around it, wrap THAT in white cotton, then boil it in water and white vinegar for 20 minutes. Soak in cold water for ten minutes afterwards, and VOILA, gorgeously patterned eggs!