On the multifunctionality of butterfly scales: a scaling law for the ridges of cover scales

The bright colors found on the wings of some butterflies have been widely examined during recent decades because they are frequently caused by nano-structures and not by pigments or dyes. Sometimes it is puzzling to discover the physical origin of these structural colors because the color-causing nano-structures are integrated into a complex structure of scales that densely covers the butterfly wings. While the color of the wings serves purposes ranging from mating to camouflage and thermoregulation, the overall structure of the scales is commonly believed to assist with aerodynamics, self-cleaning, and easy release from spider webs. This multi-functionality of butterfly scales causes various constraints for their evolutionary design. Here, we present a structural analysis of the height and distance of the ridges in cover scales of butterfly species from different families. The subsequent analysis reveals a linear scaling law. The height of the ridges is always less than half of the distance between them. Finally, we discuss possible reasons for this geometrical scaling law.