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.

中文翻译：

---

关于蝴蝶鳞片的多功能性：覆盖鳞片脊的标度律。

近几十年来，一些蝴蝶翅膀上的鲜艳颜色得到了广泛的研究，因为它们通常是由纳米结构引起的，而不是由颜料或染料引起的。有时发现这些结构色的物理起源令人费解，因为引起颜色的纳米结构被整合到一个复杂的鳞片结构中，密集地覆盖在蝴蝶翅膀上。虽然翅膀的颜色用于从交配到伪装和温度调节的目的，但通常认为鳞片的整体结构有助于空气动力学、自清洁和容易从蜘蛛网上释放。蝴蝶秤的这种多功能性为其进化设计带来了各种限制。这里，我们对来自不同科的蝴蝶物种的覆盖尺度中脊的高度和距离进行了结构分析。随后的分析揭示了线性标度定律。脊的高度总是小于它们之间距离的一半。最后，我们讨论了这种几何缩放定律的可能原因。