Amniote integumentary appendages constitute a diverse group of micro-organs, including feathers, hair and scales. These structures typically develop as genetically controlled units¹, the spatial patterning of which emerges from a self-organized chemical Turing system^2,3 with integrated mechanical feedback^4,5. The seemingly purely mechanical patterning of polygonal crocodile head scales provides an exception to this paradigm⁶. However, the nature and origin of the mechanical stress field driving this patterning remain unclear. Here, using precise in ovo intravenous injections of epidermal growth factor protein, we generate Nile crocodile embryos with substantially convoluted head skin, as well as hatchlings with smaller polygonal head scales resembling those of caimans. We then use light-sheet fluorescence microscopy to quantify embryonic tissue-layer geometry, collagen architecture and the spatial distribution of proliferating cells. Using these data, we build a phenomenological three-dimensional mechanical growth model that recapitulates both normal and experimentally modified patterning of crocodile head scales. Our experiments and numerical simulations demonstrate that crocodile head scales self-organize through compressive folding, originating from near-homogeneous skin growth with differential stiffness of the dermis versus the epidermis. Our experiments and theoretical morphospace analyses indicate that variation in embryonic growth and material properties of skin layers provides a simple evolutionary mechanism that produces a diversity of head-scale patterns among crocodilian species.

羊膜外皮附属物构成了一组不同的微器官，包括羽毛、头发和鳞片。这些结构通常发展为遗传控制单元¹（gene-controlled units），其空间模式来自具有集成机械反馈^4,5 的自组织化学图灵系统^2,3 （Turing system）。多边形鳄鱼头鳞片看似纯粹的机械图案为这种范式⁶ 提供了一个例外。然而，驱动这种模式的机械应力场的性质和来源仍不清楚。在这里，使用精确的卵内注射表皮生长因子蛋白，我们生成了具有基本卷曲头部皮肤的尼罗河鳄鱼胚胎，以及具有较小多边形头部鳞片的幼体，类似于凯门鳄的头部鳞片。然后，我们使用光片荧光显微镜来量化胚胎组织层的几何形状、胶原蛋白结构和增殖细胞的空间分布。利用这些数据，我们建立了一个现象学三维机械生长模型，该模型概括了鳄鱼头部鳞片的正常和实验修改的模式。我们的实验和数值模拟表明，鳄鱼头鳞片通过压缩折叠进行自组织，起源于近乎均匀的皮肤生长，真皮与表皮的刚度不同。我们的实验和理论形态空间分析表明，胚胎生长和皮肤层材料特性的变化提供了一种简单的进化机制，在鳄鱼物种中产生了多种头部尺度模式。