Turing’s reaction–diffusion theory of morphogenesis has been very successful for understanding macroscopic patterns within complex objects ranging from biological systems to sand dunes. However, Turing patterns on microscopic length scales are extremely rare. Here we show that a strained atomic bismuth monolayer assembled on the surface of NbSe₂—and subject to interatomic interactions and kinetics—displays Turing patterns. Our reaction–diffusion model produces stripe patterns with a period of five atoms (approximately 2 nm) and domain walls with Y-shaped junctions that bear a striking resemblance to what has been experimentally observed. Our work establishes that Turing patterns can occur at the atomic scale in a hard condensed-matter setting.

图灵的形态发生反应-扩散理论对于理解从生物系统到沙丘等复杂物体内的宏观模式非常成功。然而，微观长度尺度上的图灵模式极为罕见。在这里，我们展示了在 NbSe ₂表面组装的应变原子铋单层- 并受到原子间相互作用和动力学的影响 - 显示出图灵模式。我们的反应-扩散模型产生了周期为五个原子（约 2 nm）的条纹图案和带有 Y 形结的畴壁，与实验观察到的结果惊人地相似。我们的工作确定了图灵模式可以在硬凝聚态环境中以原子尺度发生。