复杂的无序物质对于广泛的学科来说都非常重要，包括生物学中的细菌群体和胚胎组织，材料科学中的泡沫和颗粒介质，以及天体物理学中的恒星结构。由于组成和尺度的巨大差异，比较如此不同系统之间的结构特征仍然具有挑战性。为此，我们利用Delaunay镶嵌的统计特性引入了一个数学框架，用于测量一般三维点云之间的拓扑距离。由此得到的系统无关度量揭示了细菌生物膜和斑马鱼脑区之间以及胚胎发育中微妙的结构差异。我们将该度量应用于构建一个包括细菌生物膜、雪花酵母、植物枝条、斑马鱼脑物质、器官样体和胚胎组织以及泡沫、胶体填充物、玻璃材料和恒星结构的通用拓扑地图集。生物系统在地图集中定位于一个有界的岛状区域内，反映了生物生长机制导致特征拓扑性质。

Complex disordered matter is of central importance to a wide range of disciplines, from bacterial colonies and embryonic tissues in biology to foams and granular media in materials science to stellar configurations in astrophysics. Because of the vast differences in composition and scale, comparing structural features across such disparate systems remains challenging. Here, by using the statistical properties of Delaunay tessellations, we introduce a mathematical framework for measuring topological distances between general three-dimensional point clouds. The resulting system-agnostic metric reveals subtle structural differences between bacterial biofilms as well as between zebrafish brain regions, and it recovers temporal ordering of embryonic development. We apply the metric to construct a universal topological atlas encompassing bacterial biofilms, snowflake yeast, plant shoots, zebrafish brain matter, organoids, and embryonic tissues as well as foams, colloidal packings, glassy materials, and stellar configurations. Living systems localize within a bounded island-like region of the atlas, reflecting that biological growth mechanisms result in characteristic topological properties.