  How much structural information is needed to distinguish living from
non-living systems? Here, we show that the statistical properties of Delaunay
tessellations suffice to differentiate prokaryotic and eukaroytic cell packings
from a wide variety of inanimate physical structures. By introducing a
mathematical framework for measuring topological distances between general 3D
point clouds, we 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 are found to localize within a bounded
island-like region, reflecting that growth memory essentially distinguishes
multicellular from physical packings. By detecting subtle topological
differences, the underlying metric framework enables a unifying classification
of 3D disordered media, from microbial populations, organoids and tissues to
amorphous materials and astrophysical systems.
