Self-organized tiling generates tissue-scale hyperuniformity during development

Biological tissues require branched cellular architectures to maximize spatial coverage while minimizing redundancy. Yet, how cells decode local spatial information to collectively tile territories without a global blueprint remains a key open question. Here, we develop a biophysical theory of interacting branched cells, and show that coupling their growth to short-range repulsion drives efficient tiling with minimal territorial overlap. Our model predicts that the same local mechanism simultaneously suppresses long-range density fluctuations, driving the cellular collective toward hyperuniformity. We confirm these theoretical predictions with experiments on microglial patterning in the developing retina, and show that perturbations resulting in limited cell growth disrupt both tiling and fluctuation suppression. Our results reveal that two seemingly distinct optimization principles of biological patterning, large-scale regularity and efficient tiling, are intimately linked and can arise from a single growth-repulsion feedback, suggesting a general principle for self-organized tissue coverage.