Self-enhanced mobility enables vortex pattern formation in living matter.

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation 1-4 , purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa 5 and bacteria 6 . Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 10 4 -10 5  motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length 7-9 . Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems 10 near the boundary of fluid- and solid-like behaviours 11-17 .