  Filamentous cyanobacteria can show fascinating examples of nonequilibrium
self-organization, which however are not well-understood from a physical
perspective. We investigate the motility and collective organization of
colonies of these simple multicellular lifeforms. As their area density
increases, linear chains of cells gliding on a substrate show a transition from
an isotropic distribution to bundles of filaments arranged in a reticulate
pattern. Based on our experimental observations of individual behavior and
pairwise interactions, we introduce a nonreciprocal model accounting for the
filaments' large aspect ratio, fluctuations in curvature, motility, and nematic
interactions. This minimal model of active filaments recapitulates the
observations, and rationalizes the appearance of a characteristic lengthscale
in the system, based on the Peclet number of the cyanobacteria filaments.
