Fractal tree of elastic bands in living liquid crystal*

Living liquid crystal (LLC), a synthetic material combining a lyotropic liquid crystal and swimming bacteria, demonstrates a number of out-of-equilibrium phenomena ranging from active turbulence to creation and annihilation of motile topological defects. In this talk, we report a spontaneous formation of undulation bands in circularly aligned LLC. The interplay between elasticity of liquid crystal and bacteria-induced hydrodynamic forces results in the emergence of a remarkable branched pattern of radially elongated bands of a highly curved director field. The average number of such branches is increasing with the distance from the center of the pattern and leads to the emergence of a radial fractal tree or a snowflake structure. Our experimental observations show that the shape of this structure, as well as a number of bands, is controlled by the activity of bacteria and elasticity of liquid crystal and suggest a new concept for a manipulation of active nematics at a microscale.