  Non-reciprocal interactions fueled by local energy consumption can be found
in biological and synthetic active matter at scales where viscoelastic forces
are important. Such systems can be described by "odd" viscoelasticity, which
assumes fewer material symmetries than traditional theories. Here we study odd
viscoelasticity analytically and using lattice Boltzmann simulations. We
identify a pattern-forming instability which produces an oscillating array of
fluid vortices, and we elucidate which features govern the growth rate,
wavelength, and saturation of the vortices. Our observation of pattern
formation through odd mechanical response can inform models of biological
patterning and guide engineering of odd dynamics in soft active matter systems.
