  We report the emergence of large zigzag bands in a population of reversibly
actuated magnetic rotors that behave as active shakers, namely squirmers that
shake the fluid around them without moving. The shakers collectively organize
into dynamic structures displaying self-similar growth, and generate
topological defects in form of cusps that connect vortices of rolling particles
with alternating chirality. By combining experimental analysis with
particle-based simulation, we show that the special flow field created by the
shakers is the only ingredient needed to reproduce the observed spatiotemporal
pattern. We unveil a self-organization scenario in a collection of driven
particles in an viscoelastic medium emerging from the reduced particle degrees
of freedom, as here the frozen orientational motion of the shakers.
