  Topological protection ensures stability of information and particle
transport against perturbations. We explore experimentally and computationally
the topologically protected transport of magnetic colloids above spatially
inhomogeneous magnetic patterns, revealing that transport complexity can be
encoded in both the driving loop and the pattern. Complex patterns support
intricate transport modes when the microparticles are subjected to simple
time-periodic loops of a uniform magnetic field. We design a pattern featuring
a topological defect that functions as an attractor or a repeller of
microparticles, as well as a pattern that directs microparticles along a
prescribed complex trajectory. Using simple patterns and complex loops, we
simultaneously and independently control the motion of several identical
microparticles differing only in their positions above the pattern. Combining
complex patterns and complex loops we transport microparticles from unknown
locations to predefined positions and then force them to follow arbitrarily
complex trajectories concurrently. Our findings pave the way for new avenues in
transport control and dynamic self-assembly in colloidal science.
