Self-propelling calcium-alginate motors exhibit complex interactions driven by attractive
capillary and repulsive Marangoni forces, yet how motor size influences their collective
dynamics remains unclear. Here we experimentally investigate the size-dependent oscillatory
collisions, synchronization, and self-assembly of calcium-alginate motors ranging
from two to fifteen units. Using high-speed imaging and a particle-based model incorporating
pairwise interactions, we reveal that smaller motors sustain longer oscillations,
while larger motors coordinate the motion of smaller ones, leading to vibrational-like
dynamics. Assemblies of eight or more motors form clusters characterized topologically
by Betti numbers, reflecting evolving connectivity and voids. Our findings elucidate
how size-dependent forces govern the emergent spatiotemporal patterns and self-organization
of active polymer motors, providing insights for designing intelligent collective
systems with potential applications in micro-actuation and soft robotics.
