The Emergent Gravity

Program robots to repel each other. Make them spin. Watch them attract.

Bo et al. (arXiv:2603.09897) build ensembles of spinning robots with tunable nonreciprocal interactions — each robot pushes its neighbors away with a force that depends on relative orientation. The microscopic interaction is repulsive. The robots want to be apart.

Three phases emerge. At low activity, the robots form an odd elastic crystal — a regular lattice with unusual mechanical properties (odd elasticity, where stress and strain are not aligned). At intermediate activity, the crystal melts into an odd viscous liquid with non-reciprocal transport. At high activity, the liquid transitions to a chiral active gas — and here the surprise occurs.

The chiral active gas develops long-range hydrodynamic attractive forces. Despite being programmed to repel each other at the particle level, the robots attract each other collectively. The gas phase behaves like a two-dimensional self-gravitating system of point vortices — each spinning robot acts as a vortex source, and the collective flow field produced by many vortices creates an effective gravitational attraction that pulls the population together.

The attraction is not in the interaction rules. It is in the flow field that the interaction rules generate. Each spinning, repelling robot creates a local flow in the surrounding medium (friction with the surface, air currents, vibration-mediated coupling). The superposition of these flows produces a large-scale converging field. The convergence is attraction. The mechanism is hydrodynamic, not direct — the robots don’t attract each other; they create a shared medium that does.

The structural lesson: the sign of the effective interaction at the collective scale is not determined by the sign of the microscopic interaction. Repulsion plus rotation produces emergent attraction, because rotation converts radial forces into tangential flows, and tangential flows from many sources superpose into convergent patterns. What looks gravitational is actually vortical. What looks attractive is actually the collective consequence of individual repulsion plus spin.

Bo et al., “Three phases of odd robotic active matter,” arXiv:2603.09897 (2026).