Each nanobot has no global map and no central controller. It only knows the relative position of nearby swarm-mates (within its local sensing radius) and the direction to the one target slot it was assigned during self-organized negotiation. Motion is overdamped Langevin dynamics — the regime that governs real nanoscale particles, where inertia is negligible next to drag and thermal agitation:
γ (dr/dt) = F_target + F_local + F_thermal(t)
F_target = k_t (r_target − r) (assigned-slot attraction)
F_local = Σ_j k_r (r − r_j) / |r − r_j|² for |r − r_j| < R_sense (collision avoidance)
F_thermal ~ N(0, 2 γ k_B T) (Einstein relation — random thermal kicks)
- Target buttons — pick the collective shape the swarm must self-assemble into; slot assignment is recomputed by nearest-available matching, mimicking a distributed auction each bot could run with its neighbors.
- Thermal noise (kBT) — raises the random-kick amplitude; too high and Brownian jitter overwhelms the weak per-bot control force, exactly the real engineering limit nanorobots face at this scale.
- Local sensing radius — how far a bot can "see" its neighbors; only bots within this radius exert a repulsion force, so avoidance is purely local, never global.
- Control gain kt — the strength of each bot's own actuation toward its slot, standing in for a real nanorobot's propulsion (chemical, magnetic or acoustic) fighting against thermal noise.
- Scatter & Reassemble — randomizes every position, then lets the same local rules recover the target formation with no re-programming, demonstrating self-organization and resilience without central coordination.
Real-world relevance: DNA-origami and magnetic nanorobot swarms studied for targeted drug delivery and micro-assembly rely on exactly this trade-off — local rules strong enough to beat Brownian motion, but simple enough that no single unit needs the whole picture.