Territory Capture 2D: Voronoi Partitioning & Lloyd's Algorithm

The 3D original renders "Territory Capture" as a generic decorative training-lab scene with fabricated reinforcement-learning telemetry and no real territorial mechanic behind it. This 2D companion builds the mechanic the title actually promises: every point on the field is "captured" by whichever of a handful of mobile agents is nearest to it — a live Voronoi diagram recomputed from real agent positions every frame — and a Lloyd's-algorithm centroid-pull slider drives each agent toward the center of mass of the territory it currently owns, the same decentralized coverage-control law used in multi-robot area-division research. Push the gain up and watch the partition relax into a stable, balanced tessellation; add wander noise and watch territory boundaries keep flipping indefinitely instead.