Would it be interesting to extend the Voronoi tessellation space to allow dynamically reconfiguring its cell structure based on agent positions (and thus density and clustering patterns)?

This would let agent positions directly serve as the seed points for cell generation, with environmental properties computed as aggregates of the agents within each cell. As agents move and form clusters, the tessellation continuously reconfigures, and each cell’s properties - resources, culture, risk levels, collective behaviors - emerge from the characteristics of its constituent agents. This creates a dynamic feedback system where spatial patterns in agent distributions define meaningful regions, and those regions’ aggregate properties can influence subsequent agent decisions.

The space would periodically analyze agent positions using spatial clustering algorithms (like DBSCAN or k-means) and regenerate the Voronoi diagram using cluster centroids or high-density regions as seed points, creating finer-grained cells where agents concentrate and coarser cells in sparse areas.

Example of Voronoi clustering

The implementation would integrate with AgentSet’s groupby and agg methods to efficiently compute cell-level statistics. This is particularly suited for models where the question isn’t “how do agents navigate a fixed environment?” but rather “what regional patterns emerge from agent interactions, and how do those patterns feed back into agent behavior?”
This would enable more efficient neighbor calculations in crowded regions while reducing computational overhead in empty zones - particularly useful for models with emergent spatial patterns like flocking, urban growth, or ecological niche formation.

Agents would need a migration protocol to update their cell assignments across tessellation updates.

Potential applications for an adaptive Voronoi discrete space (as examples):

1. Opinion dynamics and cultural regionalization: Agents with political views, cultural preferences, or beliefs cluster spatially, and each Voronoi cell’s aggregate “culture” emerges from its members—creating emergent regions of consensus, polarization boundaries, or echo chambers that shift as agents migrate or change opinions, useful for studying segregation, radicalization, or social cohesion.
2. Economic market territories: Firm or consumer agents define market regions through their locations and purchasing behaviors, with each cell’s aggregate demand profile, price sensitivity, or brand loyalty emerging from its agents—enabling study of how market boundaries form, compete, and evolve as businesses enter/exit or consumer preferences shift.
3. Collective intelligence and swarm decision-making: Agents exploring a solution space (foraging ants, search drones, or distributed sensors) form clusters around promising areas, with each cell’s aggregate “confidence” or “resource estimate” computed from member observations—creating emergent maps of collective knowledge that guide further exploration and reveal how distributed sensing translates into spatial understanding.​​​​​​​​​​​​​​​​