Stigmergic Swarm Construction

Colony Parameters

Response threshold θ 0.35

Pheromone evaporation k 0.35 /s

Robot count 36

Diffusion rate D 0.25

Pheromone field Robots

Build Site

Blocks placed

Active sites

Tallest tower

Peak pheromone

0.00

How it works

This is stigmergy: agents don't talk to each other, they coordinate indirectly by modifying a shared environment field and reacting to it. It's the mechanism Grassé proposed for termite mound-building, and the same principle underlies real swarm-construction robotics (e.g. the TERMES project).

Field:      ∂P/∂t = D·∇²P − k·P + deposit(x,t)
Response:   Pbuild(σ) = σⁿ / (σⁿ + θⁿ)     (Bonabeau response-threshold rule)

Every grid cell holds a pheromone level P that diffuses to neighbours (rate D) and evaporates over time (rate k) — a standard reaction-diffusion field.
A robot standing over a cell computes the build probability Pbuild from the local pheromone strength σ using the response-threshold function above (n = 2 here): weak signal → rarely builds, signal above θ → builds almost every check.
Placing a block deposits fresh pheromone at that cell — so a spot that already got one block is more likely to attract the next one, creating a positive-feedback loop that grows discrete towers instead of a flat, even layer.
θ sets colony pickiness: low θ spreads building everywhere (many short stacks); high θ needs strong reinforcement first, concentrating growth into a few tall towers.
Robots themselves move by simple chemotaxis — biased random walk climbing the local pheromone gradient — plus noise, with no map and no leader.

Placed blocks Robots Pheromone field

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