ANTFARM

06 · HOW IT WORKS

No ant knows the plan. Every tick, each one follows these rules:

1. Walk forward with a little wobble. When not carrying and the colony still needs room, dig into dirt ahead (now and then to the side).
2. Heading out, lay HOME scent. Carrying a crumb, lay FOOD scent. Each step away from the nest or the food lays a little less, so scent grows toward its source.
3. Searching ants lean toward FOOD scent, carriers toward HOME scent. A cell pulls with (k + scent)², the same shape as the choice rule (Eq. 3) that Goss et al. used, based on their own earlier experiments.
4. Every tick each cell keeps 99.6% of its scent, so an unused trail halves in about 6 seconds at 1×. This is the evaporation step of Dorigo et al.’s Ant System.
5. The queen turns two stored crumbs into an egg; crumbs you drop into her chamber go straight into the store. Eggs hatch into workers, and workers grow old and die.

No rule says “make a trail” or “take the shortcut”. Those come from the ants plus the scent they leave behind. In 1959 Pierre-Paul Grassé introduced the idea of stigmergy to explain how insects that work as if alone can still look coordinated.

The DOUBLE BRIDGE scene is a simplified version of the set-up of Goss et al. (1989). Their lab colonies of Argentine ants reached food over a bridge of two modules in a row, each with a short and a long branch; with the long branch twice as long, the colonies favoured the short one in 14 of 14 runs. In 11 of 14 runs with that ratio, more than 80% of the traffic used the short branch. The game has a single module. The SHORT BRANCH meter shows what this model does.

Try it: in DOUBLE BRIDGE, block the short branch with ROCK, wait for the long trail, then DIG it open again. When Goss et al. added the short branch later, their ants mostly kept the long trail (only 2 of 18 runs switched). Their pheromone lasted about 30 minutes, so they left evaporation out of their model. Scent here fades in seconds, so this colony usually switches.

This is a game model, not a biology simulator. The grid, the two scents, the digging budget, egg cost, lifespans and every number here are made up for play.

SOURCES

1. Goss, S., Aron, S., Deneubourg, J.-L. & Pasteels, J. M. (1989). Self-organized shortcuts in the Argentine ant. Naturwissenschaften 76(12), 579–581. doi:10.1007/BF00462870 The double-bridge experiment, the (k + S)² choice rule (Eq. 3) and the ~30-minute pheromone lifetime.
2. Dorigo, M., Maniezzo, V. & Colorni, A. (1996). Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B 26(1), 29–41. doi:10.1109/3477.484436 Trail update with evaporation, τ ← ρ·τ + Δτ (Eq. 1), and shorter tours laying more trail per edge (Eq. 3).
3. Theraulaz, G. & Bonabeau, E. (1999). A brief history of stigmergy. Artificial Life 5(2), 97–116. doi:10.1162/106454699568700 Grassé introduced stigmergy in 1959; a history of the idea.