Ant Colony Double-Bridge: Pheromone Phase-Space Map

A colony of ants connects its nest to a food source over two bridges of different length, and no single ant ever measures distance or compares the branches — each simply deposits evaporating pheromone on whichever branch it just walked and, at the next fork, chooses probabilistically toward whichever branch already smells stronger. Instead of watching that unfold as a diorama of ants on bridges, this simulator plots the colony's entire collective state directly as a point in pheromone phase space — the short-branch pheromone level on one axis, the long-branch level on the other — moving across a live-colored choice-probability field. Because trips on the short branch finish faster, that branch accumulates reinforcement faster too, and you can watch the trajectory get pulled off the neutral diagonal and driven into ever more lopsided territory by nothing but positive feedback. Adjust the length ratio, evaporation rate and the nonlinearity of the choice rule to see when the trajectory converges cleanly toward the short-branch axis, when it wanders and stays near the diagonal, and when it can even lock onto the long-branch axis by chance — the same dynamics that inspired Ant Colony Optimization as a search algorithm.