fermants

bachelor thesis · university of zurich · supervised by dr. p. saha

Fermants — a portmanteau of Fermat and ants — is an agent-based simulation exploring how foraging ants find optimal paths through pheromone-based stochastic processes.

The central thesis: the "Fermatian pathfinding" observed in ant colonies is an emergent property. Much like light refracts along the fastest route between two media (Fermat's principle), ants navigating between nest and food source converge on shortest paths — not through individual intelligence, but through collective pheromone feedback.

The simulation models ants as agents performing random walks on a discrete 2D grid. Each ant deposits pheromone trails; subsequent ants probabilistically follow stronger trails. Over successive iterations, the model introduces pheromone evaporation, refraction indices for heterogeneous terrain, directional pheromone fields, and divergence-based path evaluation.

Through ten progressive simulation runs, the work demonstrates how simple local rules — deposit, evaporate, follow — produce globally optimal paths. Average path lengths decrease dramatically over time, converging toward the geometric shortest route.

The work builds on Christopher Langton's emergent behavior research, Marco Dorigo's ant colony optimization algorithms, and experimental studies from the University of Regensburg on real ant foraging behavior.

„Gehe hin zur Ameise, du Fauler! Sieh ihre Wege und werde weise." — Buch der Sprüche Salomos 6, 6