Maze-solving with density-driven swarms (2509.18359v1)

Abstract: We propose a new kind of collective motion where swarms of simple agents are able to find and fix the solution of two-dimensional mazes. The model consists of active memoryless particles interacting exclusively via short-ranged perception of local density and orientations. This system generates traveling density waves when constrained in one dimension, and self-organized swarms exploring local branches in two-dimensional mazes. Depending on a single kinetic parameter, the swarms can develop large tails and further gain long-term persistence, which ultimately allows them to robustly solve mazes of virtually any kind and size. By systematic exploration of the parameter space, we show that there exists a fast solving regime where the resolution time is linear in number of squares, hence making it an efficient maze-solving algorithm. Our model represents a new class of active systems with unprecedented contrast between the minimality of the processed information and the complexity of the resolved task, which is of prime importance for the interpretation and modeling of collective intelligence in living systems as well as for the design of future swarms of active particles and robots.