Bacterial Route-finding and Collective Escape in Mazes and Fractals

Bacteria which grow not on the featureless agar plates of the microbiology lab but in the real world must navigate topologies which are non-trivially complex, such as mazes or fractals. We show that chemo-sensitive motile {\em E. coli} can efficiently explore non-trivial mazes in times much shorter than a no-memory (Markovian) walk would predict, and can collectively escape from a fractal topology. The strategies used by the bacteria include individual power-law probability distribution function exploration, the launching of chemotactic collective waves with preferential branching at maze nodes and defeating of fractal pumping, and bet hedging in case the more risky attempts to find food fail.