Bacteria which grow not on the featureless agar plates of the microbiology lab but
in the real world must navigate topologies which are nontrivially complex, such as
mazes or fractals. We show that chemosensitive motile E. coli can efficiently explore
nontrivial 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.
