  Physarum Polycephalum is a slime mold that is apparently able to solve
shortest path problems.
  A mathematical model has been proposed by biologists to describe the feedback
mechanism used by the slime mold to adapt its tubular channels while foraging
two food sources s0 and s1. We prove that, under this model, the mass of the
mold will eventually converge to the shortest s0 - s1 path of the network that
the mold lies on, independently of the structure of the network or of the
initial mass distribution.
  This matches the experimental observations by the biologists and can be seen
as an example of a "natural algorithm", that is, an algorithm developed by
evolution over millions of years.
