  In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated
its ability to solve shortest path problems and to design efficient networks.
For the shortest path problem, a mathematical model for the evolution of the
slime is available and it has been shown in computer experiments and through
mathematical analysis that the dynamics solves the shortest path problem. In
this paper, we introduce a dynamics for the network design problem. We
formulate network design as the problem of constructing a network that
efficiently supports a multi-commodity flow problem. We investigate the
dynamics in computer simulations and analytically. The simulations show that
the dynamics is able to construct efficient and elegant networks. In the
theoretical part we show that the dynamics minimizes an objective combining the
cost of the network and the cost of routing the demands through the network. We
also give alternative characterization of the optimum solution.
