Formation and structure of ramified charge transportation networks in an electromechanical system

We present findings in an experiment where we obtain stationary ramified transportation networks in a macroscopic nonbiological system. Our purpose here is to introduce the phenomenology of the experiment. We describe the dynamical formation of the network which consists of three growth stages: (I) strand formation, (II) boundary formation, and (III) geometric expansion. We find that the system forms statistically robust network features, like the number of termini and the number of branch points. We also find that the networks are usually trees, meaning that they lack closed loops; indeed, we find that loops are unstable in the network. Finally, we find that the final topology of the network is sensitive to the initial conditions of the particles, in particular to its geometry.