  We study the stationary state of a Poisson problem for a system of N
perfectly conducting metal balls driven by electric forces to move within a
medium of very low electrical conductivity onto which charges are sprayed from
outside. When grounded at a confining boundary, the system of metal balls is
experimentally known to self-organize into stable fractal aggregates. We
simulate the dynamical conditions leading to the formation of such aggregated
patterns and analyse the fractal properties. From our results and those
obtained for steady-state systems that obey minimum total energy dissipation
(and potential energy of the system as a whole), we suggest a possible
dynamical rule for the emergence of scale-free structures in nature.
