STATIONARY SELF-ORGANIZED FRACTAL STRUCTURES IN AN OPEN, DISSIPATIVE ELECTRICAL SYSTEM

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