Stationary Self-Organized Fractal Structures in an Open,Dissipative Electrical System

TL;DR

This paper investigates how a system of metal balls driven by electric forces self-organizes into stable fractal structures, combining experiments and simulations to analyze the formation and properties of these patterns.

Contribution

It introduces a dynamical rule explaining the emergence of scale-free fractal structures in an open, dissipative electrical system, supported by simulation and experimental analysis.

Findings

Metal balls form stable fractal aggregates under electric forces.

Fractal properties of the structures are quantitatively analyzed.

A possible dynamical rule for scale-free structure emergence is proposed.

Abstract

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.