Fractal charge distribution on closed surfaces generated by finite element triangles.

Abstract

A finite element method is employed to calculate the spatial electric potential generated by isolated conductors, where free charges distribute themselves in accordance with classical electrostatics. Remarkably, a novel fractal structure emerges in the surface charge distribution on curved geometries such as spheres and tori. This fractal behavior is distinct from that of the finite element area distribution, highlighting a fundamental difference: the fractal patterns that arise under physical constraints-specifically, Coulomb's law in this study-differ significantly from those produced by purely geometrical operations.