We derive a fractal model for current transport in Lichtenberg-type resistor networks and analyze its electrical and transport properties in the infinite-branch limit. By assigning a fractional dimensionality to the branching geometry, motivated by its equivalence with Sierpinski-type fractals, we obtain a closed-form expression for the equivalent resistance as a function of the fractal dimension and scale factor. We show that only fractal branching configurations yield a finite, strictly positive resistance for an infinite number of resistive elements, in contrast to purely series or parallel arrangements. This result implies finite power dissipation under finite applied voltage and provides a geometric explanation for the emergence of fractal discharge patterns at high voltages. The model further predicts finite traversal times for charge carriers and a scale-invariant charge mobility across the network. These results establish a direct link between fractal geometry and macroscopic transport parameters relevant for electrically active and semiconductor-like systems.
Octavian Postavaru (Tue,) studied this question.
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