# Walker diffusion method for solution of ohmic circuit problems

## TL;DR

This paper introduces a probabilistic Walker diffusion method for solving complex ohmic circuit problems, offering an alternative to traditional linear algebra approaches, demonstrated on a fractal-like circuit.

## Contribution

A novel probabilistic Walker diffusion approach for solving complex ohmic circuits, especially those with intricate connectivity like fractal structures.

## Key findings

- The method effectively solves circuits with complex connectivity.
- It provides an alternative to matrix-based solutions.
- Demonstrated on a Sierpinski triangle circuit.

## Abstract

A probabilistic method is derived for solution of ohmic circuit problems. It is compared to the standard approach, which is construction and solution of a set of coupled, linear equations manifesting Kirchhoff's laws. An example is made of an electrical circuit that has the complicated connectivity of a bond-and-node Sierpinski triangle, which would be tedious to solve by matrix methods.