Plane Electrical Networks

Plane Electrical Networks

Plane electrical networks are connected to square tilings of rectangles. In this instance, a 10x10 grid is used as an electrical network between two opposite corners. The resulting square tiling is shown, where the aspect ratio of the rectangle equals the effective resistance of the network. These tilings can be used to prove the existence of harmonic Dirichlet functions on transient planar graphs.- Russell Lyons