Stepped Leader Growth: Lattice Dielectric Breakdown Model (2D)

This 2D companion to the 3D stepped-leader simulator implements the dielectric breakdown model the way the original 1984 Niemeyer–Pietronero–Wiesmann paper describes it: as a lattice problem. Every frame, a successive-over-relaxation solver iterates Laplace's equation for the electric potential across a grid, holding the growing leader channel (and the cloud plane above it) fixed at high potential and the ground (plus a movable grounded rod) fixed at zero. Every empty cell touching the channel is scored by the actual potential drop the solver just computed across that bond, raised to a tunable branching exponent η, and the next cell to ionize is drawn from that true field-weighted distribution over the whole perimeter at once — so the channel's fractal branching, its funnelling toward high η, and its attraction to the grounded rod all emerge directly from one shared partial-differential-equation solve rather than from separate hand-coded rules.