The science
A lightning leader advances in steps toward the ground along the path where the electric field is strongest. The dielectric breakdown model (Niemeyer, Pietronero & Wiesmann, 1984) reproduces the branching shape with two ingredients.
- Potential: the grid solves Laplace's equation
∇²φ = 0 by successive over-relaxation, with the growing channel held at the cloud potential (φ=1) and the ground at 0.
- Growth rule: a cell next to the channel joins it with probability
p ∝ (1 − φ)η (1 − φ is the potential measured from the channel, proportional to the local field next to the tip). η = 1 gives the bushy fractal with D ≈ 1.7; larger η gives thin near-straight channels, η → 0 a dense blob.
- Energy: potential
V = E H (mean leader field times cloud height, e.g. 0.21 MV/m × 2 km ≈ 420 MV); stroke energy W = ½ Q V; thunder delay t = d / 343 m/s.
Honest simplifications: this is a statistical 2D model, not a plasma simulation. It ignores streamers, charge transport, air chemistry and the return-stroke current (the bright flash is just an animation of the main channel); the field strength is a typical mean value for a leader, not the 3 MV/m breakdown field of still air. The grid is 100×96 cells, so the fractal dimension is a rough box-counting fit over 1–16 cells.