Dielectric Breakdown
Apply a voltage across an insulator and watch fractal lightning grow. Each step, the boundary extends where the electric potential is highest — producing the branching Lichtenberg figures found in struck acrylic, frozen lightning, and high-voltage discharges.
φ(x) probability ∝ |∇φ|η
and begin growth
The physics
Dielectric breakdown occurs when an insulating material is subjected to a voltage high enough to free bound electrons, creating a conducting path. The resulting discharge carves Lichtenberg figures — fractal branching trees named after Georg Christoph Lichtenberg, who first observed them in 1777 by pressing charged resin onto paper.
The model
This simulation uses a stochastic growth model inspired by the dielectric breakdown model (DBM) introduced by Niemeyer, Pietronero, and Wiesmann in 1984. Growth candidates at the boundary of the existing structure are selected with probability proportional to the local electric field raised to the power η. Higher η concentrates growth along the strongest field lines (more linear, less branching), while lower η produces bushier, more fractal structures.
The coloring
Branches are colored by depth: bright white-blue at the growing tips fades through purple to gold at the trunk, mimicking the luminous plasma channels of real electrical discharges. Thicker lines near the root represent the higher current density in the primary channels.