Lichtenberg Figures
Electrical breakdown creates fractal branching patterns — the same structures found in lightning, river networks, and the feathery scars left on skin or acrylic by high-voltage discharge. Click anywhere to place a seed electrode and watch the tree grow.
P(growth) ∝ |E|η · DLA with electric field bias
Lichtenberg figures and dielectric breakdown
In 1777, the German physicist Georg Christoph Lichtenberg discovered that dust sprinkled on the surface of an insulating plate would arrange itself into branching, tree-like patterns after the plate was exposed to a high-voltage spark. These Lichtenberg figures were among the first fractals ever recorded, though the word “fractal” would not be coined for another two centuries. The same branching geometry appears in lightning bolts, in the vasculature of leaves, in river deltas, and in the scars sometimes left on human skin by lightning strikes. The ubiquity of the pattern is not coincidental: it arises whenever a growth process is governed by a field that concentrates at the tips of an advancing front.
The physics of electrical treeing
When a strong electric field is applied across an insulator, the field is not uniform — it concentrates at sharp points, defects, and the tips of any conducting channel that has already formed. Once the local field exceeds the dielectric strength of the material, a thin conducting channel (a “streamer”) punches through, extending the electrode. This new tip further concentrates the field, and the process repeats. At each step, the channel may branch because multiple nearby sites can exceed the breakdown threshold simultaneously. The probability of growth at any candidate site scales as |E|η, where η is a parameter controlling how strongly the field concentrates growth. Higher η produces sparser, more dendritic trees; lower η produces denser, bushier patterns.
Diffusion-limited aggregation
This simulation uses a variant of diffusion-limited aggregation (DLA), a model introduced by Witten and Sander in 1981. In classic DLA, random walkers diffuse until they contact a growing cluster and stick. The electric-field variant replaces the random walk with a biased probability field: candidate growth sites near existing branch tips are weighted by the local electric potential gradient, raised to the power η. The resulting structures have a fractal dimension that depends on η — typically around 1.7 for two-dimensional dielectric breakdown, close to the fractal dimension of real lightning.
From physics to art
Modern Lichtenberg figures are often created by injecting electrons from a linear accelerator into a block of clear acrylic (polymethyl methacrylate). The trapped charge is then released by touching a grounded point to the surface, and the resulting discharge carves a permanent, glowing fractal tree inside the acrylic. These “captured lightning” sculptures have become prized both as scientific demonstrations and as art objects. The simulation here captures the essential growth dynamics — field-biased, probabilistic branching from a seed point toward a circular ground boundary — while letting you explore how the parameters shape the resulting figure in real time.