The beautiful, branching patterns that reveal the hidden mechanics of electricity

Ideas & Philosophy · Published 2 October 2026 Swipe more like this →

In short: When high-voltage discharges strike an insulator, they leave behind intricate, fern-like scars known as Lichtenberg figures. These fractal patterns are more than just visual curiosities; they are vital diagnostic tools for engineers and the precursors to the modern photocopier.

Named after the German physicist Georg Christoph Lichtenberg, these figures were first studied in 1777. By using a large electrophorus to generate static electricity and sprinkling powdered materials onto an insulator, Lichtenberg recorded radial patterns that eventually led to the discovery of the fundamental principles behind modern xerography. At the time, scientists believed these characteristic shapes might reveal the nature of positive and negative electric 'fluids.'

The formation of these figures depends heavily on electrical polarity. When using a mixture of sulfur and red lead, the resulting colors reveal the charge distribution: sulfur particles acquire a negative charge while red lead becomes positive. A positive charge typically creates a dense nucleus with radiating branches, whereas negative areas appear smaller with sharp, fan-like boundaries. This difference is tied to how sparks propagate through air, a property now used to measure lightning surges on power lines.

Beyond their aesthetic appeal, these patterns represent a fundamental physical principle. The branching, self-similar structures are examples of fractal properties, often related to a process called diffusion-limited aggregation. In 1996, Duke professor Adrian Bejan proposed the 'constructal law' to explain such patterns, suggesting that nature evolves these tree-like designs to facilitate the most efficient movement of currents through a system.

Today, the study of these figures extends into three dimensions. Researchers use electron beam accelerators, such as a LINAC, to inject high-energy electrons into materials like acrylic. This creates internal 'electron trees' or 'lightning trees' through dielectric breakdown. While artists use similar principles for 'fractal burning' on wood, this practice is extremely dangerous and results in annual deaths from electrocunning.

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