Unseen · charge finding ground

Lichtenberg — the path electricity chooses, dielectric breakdown branching through acrylic to ground

Trap enough charge in a slab of acrylic and it cannot stay. It finds ground the only way it can — branching, splitting, racing outward along the invisible field — and freezes the instant it arrives: a fossil of the path the electricity chose.

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0 Filaments grown

0mm Reach to ground

0 Branch order

— Potential φ at cursor

Branch density by radius

It doesn't take the short way. It takes the likely way.

There is no wire in the acrylic, no channel cut ahead of time. The charge sits trapped, straining against a slab that will not conduct — until the field somewhere exceeds what the material can hold, and a single bond gives way. From that first breach the discharge grows, and at every step it faces the same blind question: which piece of the insulator breaks next?

It answers by chance, weighted by the field. Where the potential steepens, breakdown is more likely — so the tree reaches toward ground, but never straight. Small advantages compound; a tip that gets ahead draws more of the field to itself and pulls further ahead still. The result is not a line but a fractal — the same feathered fork whether you read the whole figure or a single twig.

The empty acrylic holds a smooth, invisible potential field between the trapped charge and ground.

Each new filament is chosen at random, weighted by the local field raised to a power η — the dielectric-breakdown rule that governs everything from this block to a strike of lightning.

The finished figure is self-similar across scale, filling the plane to a fractional dimension near D ≈ 1.7.

What the discharge already knows

01 · the field A smooth invisible slope ∇²φ = 0 Across the empty insulator the potential is smooth and Laplacian — a gradient the eye can't see but the breakdown reads at every tip.

02 · the choice Chance, weighted by field p ∝ |∇φ|^η The next bond to break is random, biased toward the steepest field. With η near one the tree grows open and feathered, not dense.

03 · the fossil Self-similar at every scale D ≈ 1.7 The figure fills the plane only fractionally — the same branching fern whether you look at the trunk or the finest tendril.