Dielectric Breakdown Lightning (2D)

Field & Grid

Grid resolution 32 cols

Branching probability 0.45

Visual jaggedness 4

Growth reveal speed 10

Show potential field

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Solving potential field…

Grid cells

Path cells

Branch points

Reached ground

–

Relax sweeps

Solve time

0 ms

How this works

This is a genuine Dielectric Breakdown Model (DBM) — the same Laplacian-growth algorithm behind the Niemeyer–Pietronero–Wiesmann model of real electrical discharge. A scalar potential φ is solved on the grid so that ∇²φ = 0 everywhere except the conductor (the growing leader, held at φ = 0) and the cloud plate above row 0 (held at φ = 1), using Gauss–Seidel over-relaxation swept across the grid until it converges.

After each solve, every empty cell touching the current leader is a growth candidate. Each candidate's weight is φ^η at that cell — literally the local field strength raised to a selectivity exponent η (the Branching probability slider controls η: low η → more forks, high η → a straighter channel).
One candidate is chosen at random, weighted by that field, and becomes part of the conductor. The field is then re-solved (warm-started from the previous solution) and the process repeats until a branch reaches the bottom row.
Grid resolution changes how finely the potential field is discretised — a coarser grid gives a blockier field and fewer distinct paths; a finer grid resolves subtler field gradients and produces noticeably different, more delicate branching.
Jaggedness is purely cosmetic: each grid segment is redrawn with recursive midpoint displacement so the channel looks like a hand-drawn spark. It never influences which cell grows next — that decision comes only from φ.

Field-driven growth: every fork is a real relaxation-solved potential, not a random walk