Sketch · 2026-06-10
Diffusion-limited aggregation.
A single pixel sits at the center. Walkers spawn on a faint circle just outside the cluster, take random steps, and freeze the moment they brush against the tree. The dendrites that grow are the shape minerals draw in fractured rock and the shape soot leaves on a cold window.
What you are seeing
The bright dot at the middle is the seed. Everything around it is a record of which random walker happened to arrive at which spot, in what order. Walkers appear on the faint ring, do a random walk, and either touch the cluster and freeze, or wander past a kill radius and respawn. Cells are colored by the order they were captured: the oldest sticks sit warm and amber near the center, the newest land cool and bright on the outer fringe. The ring expands as the cluster grows, so walkers always spawn close to where the action is.
The rules
The grid is 280 by 280. One cell at the middle starts as stuck. Each frame, every walker takes one step. When a walker is far from the cluster, the step is continuous and its length is its distance to the cluster boundary, so walkers cross empty space in a few hops. Within four pixels of the cluster, the step shrinks to a single grid cell in one of four directions. If a walker lands next to a stuck cell, it becomes stuck itself with probability set by the stickiness slider. At one, walkers stick on first contact and the classical sparse dendrite grows. Slide it down and walkers bounce off until they wander into an inner pocket, so the branches thicken and the cluster fills in. The walker readout controls how many ghosts are drifting at once, which mostly sets how fast the tree grows.
Source
T. A. Witten and L. M. Sander, Diffusion-limited aggregation, a kinetic critical phenomenon, Physical Review Letters 47:19 (1981), pages 1400 to 1403. The real-world objects that share this geometry include copper sulfate electrodeposition, manganese dendrites in agate, viscous fingering in a Hele-Shaw cell, and the channels lightning carves through air.