Diffusion-Limited Aggregation

Simple DLA

In its simplest form, DLA occurs on a roughly circular grid of square cells.
The cell at the center of the circle is the location of the seed point, a particle stuck at that square.
Now pick a square on the perimeter of the grid and place a wandering particle on that square.
With each tick of the clock, this particle moves to one of the four adjacent squares, left, right, above, or below.
If the moving particle wanders too far from the seed, it falls off the edge of the grid and another wandering particle is started at a randomly chosen edge point.
When a wandering particle arrives at one of the four squares adjacent to the seed, it sticks there forming a cluster of two particles, and another moving particle is released.
When a moving particle arrives at one of the squares adjacent to the cluster, it sticks there.
Click the picture to animate.
Continuing in this way, with patience we can build up a large aggregate.
This process is called diffusion-limited aggregation because the growth of the cluster is governed by the particles' diffusing across the grid.
Here are two small DLA clusters.

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