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DLA is short for "diffusion limited aggegration"[0]. There are particles performing a random walk [1] and they aggregate (= stick together) if they come close enough to each other.

In the second experiment with directional bias the particles are experiencing a constant drift on top of the random walk (or are maybe having unequal probabilities of moving in different directions?)

[0] https://en.m.wikipedia.org/wiki/Diffusion-limited_aggregatio...

[1] https://en.wikipedia.org/wiki/Random_walk