DLA stands for "Diffusion Limited Aggregation". Diffusion is the process under which particles move by Brownian motion. DLA starts with a seed particle in the middle of the image and then particles diffuse one at a time across the image doman. If any individual particle touches the initial seed particle, it sticks and is added to the cluster. After lots of particles, the final cluster is a self similar fractal.
In the animation shown here, the DLA cluster is shown at different times during its growth. The color legend indicates the time at which particles were added to the cluster.