Imagine a particle is fixed at some point on a plate. Then, another particle is droped somewhere else onto the plate and allowed to move randomly by diffusion. When it eventually hits the fixed particle it will stick to it as the people that touch the golden goose in the fairy tale stick to the goose. And, as the people that touched other people already connected to the goose also get stuck, subsequently dropped particles also stick to other particles that already got stuck before. Did you never ask yourself why all the drawings of the situation in the fairy tale show these people assembled in a single line and not in a wildly branched multitude?

Because, dropping more and more particles onto the plane and applying the same rule as above one obtains a branched structure that seems to look the same independently which length scale you look at:  branches, twigs or even smaller parts.  So people numerically computed a lot of these aggregates, studied their properties, changed the rules, compared the results to aggregates occuring in nature and started to make theoretical models about the numerical aggregates to understand the amazingly universal features.

I did a little bit on this in my diploma work, read lots of articles and wrote at the end a small one, that shows you may work around certain problems but at the end you come to the same problem you started with only that it appears at a different point. And sometimes this makes the difference. But in my case it did not.