This idea was originally derived from models of gas aggregation and is an easy way to produce power laws from simple computer models. The idea is that particles randomly move around and aggregate with each other. Then the aggregated particles move just like the singletons and continue to aggregate. So many groups of one eventually become one group of many. These are the end states, but the really interesting stuff happens in the dynamic states in between. The graph shows hows groups of two for instance build up and decay as the model progresses, and how all the other sized groups grow and decay. The mathematical formula turns out to be simple and interesting.

Perhaps this type of pattern is fundamental to all natural systems that develop by aggregation. For instance all of evolution and life could be viewed as a series of aggregation and disintegration events. People made of millions of cells, bees, cells, and fundamentally all of life and the arrow of time is determined by development through patterns of aggregation.

Anyhow, I applied this type of model to patterns of tuna aggregation in the Great Australian Bight.