I was going through some old papers in my office recently and I came across a paper entitled Scaling of Differentiation in Networks: Nervous Systems, Organisms, Ant Colonies, Ecosystems, Businesses, Universities, Cities, Electronic Circuits, and Legos. Crazy collection of systems aside, let’s focus on the last one. These scientists studied Legos to understand networks! It’s great.

The argument of the paper is essentially that when a system is under some form of selection (and in the case of Lego, they argue for some form of economic selection), the number of distinct types of components in a system rises along with the size of the system itself. However, they find that there are fewer types of components in natural systems than in human-created systems and make an evolutionary argument to explain that.

But back to the Legos: using a dataset of 389 Lego sets (this was done back in 2002, so if anyone can download the data easily, I would love to see if the results hold up with a richer dataset), they examined the number of distinct types of pieces in a set versus the total number of pieces. And they found that it could be fit nicely to a power law. Here it is on a log-log scale:

I have seen other research that uses Lego pieces as building blocks, but this is the first study I have come across that actually examines pre-existing Lego sets as systems themselves.