The Mathematics of Lego

Lego, meet Math:

This curve demonstrates that as the number of pieces in a set grows, so do the number of piece types. However, the number of piece types grows sublinearly: while a larger set uses more piece types, as sets becomes larger, they use progressively fewer additional piece types (so larger sets actually use fewer types per piece). This is similar to other sublinear curves, where larger animals use less energy per cell for metabolism or larger cities actually need fewer gas stations per capita. Essentially, larger sets become more efficient, using the same pieces that smaller sets do, but in a more complex and diverse way.  

While the authors use a rather complicated optimization argument, this can be seen somewhat more intuitively: when a system is under some form of selection (and in the case of Lego, they argue for some form of economic selection), it becomes more costly to grow the system and create new types of pieces. Therefore, it makes sense to use the same types of pieces more efficiently. Intriguingly, the authors also find that there are fewer types of components in natural systems than in human-created systems (for a given size), which makes sense, as evolution takes more time to invent a new part than a designer and a factory do to create a new customized Lego piece.