A recent study from the Santa Fe Institute reveals that diverse complex systems—from microbial cells to corporations to cities—follow universal mathematical growth patterns governed by Heaps’ law. As these systems expand, they add new functions at an increasingly slower rate, a phenomenon called sublinear growth, meaning that doubling a system’s size doesn’t double its functional diversity. Instead, growth relies on a “rich-get-richer” dynamic where systems scale up existing functions rather than inventing entirely new ones. Most organism-like systems (cells, universities, companies) follow this sublinear power-law pattern, while cities—which operate as decentralized ecosystems—grow even more slowly by adding genuinely new functions at a logarithmic rate. This discovery highlights a universal tradeoff between innovation and expansion that shapes how complexity scales across both natural and human-made worlds.