Urn schemes with expansion into the adjacent possible

Abstract This chapter introduces a new family of generative models called Urn Models with Triggering (UMT). These models provide a formal framework for exploring the concept of the Adjacent Possible. The key mechanism behind UMT is a positive feedback loop: when a novelty occurs, it triggers further possibilities, reshaping the underlying sample space. This framework successfully replicates three empirical laws associated with innovation processes—Zipf’s Law, Heaps’ Law and Taylor’s Law. Additionally, we introduce extensions that incorporate semantic relationships and a bias between exploration and exploitation. These extensions help explain more complex phenomena, such as temporal clustering and waves of novelties.