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Zipf's, Heaps' and Taylor's laws are ubiquitous in many different systemswhere innovation processes are at play. Together, they represent a compellingset of stylized facts regarding the overall statistics, the innovation rate andthe scaling of fluctuations for systems as diverse as written texts and cities,ecological systems and stock markets. Many modeling schemes have been proposedin literature to explain those laws, but only recently a modeling framework hasbeen introduced that accounts for the emergence of those laws without deducingthe emergence of one of the laws from the others or without ad hoc assumptions.This modeling framework is based on the concept of adjacent possible space andits key feature of being dynamically restructured while its boundaries getexplored, i.e., conditional to the occurrence of novel events. Here, weillustrate this approach and show how this simple modelling framework,instantiated through a modified Polya's urn model, is able reproduce Zipf's,Heaps' and Taylor's laws within a unique self-consistent scheme. In additionthe same modelling scheme embraces other less common evolutionary laws (Hoppe'smodel and Dirichlet processes) as particular cases.

Zipf's, Heaps' and Taylor's laws are determined by the expansion into the adjacent possible