One of the strongest large cardinal axioms we have posits the existence of an elementary embedding \(j\) from \(V_\lambda\) to \(V_\lambda\) for some limit ordinal \(lambda\). A peculiarity of it is that one such \(j\) will generate infinitely many more, not only through composition but also through the process of applying one embedding to the graph of another.
I will talk about the structure generated in this way, and in particular the critical points of these embeddings.