For a group $G$ and automorphism $\phi$, the algebraic mapping torus is the group $G \rtimes_{\phi} \mathbb{Z}$. These groups include the fundamental groups of topological mapping tori. A natural theme in the study of these groups is: "what can we learn about the mapping torus from the automorphism $\phi$ used to construct it?". I will describe how the Dehn functions for mapping tori of 3-generator right angled Artin groups can be read off from properties of $\phi$, and provide motivation for this result. This work is joint with Tim Riley.