  Graphical chip-firing is a discrete dynamical system where chips are placed
on the vertices of a graph and exchanged via simple firing moves. Recent work
has sought to generalize chip-firing on graphs to higher dimensions, wherein
graphs are replaced by cellular complexes and chip firing becomes
flow-rerouting along the faces of the complex. Given such a system, it is
natural to ask (1) whether this firing process terminates and (2) if it
terminates uniquely (e.g. is confluent). In the graphical case, these questions
were definitively answered by Bjorner--Lovasz--Shor, who developed three
regimes which completely determine if a given system will terminate. Building
on the work of Duval--Klivans--Martin and Felzenszwalb-Klivans, we answer these
questions in a context called flow-firing, where the cellular complexes are
2-dimensional.
