  Many natural processes occur over characteristic spatial and temporal scales.
This paper presents tools for (i) flexibly and scalably coarse-graining
cellular automata and (ii) identifying which coarse-grainings express an
automaton's dynamics well, and which express its dynamics badly. We apply the
tools to investigate a range of examples in Conway's Game of Life and Hopfield
networks and demonstrate that they capture some basic intuitions about emergent
processes. Finally, we formalize the notion that a process is emergent if it is
better expressed at a coarser granularity.
