Or maybe just taking some precautions when setting up the division scheme for a particular cellular automaton might be good enough in other cases, depending on how dynamic and non-homogeneous the behavior over the grid will be.

For fixed n this is, of course, a cellular automaton. You can allow any positive integer states for each of the n cells. The transition rule is such that if a cell has state x >=2 then the state never exceeds x and if it has state x < 2 then it either stays the same or increase by 1 or 2.

The paper concludes:
The Busy Boxes variant of the SALT family of reversible cellular automata has shown itself to possess an intriguing number of features that are worthy of further study and analysis. Physicist Gerard T'Hooft has written about the possibility that reversible CA's such as this one may help elucidate some aspects of physics in the quantum realm [5]. We believe that the study of emergent, qualitative, and statistically predictable behavior of these kinds of discrete, deterministic systems can indeed shed light on questions in physics, and may also help to clarify the deeper principles of entropy and the origin of complex, self-propagating systems such as those found in our biosphere

Hello, I have recently constructed a cellular automaton in Golly, with a starting population of roughly 899 million, that produces Shierpinski's triangles.

Cellular automaton

Meaning

Noun