Non-uniform number-conserving elementary cellular automata

In this paper, we investigate non-uniform elementary cellular automata (i.e., one-dimensional whose cells can use different Wolfram rules to update their states) in the context of number conservation. As a result, obtain an exhaustive characterization such number-conserving on all finite grids both with periodic and null boundary conditions. The obtained allows, inter alia, enumerate automata, particular those that are reversible. Surprisingly, numbers closely related Fibonacci sequence.