I don't understand how this is obvious -- non-locality does not inherently imply that iteration increases complexity. For a concrete not-entirely-trivial counte

I don't understand how this is obvious -- non-locality does not inherently imply that iteration increases complexity. For a concrete not-entirely-trivial counterexample, von Neumann's middle-square method also appears "non-local" (in that every output bit is a function of a majority of the input bits including well-separated ones) but famously tends to converge to short orbits if not a single constant value.