I don't understand how this shows Turing completeness. The implementation of the rule 110 automaton seems to be limited by both width (not Turing complete because there is a finite number of states of a given width) and iteration limit (not be Turning complete because it always terminates).
Can you write an implementation of rule 110 with arbitrary (i.e. unbounded) width and depth?
Can you write an implementation of rule 110 with arbitrary (i.e. unbounded) width and depth?