Simulating mobile automata

Given a mobile automaton like the one from page 73 with rules in the form used on page 887—and behavior of any complexity—the following will yield a causal-invariant substitution system that emulates it:

Map[StringJoin, Map[{"AAABB", "ABABB", "ABAABB"}〚# + 1〛 &, Map[Insert[#〚1〛, 2, 2]  Insert[#〚2, 1〛, 2, 2 + #〚2, 2〛] &, rule], {2}], {2}]