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Can interesting behavior happen with just a single rule?
Select[Table[RandomSMW[1,8],{10000}],InterestingRuleQ]
{}
Table[RandomSMW[1,5],{10}]
{{BBABB},{BBAABAA},{ABBBBABBBA},{BAAAB},{AAAAABAA},{AABAABB},{AABBBBAA},{ABAABB},{BAAAAA},{ABAAAABAB}}
MapIndexed[Show[LabelWrapper[SMWXGraphicsStreamed[ChopEvolution@SMWEvolveListX[#,"ABAAB",20],2.5],#2]]&,%];
Exponential behavior is clearly possible: e.g. "A"->"AA"; periodic behavior comes from "A"->"AB".
MapIndexed[Show[LabelWrapper[SMWXGraphicsStreamed[ChopEvolution@SMWEvolveListX[#,"ABAAB",5],2.5],#2]]&,{{"A"->"AA"},{"A"->"AB"},{"AB"->"BA"}}];
Last case corresponds to sorting of the initial condition....
Show[SMWXGraphicsStreamed[SMWEvolveListX[{"AB"->"BA"},RandomString[50],50],2.5]];
Show[SMWXGraphicsStreamed[SMWEvolveListX[{"AB"->"BA"},RandomString[20],15],2.5]];
The following also sorts, but it takes longer.