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I'm working with a multiway system and I have a number of different mutation rule lists. I need an efficient way of managing which rule lists I apply.

Here is the basic multiway system code that I'm using:


MWStep[rule_List, slist_List] := 
  Union[Flatten[Map[Function[s, Map[MWStep1[#, s] &, rule]], slist]]];

MWStep1[p_String -> q_String, s_String] := 
  Map[StringReplacePart[s, q, #] &, StringPosition[s, p]];

MWEvolveList[rule_, init_List, t_Integer] := 
  NestList[MWStep[rule, #] &, init, t];

StepNtimes[Rule_, string_, n_] := (
   i = 1;
   Subfunc[x_] := MWStep[Rule, x];
   Results = Flatten[NestList[Subfunc, string, n]] )

So for example, with a rules list "M1", I might do

StepNtimes[M1, SampleString, 5]

But say I have Rule lists M1,M2,M3,M4,...,MK

And I want to apply them in different patterns and save the results after each application. That is, if

ResultSetA = StepNtimes[M1, SampleString, 5]
ResultSetB = StepNtimes[M2, ResultSetA, 5]

... I want

FinalResults = Flatten[{ResultSetA, ResultSetB, ...}]

Nested Functions? Composition?

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k[{data_, {}}] := {}
k[{data_, rulez_}] := k[{Sow@StepNTimes[data, rulez[[1]], 5], Rest@rulez}]
Reap@k[{data, {M1, M2}}]

(* {{}, {{StepNTimes[data, M1, 5], StepNTimes[StepNTimes[data, M1, 5], M2, 5]}}} *)
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