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target = "METHINKS IT IS LIKE A WEASEL";
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alphabet = Append[CharacterRange["A", "Z"], " "];
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fitness = HammingDistance[target, #] &;
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mutate[str_String, rate_ : 0.01] := StringReplace[
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str,
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_ /; RandomReal[] < rate :> RandomChoice[alphabet]
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]
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mutationRate = 0.02; c = 100;
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NestWhileList[
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First@MinimalBy[
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Thread[mutate[ConstantArray[#, c], mutationRate]],
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fitness
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] &,
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mutate[target, 1],
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fitness@# > 0 &
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] // ListAnimate
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