s/((.)\2{$n})\2*/$1/g;

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Shouldn't the  \2* (zero or more of...) term in the regex above be  \2+ (one or more of...) instead? I.e.:
    s/((.)\2{$n})\2+/$1/g;
Won't the  \2* version lead to useless replacement of sub-strings of n identical characters with the same n-character sub-string (Update: where n is the maximum number of contiguous identical characters originally defined)?

Update: This really should have been posted as a reply to Re: Supress similar chars in the string.

In reply to Re^3: Supress similar chars in the string by AnomalousMonk
in thread Supress similar chars in the string by Lana

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