s/(.)(\.+)/$1 x (1+length $2)/seg;

##</code><code>##

$ perl -wle'
    $_ = "III...MMMMMOOOO....MMMIIIII";
    print;
    s/(.)(\.+)/$1 x (1+length $2)/seg;
    print;
'
III...MMMMMOOOO....MMMIIIII
IIIIIIMMMMMOOOOOOOOMMMIIIII

##</code><code>##

$ perl -wle'
    $_ = "III...MMMMMOOOO....MMMIIIII";
    print;
    1 while s/(.)(\.)/$1$1/sg;
    print;
'
III...MMMMMOOOO....MMMIIIII
IIIIIIMMMMMOOOOOOOOMMMIIIII