If you look at your grep statement, you're only selecting files that start with a "dot". Ok; this is well and good. Indeed, it works just as I would expect (I run it and get this:

.
..
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with no new line on the last line of output)

I'm thinking this is the opposite of what you want, which is probably the files which don't start with a period, in which case your grep statement would look like this:

my @dots = grep { ! /^\./} readdir(DIR);
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which will take out files which start with a period instead of the files which don't. As an (possibly preferable) alternative, you could use this:

my @dots = glob("*"); # adjust argument to glob as needed
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Most of the time, I tend to prefer glob, mostly because I'm lazy (it saves a lot of typing). The exception is when I've got to deal with Windows (which is most of the time), where I find that glob seems to get confused with filenames containing blanks (yeah, I could escape them).