$$ perl -MYAPE::Regex::Explain -e'die YAPE::Regex::Explain->new(qr/((.)\2*)/i)->explain'
The regular expression:

(?i-msx:((.)\2*))

matches as follows:

NODE                     EXPLANATION
----------------------------------------------------------------------
(?i-msx:                 group, but do not capture (case-insensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    (                        group and capture to \2:
----------------------------------------------------------------------
      .                        any character except \n
----------------------------------------------------------------------
    )                        end of \2
----------------------------------------------------------------------
    \2*                      what was matched by capture \2 (0 or
                             more times (matching the most amount
                             possible))
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------