How can I use regular expressions to count vertical formations of three consecutive 'X' characters in an ASCII 'image'?

Vertical Regex Matching in an ASCII "Image"

Problem Statement

In a text-based representation of an image composed of ASCII characters, we seek to identify vertical formations of three consecutive "X" characters. The width and number of lines in the image can vary.

Matching Existence (Question 1)

To determine the existence of such a formation, we can employ the following regex:

(?xm)
^                        # Beginning of line
(?:
    .                    # Any character except newline
    (?=                  # Lookahead
        .*+\n            # Move to next line
        ( ?+ . )       # Add a character to capturing group 1
        .*+\n            # Next line
        ( ?+ . )       # Add a character to capturing group 2
    )
)*?                      # Repeat as necessary
X .*+\n                  # X on first line, advance to next line
?+                     # If capturing group 1 is defined, use it
X .*+\n                  # X on second line, advance to next line
?+                     # If capturing group 2 is defined, use it
X                        # X on third line

This expression leverages lookaheads with self-referencing capturing groups to add a character for each line repetition and "count" them. Only when all the conditions are met will the regex match, indicating the presence of the formation.

Counting Occurrences (Question 2)

Matching Using Length

While PCRE and Perl (and similar flavors) cannot directly count occurrences using a regex, an alternative solution is to use the length of the substitution result as a measure. By replacing all occurrences of the following expression with "$3," the resulting string's length provides the count:

^
(?:
    (?:                   # Match .+? characters
        .
        (?=               # Count the same number on the following two lines
            .*+\n
            ( ?+ . )
            .*+\n
            ( ?+ . )
        )
    )+?
    (?<= X )              # Till the above consumes an X
    (?=                   # That matches the following conditions
        .*+\n
        ?+
        (?<= X )
        .*+\n
        ?+
        (?<= X )
    )
    (?=                   # Count the number of matches
        .*+\n
        ( ?+ . )        # Number of matches = length of 
    )
)*                        # Repeat as long as there are matches on this line
.*\n?                     # Remove the rest of the line

This expression employs a similar approach to Question 1 but includes X in the counted characters and quantifies the number of matches using a lookahead.

Matching Using Matches

Although variable length lookbehinds are unavailable in most regex flavors, some, like Java and .NET, can provide partial solutions. By using lookbehinds, it's possible to directly count the occurrences without relying on the length of the substitution result.

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