Here's my try at it. It uses two forms of string replacement - one transliteration, replacing every G with a space, and one regular expression, replacing a single character, followed by one or more spaces and then that character again, with two more spaces.

#!/usr/bin/perl -w
use strict;
my $line;

print( $line = join( "", ('A' .. 'G'), reverse ( 'A'..'F' )), "\n" );
$line =~ tr/G/ /;
print( $line, "\n" );

while ($line !~ /^\s+$/) {
  $line =~ s/(\S)(\s+)\1/ $2 /;
  print( $line, "\n");
};
[download]

This is obviously not the smallest possible code, but a bit more Perlish and elegant (IMholyO) :-)