Algorithmically, you can think of this as a tensor product of 2 2x2 matrices. In code, you could represent this as

for my $a (0,1) {
   for my $b (0,1) {
      print "Quadrant $a,$b:\n";
      for my $i (0,1) {
         for my $j (0,1) {
            my $row = 2*$a + $i;
            my $col = 2*$b + $j;
            print "  element $i,$j => matrix coord $row, $col\n";
         }
      }
   }
}
[download]

If you wanted to convert in the opposite direction, just use the inverse equations:

for my $row (0..3) {
   for my $col (0..3) {
      print "Quadrant ", int($row/2),',',int($col/2);
      print "  Element ", $row % 2,',', $col % 2,"\n";
   }
}
[download]

Update: added inverse operation.

---

---

Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!

Read Where should I post X? if you're not absolutely sure you're posting in the right place.

Please read these before you post! —

• How do I compose an effective node title?
• How do I post a question effectively?
• Markup in the Monastery

Posts may use any of the Perl Monks Approved HTML tags:

a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr

Outside of code tags, you may need to use entities for some characters:

	For:		Use:
	&		&
	<		&lt;
	>		&gt;
	[		&#91;
	]		&#93;

Link using PerlMonks shortcuts! What shortcuts can I use for linking?

See Writeup Formatting Tips and other pages linked from there for more info.