Nested Zeds

A pattern of fractally traversing a quadrant of a plane of integers such that the plane is equally divided into 4^n parts for integer values of n, like so:

  01 02 05 06 17 ...    
  03 04 07 08 19 ...
  09 10 13 14 25 ...
  11 12 15 16 27 ...
  33 34  etc ...

Is there any good use for this, or is it just a cool pattern? Does it already exist under another name?

It looks like a MortonOrder? matrix to me. (Also known as Z-order, so you were thinking along the same lines as others.) When I was in graduate school, one of the professors was researching using the MortonOrder? matrix representation to improve data locality. http://portal.acm.org/citation.cfm?id=379559 --BrookeChenowethCreel?

I use it for music notation, see SyntaxOfMusic.