title: Zip-file that contains nothing but itself?
body: <p>Just out of curiosity, does there exist a valid zip-file (according to format spec) that, contains nothing but itself?</p>
  
  <p>Put another way, does the function implemented by <code>unzip</code> have a fix-point?</p>
  
  <p>Can I write a program to search for such a fix-point in a intelligent (not-exhaustive) way?</p>
  
  <p>I've thought about the opposite as well, i.e. if <code>zip</code> has a fix-point, but presumably a file can be compressed in different ways (different algorithms, different levels of compression and so on), thus whether or not <code>f = zip(f)</code> holds for some file <code>f</code> is probably implementation dependent. Since the zip-compression is loss-less however, the case for <code>unzip</code> should probably have a "formal" answer.</p>
  
  <p>Has anyone explored this? Any pointers to related URLs are appreciated.</p>