diff -rc v5/Makefile v6.1/Makefile
*** v5/Makefile	Tue Nov 11 09:24:59 2008
--- v6.1/Makefile	Wed Nov 19 03:03:52 2008
***************
*** 1,21 ****
  all:	Pub/.copied
  
! SOURCES=makeindex.php.txt hilbert.py hilbert_test.py Makefile
! PUBFILES=${SOURCES} index.html hilbert_thumb.gif v4_v5_diff.txt
  
! v4_v5_diff.txt:	old/v5/.copied
! 	(cd old; diff -rc v4 v5 >../v4_v5_diff.txt; true)
  
! old/v5/.copied:	${SOURCES}
! 	cp ${SOURCES} old/v5
! 	touch old/v5/.copied
  
  Pub/.copied:	${PUBFILES}
  	cp ${PUBFILES} Pub
  	touch Pub/.copied
  
! index.html:	makeindex.php.txt
  	rm -f index.html
  	touch datefile
! 	php makeindex.php.txt >index.html
  	chmod a-w index.html
--- 1,36 ----
  all:	Pub/.copied
  
! VERNUM=6.1
! PREVNUM=5
! VER=v${VERNUM}
! PREV=v${PREVNUM}
  
! SOURCES=makeindex.php.txt hilbert.py hilbert_test.py hilbert_pic.py \
! 	Makefile
  
! DIFFS=v4_${VER}_diff.txt ${PREV}_${VER}_diff.txt 
! 
! PUBFILES=${SOURCES} ${DIFFS} index.html hilbert_thumb.gif hilbert_pic.pdf
! 
! v4_${VER}_diff.txt:	old/${VER}/.copied
! 	(cd old; diff -rc v4 ${VER} >../v4_${VER}_diff.txt; true)
! 
! ${PREV}_${VER}_diff.txt:	old/${VER}/.copied
! 	(cd old; diff -rc ${PREV} ${VER} >../${PREV}_${VER}_diff.txt; true)
! 
! old/${VER}/.copied:	${SOURCES}
! 	cp ${SOURCES} old/${VER}
! 	touch old/${VER}/.copied
  
  Pub/.copied:	${PUBFILES}
  	cp ${PUBFILES} Pub
  	touch Pub/.copied
  
! index.html:	${SOURCES} ${DIFFS}
  	rm -f index.html
  	touch datefile
! 	php makeindex.php.txt ${VERNUM} >index.html
  	chmod a-w index.html
+ 
+ hilbert_pic.pdf:	hilbert.py hilbert_pic.py
+ 	hilbert_pic.py >hilbert_pic.pdf
diff -rc v5/hilbert.py v6.1/hilbert.py
*** v5/hilbert.py	Tue Nov 11 09:24:59 2008
--- v6.1/hilbert.py	Wed Nov 19 03:03:52 2008
***************
*** 4,9 ****
--- 4,11 ----
  #        int_to_Hilbert( 0, nD ) ==> ( 0, 0, 0, ... 0 ) Start at origin.
  #        int_to_Hilbert( 1, nD ) ==> ( 1, 0, 0, ... 0 ) 1st step is along x.
  #    Hilbert_to_int( ( x, y, z ) ) ==> i
+ # Steve Witham ess doubleyou at tiac remove-this dot net.
+ # http://www.tiac.net/~sw/2008/10/Hilbert
  
  
  from sys import argv
Only in v5: hilbert.pyc
Only in v6.1: hilbert_pic.py
diff -rc v5/hilbert_test.py v6.1/hilbert_test.py
*** v5/hilbert_test.py	Tue Nov 11 09:24:59 2008
--- v6.1/hilbert_test.py	Wed Nov 19 03:03:52 2008
***************
*** 121,160 ****
  #
  # visited is a dictionary (or "hash" or associative array) whose key
  # is a tuple representing the point coordinates.  Prefix is a list
! # of coordinates that's built up by recursion to the right size.  
! # "tuple(prefix) in visited" converts the list to a tuple 
  # and asks whether an entry with that key is in the dictionary.
! def check_visited( visited, prefix, size, nD ):
      if nD > 0:
!         for i in range( size ):
!             check_visited( visited, prefix + [i], size, nD - 1 )
      else:
          if not tuple( prefix ) in visited:
              print "missing", prefix
  
  
! def int_to_Hilbert_test( n, nD ):
!     ld = int( n ** (1./nD) )
!     assert ld ** nD == n
      visited = {}        
      for i in range( n ):
          pt = tuple( int_to_Hilbert( i, nD ) )
!         print pt,
!         visited[ pt ] = True      # Add pt to visited dictionary.
          j = Hilbert_to_int( pt )
          if j != i:
              print "BZZT, decodes to", j,
!         if i > 0:
              nDiffs = sum( [ pt[k] != prev_pt[k] for k in range( nD ) ] )
              if nDiffs != 1:
                  print "BZZT, different along", nDiffs, "dimensions",
              maxDiff = max( [ abs(pt[k] - prev_pt[k]) for k in range( nD ) ] )
              if maxDiff != 1:
                  print "BZZT, max difference is", maxDiff,
          prev_pt = pt
!         if ( i + 1 ) % 8 == 0:
!             print
!     check_visited( visited, [], ld, nD )
  
  
  if argv[0].endswith( "/hilbert_test.py" ) or argv[0] == "hilbert.py":
--- 121,173 ----
  #
  # visited is a dictionary (or "hash" or associative array) whose key
  # is a tuple representing the point coordinates.  Prefix is a list
! # of coordinates that's built up by recursion to the right number of
! # dimensions.  "tuple(prefix) in visited" converts the list to a tuple 
  # and asks whether an entry with that key is in the dictionary.
! def check_visited( visited, prefix, linear_size, nD ):
      if nD > 0:
!         for i in range( linear_size ):
!             check_visited( visited, prefix + [i], linear_size, nD - 1 )
      else:
          if not tuple( prefix ) in visited:
              print "missing", prefix
  
  
! def tuple_print_width( n ):  # tuple with n 1-digit numbers and trailing sp
!     if n == 0:  return 3   # ()_
!     if n == 1:  return 5   # (1,)_  special case
!     else:       return n * 3 + 1
! 
! 
! def int_to_Hilbert_test( n, nD, doPrint=True ):
!     tups_per_line = 2**( int( log( 80 / tuple_print_width( nD ), 2 ) ) )
!     linear_size = int( ( n + .5 ) ** (1./nD) )
!     isCube = linear_size ** nD == n
!     if not isCube:
!         print "(This is not a complete cube:)"
      visited = {}        
      for i in range( n ):
          pt = tuple( int_to_Hilbert( i, nD ) )
!         if doPrint: print pt,
!         visited[ pt ] = True      # Add pt to "visited" dictionary.
          j = Hilbert_to_int( pt )
          if j != i:
              print "BZZT, decodes to", j,
! 
!         if i > 0:  # Check that we have stepped one unit, along one dim:
              nDiffs = sum( [ pt[k] != prev_pt[k] for k in range( nD ) ] )
              if nDiffs != 1:
                  print "BZZT, different along", nDiffs, "dimensions",
              maxDiff = max( [ abs(pt[k] - prev_pt[k]) for k in range( nD ) ] )
              if maxDiff != 1:
                  print "BZZT, max difference is", maxDiff,
+ 
          prev_pt = pt
!         if ( i + 1 ) % tups_per_line == 0:
!             if doPrint: print
! 
!     if isCube:
!         check_visited( visited, [], linear_size, nD )
  
  
  if argv[0].endswith( "/hilbert_test.py" ) or argv[0] == "hilbert.py":
***************
*** 166,175 ****
      print
      int_to_Hilbert_test( 64, 3 )
      print
      for nD in [ 2, 3, 4, 5 ]:
          pt = [ 0 ] * nD
!         pt[0] = 1000000
          x = Hilbert_to_int( pt )
          print x, log( x, 10 )
!         print int_to_Hilbert( 1000000, nD )
  
--- 179,205 ----
      print
      int_to_Hilbert_test( 64, 3 )
      print
+     int_to_Hilbert_test( 4096, 3, doPrint=False ) # nChunks > nD
+     print
+     int_to_Hilbert_test( 4096, 4, doPrint=False )
+     print
+     k = 10**12  # definitely a long
      for nD in [ 2, 3, 4, 5 ]:
+         # Decode point ( k, 0, 0... ) to an int...how many digits?:
          pt = [ 0 ] * nD
!         pt[0] = k
          x = Hilbert_to_int( pt )
          print x, log( x, 10 )
!         # Double-check:
!         pt2 = list( int_to_Hilbert( x, nD ) )
!         if pt2 != pt:
!             print "BZZT!  Encodes to ", pt2
! 
!         # Encode k to an nD point:
!         pt = int_to_Hilbert( k, nD )
!         print pt
!         # Double-check:
!         y = Hilbert_to_int( pt )
!         if y != k:
!             print "BZZT!  Decodes to", y
  
diff -rc v5/makeindex.php.txt v6.1/makeindex.php.txt
*** v5/makeindex.php.txt	Tue Nov 11 09:24:59 2008
--- v6.1/makeindex.php.txt	Wed Nov 19 03:03:52 2008
***************
*** 1,5 ****
  <?php // I create the actual index.html file like this:
!       //     php makeindex.php.txt >index.html
  ?>
  <HTML>
  <!--
--- 1,5 ----
  <?php // I create the actual index.html file like this:
!       //     php makeindex.php.txt (version-number) >index.html
  ?>
  <HTML>
  <!--
***************
*** 23,30 ****
  </HEAD>
  <BODY>
  
  <h3>Hilbert Curves in More (or fewer) than Two Dimensions</h3>
! <font size="-1">version 0.5</font>
  <p>
  
  Let's develop Python functions to map between a point on a
--- 23,42 ----
  </HEAD>
  <BODY>
  
+ 
+ <table width="100%" border="0">
+   <tr>
+     <td width="129" align="center">
+       <img src="http://www.mac-guyver.com/switham/thumbnails/hilbert_thumb4.gif" 
+                                     width="109"></td>
+     <td valign="top"> 
+ <p>
  <h3>Hilbert Curves in More (or fewer) than Two Dimensions</h3>
! <font size="-1">version 0.<?php echo "$argv[1]"?></font>
!     </td>
!   </tr>
! </table>
! 
  <p>
  
  Let's develop Python functions to map between a point on a
***************
*** 345,364 ****
      return 0,  2**( ( -nChunks - 1 ) % nD )  # in Python 0 <=  a % b  < b.
  </font></pre>
  
! <h3>The Code and Test Code</h3>
  
  <?php
  $cmt = array(
  "hilbert.py" => "index <==> Hilbert and support functions.",
  "hilbert_test.py" => "Tests hilbert.py functions for 1 to 3 dimensions.",
! "makeindex.php.txt" => "PHP source for this page (inserts this listing)."
  );
  
  $subst_url = array(
  );
  
  echo "<table>\n";
! exec( "/bin/ls -ld hilbert.py hilbert_test.py makeindex.php.txt *diff.txt", $lines );
  foreach( $lines as $line ) {
     echo "<tr>\n";
     $parts=explode( " ", $line );
--- 357,379 ----
      return 0,  2**( ( -nChunks - 1 ) % nD )  # in Python 0 <=  a % b  < b.
  </font></pre>
  
! <h3>The Code, Tests &amp; Demos</h3>
  
  <?php
  $cmt = array(
+ "Makefile" => "how this directory is prepared for publishing",
  "hilbert.py" => "index <==> Hilbert and support functions.",
  "hilbert_test.py" => "Tests hilbert.py functions for 1 to 3 dimensions.",
! "makeindex.php.txt" => "PHP source for this page (inserts this listing).",
! "hilbert_pic.pdf" => "Exploded views of 3D Hilbert walks.",
! "hilbert_pic.py" => "Python/pdfgen code that generates hilbert_pic.pdf"
  );
  
  $subst_url = array(
  );
  
  echo "<table>\n";
! exec( "/bin/ls -ld hilbert.py hilbert_test.py makeindex.php.txt *diff.txt hilbert_pic.py hilbert_pic.pdf Makefile", $lines );
  foreach( $lines as $line ) {
     echo "<tr>\n";
     $parts=explode( " ", $line );
***************
*** 368,380 ****
     foreach( $pieces as $file ) {
     } ; // Empty loop leaves file as last part
     $size=ceil( filesize($file) / 1024 );
!    echo '<td width="40%" valign="top">';
     if( isset( $subst_url[$file] ) )  $url = $subst_url[ $file ];
     else                              $url = $file;
     if( $line[0]=="d" ) {
        echo "<code><a href=\"$url/index.html\"\n>$file/</a></code>";
     } else {
!       echo "<code><a href=\"$url\"\n>$file</a> (${size}K)</code>";
     }
     echo "</td>\n";
     if( isset( $cmt[$file] ) ) {
--- 383,397 ----
     foreach( $pieces as $file ) {
     } ; // Empty loop leaves file as last part
     $size=ceil( filesize($file) / 1024 );
!    echo '<td valign="top">';
     if( isset( $subst_url[$file] ) )  $url = $subst_url[ $file ];
     else                              $url = $file;
     if( $line[0]=="d" ) {
        echo "<code><a href=\"$url/index.html\"\n>$file/</a></code>";
+       echo '</td><td valign="top">';
     } else {
!       echo "<code><a href=\"$url\"\n>$file</a></code>";
!       echo "</td><td valign=\"top\"><code>(${size}K)</code>";
     }
     echo "</td>\n";
     if( isset( $cmt[$file] ) ) {
***************
*** 438,444 ****
     ~999999999999      == -1000000000000</pre>
  <p>
  
! Unlike in C and Java, Python's '/' is divide-with-floor, and '%' is
  modulo, so that, e.g.,<pre>
     -5 / 2 == -3
     -5 % 2 == 1</pre>
--- 455,462 ----
     ~999999999999      == -1000000000000</pre>
  <p>
  
! Unlike in C and Java, Python's '/' with integer arguments is 
! divide-with-floor, and '%' is
  modulo, so that, e.g.,<pre>
     -5 / 2 == -3
     -5 % 2 == 1</pre>
***************
*** 458,464 ****
  <p>
  
  <a id="Jaffer">
! [Jaffer] Aubrey Jaffer, <a href="http://people.csail.mit.edu/jaffer/Geometry/HSFC">Hilbert Space-Filling Curves</a>
  <p>
  
  <a id="Lawder">
--- 476,482 ----
  <p>
  
  <a id="Jaffer">
! [Jaffer] Aubrey Jaffer, <a href="http://people.csail.mit.edu/jaffer/Geometry/MDSFC">Multidimensional Space-Filling Curves</a>
  <p>
  
  <a id="Lawder">