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| [[Category:Free_Software]] | | [[Category:Free_Software]] |
| [[Category:Python]] | | [[Category:Python]] |
| + | This is a fractal algorithm I created for generating mazes. I think it's pretty neat. The original was written in C for a computer science class I was taking at UCSC. This version is in Python. The original would print spaces and hashes (#) to display the maze. |
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− | This is a fractal algorithm I created for generating mazes. I think it's pretty neat. The original was written in C for a computer science class I was taking at UCSC. This version is in Python. The original would print spaces and hashes (#) to display the maze. This version also generates HTML.
| + | In this version I also added HTML output. When I came up with the algorithm there were fewer than 1000 web sites -- it wasn't popular yet. My original C source has this comment explaining the limit to the number of recursive iterations that could be done: |
| + | <pre> |
| + | /* Six is the max value that seems to work on a 640K DOS machine */ |
| + | </pre> |
| + | Nowadays, my Apple Mac Mini with a dual core 1 GHz CPU can run the interpreted Python version in less than 400 ms when set for 6 iterations. It can do 10 iterations in under 2 minutes producing an output of 2047 columns by 2047 rows, taking 4 MB of ASCII text (XPM format). This is easily converted to PNG. You may click on the following link to view the maze: [[Media:big_maze.png]] |
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− | This generates a random maze with no loops -- a single connected path links all elements of the maze. This maze also has the property that it is space filling. | + | This generates a random maze with no loops. It is a Lattice Graph [http://en.wikipedia.org/wiki/Spanning_tree_%28mathematics%29 spanning tree] -- ''a connected, undirected graph that uses all the vertices in a graph with no cycles''. This program will also optionally "solve" the maze. That means it will show you two points that are as far apart as possible. The corresponds to the diameter of the tree. There may be more than one path that has a length equal to the longest path length. The full path is not shown. Only the beginning and end points are shown... This is a very slow calculation. |
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− | You can run the brain maze algorithm by clicking here: [http://www.noah.org/cgi-bin/brainmaze.py brainmaze.py] | + | You can run the brain maze algorithm by clicking here: [http://www.noah.org/cgi-bin/brainmaze.py Generate a Brainmaze] |
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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Line 349: |
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td> | + | <td width="9" height="9" bgcolor="#ff0000"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
Line 374: |
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| </tr> | | </tr> |
| <tr> | | <tr> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
Line 397: |
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
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| </tr> | | </tr> |
| <tr> | | <tr> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | </tr>
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− | <tr>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | </tr>
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− | <tr>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
Line 551: |
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
Line 559: |
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
Line 588: |
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| </tr> | | </tr> |
| <tr> | | <tr> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td> | + | <td width="9" height="9" bgcolor="#00ff00"></td> |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
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− | <td width="9" height="9" bgcolor="#ffffff"></td>
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| <td width="9" height="9" bgcolor="#000000"></td> | | <td width="9" height="9" bgcolor="#000000"></td> |
| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
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| <td width="9" height="9" bgcolor="#ffffff"></td> | | <td width="9" height="9" bgcolor="#ffffff"></td> |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
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| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | </tr>
| |
− | <tr>
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
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| |
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| |
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| |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | </tr>
| |
− | <tr>
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
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| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
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| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | <td width="9" height="9" bgcolor="#000000"></td>
| |
− | <td width="9" height="9" bgcolor="#ffffff"></td>
| |
− | </tr>
| |
− | <tr>
| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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| |
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− | Download [http://www.noah.org/downloadsvn.php?url=file:///home/svn/src/python/brainmaze.py brainmaze.py]
| + | The mazes generated by this algorithm are made up of the following maze '''atoms'''. This is the number of trees in a 2x2 Grid Tree. |
− | <include svncat src="file:///home/svn/src/python/brainmaze.py" highlight="python" /> | + | |
| + | <pre> |
| + | # # ### ### ### # # ### |
| + | # # # # # # ### # |
| + | ### # # ### ### # # ### |
| + | </pre> |
| + | |
| + | This can be simplified by removing rotated copies to these two maze atoms: |
| + | |
| + | <pre> |
| + | ### # # |
| + | # # ### |
| + | # # # # |
| + | </pre> |
| + | |
| + | Click here to download: [http://www.noah.org/engineering/src/python/brainmaze.py brainmaze.py] |
| + | <include src="/home/noahspurrier/noah.org/engineering/src/python/brainmaze.py" highlight="python" /> |
| + | |
| + | = Simplified Brain Maze = |
| + | |
| + | This removes the middle connectors to give only the following atoms: |
| + | <pre> |
| + | ### ### # # ### |
| + | # # # # # # |
| + | ### # # ### ### |
| + | </pre> |
| + | |
| + | Connect 3 at any of the four corners. |
| + | <pre> |
| + | ### ### |
| + | # # # |
| + | ##* * # |
| + | |
| + | # * *## |
| + | # # # |
| + | ### ### |
| + | </pre> |
| + | <pre> |
| + | ### ### |
| + | # # # |
| + | ##*-* # |
| + | | | |
| + | # *-*## |
| + | # # # |
| + | ### ### |
| + | </pre> |
| + | |
| + | <pre> |
| + | ### ### ### ### |
| + | # # # # # # |
| + | ##*-* # ##*-* # |
| + | | | | | |
| + | # *-*## # *-*## |
| + | # # # # # # |
| + | ### ##*-*## ### |
| + | | | |
| + | ### ##*-*## ### |
| + | # # # # # # |
| + | ##*-* # ##*-* # |
| + | | | | | |
| + | # *-*## # *-*## |
| + | # # # # # # |
| + | ### ### ### ### |
| + | </pre> |