Saturday, February 25, 2017

Alice and the Fractal Hedge Maze


This is an entry to the 12th fortnightly challenge.





Alice: Would you tell me, please, which way I ought to go from here?
Cheshire Cat: That depends a good deal on where you want to get to.
Alice: I don't much care where...
Cheshire Cat: Then it doesn't much matter which way you go!
Alice: ... so long as I get somewhere.
Cheshire Cat: Oh, you're sure to do that, if only you walk long enough.




Alice is in the most puzzling part of Wonderland yet. Following the white rabbit, she emerged found herself in the middle of a hedge maze. The rabbit provided her with a map before scurrying off, but it only seemed to make her more confused. She needs your help to figure out how to escape the maze.


The maze has 12 potential exits, numbered on the map. Each of the squares labeled A, B, C and D represent smaller copies of the entire maze. These submazes each have their own submazes, like infinitely many nested Matryoshka dolls, except that every doll has four dolls nested inside it.


Below the map is a bird's eye view of the actual maze, where you can see how the passages become smaller and smaller in a fractal fashion (only three levels of recursion are actually pictured). Fortunately, Alice has an ample supply of cakes and elixirs to change her size as necessary.


One last note: the little orange curve between B and D is a bridge which can be crossed over and walked under, but jumping from the bridge to the path below is not allowed.



enter image description here



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Though I created this particular puzzle, the concept of a fractal maze is nothing new. Here are some other notable examples of cool fractal mazes, which served as inspiration for this one.




  • As far as I can tell, the concept of a fractal maze was created my Mark J. P. Wolf. He has made at least two mazes, taken from mathpuzzle.com.





  • These are from the blog Skeptic's Play:






  • Two devious looking mazes which I found referenced in this forum, but couldn't find the original sources for.






Answer



Here is a link to a prezi. If there is anyway to export it that would be great but I'm not exactly sure how it works.


Just keep clicking next through it.


https://prezi.com/oh2efo-ejbv9/untitled-prezi/?utm_campaign=share&utm_medium=copy


GIF



enter image description here


And the path in the format from-to (level). If the number includes a letter it comes from/goes to an internal maze box, if it does not it goes to the outside of the current level.



IN-A3 (1)
3-B1 (2)
1-12 (3)
B12-B11 (2)
11-A10 (3)
10-C4 (4)
4-B6 (5)

6-D8 (6)
8-10 (7)
D10-7 (6)
B7-7 (5)
D7-9 (4)
A9-8 (3)
B8-D3 (2)
3-B4 (3)
4-B6 (4)
6-D8 (5)

8-10 (6)
D10-7 (5)
B7-D10 (4)
10-8 (5)
D8-6 (4)
B6-4 (3)
D4-5 (2)
A5-1 (1)
OUT




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