Hello again! I noticed Mark Wolf's new fractal Maze. Although it's smaller than the first one, it has a solution that goes twice as deep. Below is a solution of depth four. Let's label the 16 pins around the outside as follows: Pins 0-3 go from left to right across the top, pins 4-7 go from top to bottom down the left side, pins 8-11 go from left to right across the bottom, and pins 12-15 go from top to bottom down the right side. 0 1 2 3 4 12 5 A B 13 6 / C 14 7 15 8 9 10 11 From - enter A8 Stack: From 8 leave 2 Stack: A From A2 enter C13 Stack: From 13 enter B15 Stack: C From 15 enter A9 Stack: CB From 9 enter A6 Stack: CBA From 6 leave 9 Stack: CBAA From A9 leave 10 Stack: CBA From A10 enter A4 Stack: CB From 4 leave 0 Stack: CBA From A0 leave 4 Stack: CB From B4 enter A15 Stack: C From 15 enter A9 Stack: CA From 9 leave 6 Stack: CAA From A6 leave 9 Stack: CA From A9 leave 10 Stack: C From C10 goto + Stack: Not all traditional Mazes can be solved with the left-hand or right-hand rule. Wall following will fail to find a solution for Mazes where the start and goal are on separate islands of walls, because your path will take you in a loop around the starting island and you'll find yourself back at the start. To guarantee a solution through a traditional Maze when walking through it, use Tremaux's Algorithm or something similar to mark your path, to keep from going in circles and to ensure you try all paths. Wall following (and Tremaux's Algorithm for that matter) will probably fail to find the solution to a recursive fractal Maze, since the Maze is effectively infinite size, meaning you can go down a false path forever. What you can do in a fractal Maze (or any other Maze for that matter) is define a distance threshold beyond which you won't go. That distance can be defined in terms of depth (e.g. don't enter a chip beyond depth 2) or in terms of junctions (e.g. don't follow more than 2 junctions from the start). Then do Tremaux's algorithm or whatever to try to find a solution. If that fails to find any solution, increase the distance by one, and try again. Eventually you'll find a solution, which will be a shortest solution in terms of nesting/junction distance. This is basically a person inside a Maze implementing a breadth first search, or rather a depth first search with cutoff (which is a simple way of implementing a breadth first search). O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O * Walter D. "Cruiser1" Pullen :) ! * O Follow the "Path" in life's Maze: http://www.astrolog.org/labyrnth.htm O *O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O*O* --------------------------------------------------------------- Wow, this was tougher than the bigger maze. The first solution I found went three levels deep, and I don't know if it's the shortest or the shallowest, but I don't intend to look for any more! :) In this notation, the North and South exits are labelled 1-4 from left to right, and the West and East exits are labelled 1-4 from top to bottom. Parentheses are used to indicate a sub-maze, and I put the letter of the sub-maze both before AND after the parentheses, so I wouldn't get lost. [-] - A(S1-A(E1-B(N4-B(N1-W1)B-A(E4-S3)A-A(W1-N1)A-W1)B-A(E4-S3)A-A(W1-N1)A-W1)A-A(S3-A(S2-W3)A-S2)A-E4)A - B(W1-A(N1-W1)A-A(S3-A(S2-W3)A-W3)A-W3)B - C(W2-A(N1-W1)A-A(S3-A(S2-W3)A-S2)A-S3)C - [+] I have no idea what algorithm could be used by someone INSIDE the maze. It may depend on whether or not there is some indicator when the person is entering or exiting a sub-maze; would there be a door, or would the corridor just continue? And I guess any marks left on a corridor won't appear in the sub-mazes. The person in the maze might just have to resort to making a map. But what if the person doesn't know it's a fractal maze? Could he eventually figure it out by mapping it? The more I think about this, it seems there's a potential sequel to the movie "Cube" here... --Eric --------------------------------------------------------------- --------------------------------------------------------------- --------------------------------------------------------------- --------------------------------------------------------------- --------------------------------------------------------------- --------------------------------------------------------------- --------------------------------------------------------------- ---------------------------------------------------------------