Friday, October 29, 2010

Fractal Maze hints

Last month, I designed and posted a fractal maze.  I'm not sure that anyone could solve it.  Haha, sometimes I get a little overzealous with my puzzles.  Rather than posting the solution, I'm going to explain how I designed the maze.  If you understand the process, it will provide insight into how to solve it.

When designing this maze, drawing out the maze was the last step.  The first step was to consider the maze more abstractly, and decide what would connect to what.

So I decided that there would be two smaller copies of the maze, called A and B.  Each copy of the maze can be specified with a finite sequence of As and Bs.  For instance, if I go down a level into B, and then down a level into A, this can be described with the sequence BA.

But to fully describe a position within the maze, we need more than just As and Bs to specify which copy of the maze we're talking about.  We also need to specify where we are within that copy.  So I decided there would be two checkpoints, called 1 and 2.

From each of these checkpoints, there is a set of actions you can take to move from one place to another.  For instance, starting at position 2, you can go down A, down B, and end up at position 1.  I denoted this action as 2-AB-1, because it starts at 2, ends at 1, and goes down AB.

Some of the actions would also go up a level.  I denoted those with inverse notation, like A-1.  Note that you can also take any of these actions backwards.

Here's the list of actions I came up with:
  1. 1-BBA-1
  2. 1-A-2
  3. 1-B-1A-1-2
  4. 1-A-1B-2
  5. 2-A-1BA-2
  6. 2-A-1-1
  7. 2-AB-1
  8. 2-B-1A-1
And with this simple list of eight actions (some of which are redundant), I was practically done!  The rest was just a matter of presenting the above in a somewhat aesthetic fashion.