## Thursday, October 7, 2010

### Fractal Maze

Oh boy, I've always wanted to design one of these!  It's a fractal maze!

Both of the circles on the left and right represent copies of the entire maze (excluding the start and finish lines).  The circles labeled 1 and 2 are meaningless, they're just checkpoints to help me design the maze and you solve it.

My goal in designing this maze was to make it very difficult if you have no idea what you're doing.  Let's see if I achieved that.  You can send your solutions to skepticsplay at gmail dot com.

Note that while this is an original fractal maze, the idea of a fractal maze is not original.  You can find multiple examples of fractal mazes on the internet, usually with a microchip motif.

A solution will not be posted, but I've had some discussion which should provide hints.

Anonymous said...

Ooh, looks fun! I've never heard of the idea before, but it's an excellent one.

Just for clarification purposes, which crossings between curves of different colors are we supposed to regard as being connected? I assume that most of the places where different colors cross are not meant to be connected since this would make the maze trivial.

Also, what counts as a solution, a path that crosses finitely many nodes or simply any path of finite length (even if it goes infinitely deep into the fractal)?

miller said...

Crossings are not connected unless they're the same color. You may not travel along the circumference of any of the circles.

The solution only goes finitely deep into the fractal. Actually, I'm not even sure if it's possible to design a maze that requires going infinitely deep. I'll have to reflect on that question.

Larry Hamelin said...

Hmm... not really getting this...

Presumably, we have to start going up the green line from "Start", through (1), and we have to end up on the curved red line coming from (A) and then to "Finish".

But I don't see the curved red line connect to anything. What am I missing?

Larry Hamelin said...

Or does the red line connect to the purple line in (A)?

miller said...

Yeah, the red line connects to the purple line. Sorry, my graphics were not aligned perfectly. I've moved around a few pixels to fix it.

Anonymous said...

"Crossings are not connected unless they're the same color."

"Yeah, the red line connects to the purple line."

Huh?

miller said...

Rules are: If two lines cross, you can't jump from one to the other unless they're the same color. You can change colors as you go down or up a level (ie in or out of A or B). You can't go along the circumference of any of the circles.

Anonymous said...

Oh I see, I misunderstood crossings to refer to A/B transitions as well. Thanks!

Sachs said...

From Start, I went up green through 1, straight into B, purple into B, blue straight into A, green through 1, left into A, red straight, straight out of A, yellow left into B, left into A, red straight, straight out of A, green right, through 1, out of B, purple out of A, red left out of B, blue straght into A, green through 1, left into A, red straight, straight out of A, yellow left into B, left into A, red straight, straight out of A, green right, through 1, out of B, purple out of A, red left out of B, blue straight into A, green through 1, left into A, red straight, straight out of A, yellow left into B, left into A, red straight, straight out of A, green right, through 1, out of B, purple out of A, red right, finaly left into Finish. I had a lot of fun, thank you, but I feel there is a shorter way.

miller said...

One of the great things about fractal mazes is that they can be relatively simple yet require complicated solutions.

I don't know of a shorter solution, though it's possible to organize it into subroutines that get repeated multiple times.