## Monday, February 24, 2014

### Fractal Maze 2: Sierpinski paths

Years ago I created a fractal maze, which was rediscovered by reader Nathaniel Arnest.  Nathaniel and I had a great e-mail discussion about fractal mazes.  Later I may post my thoughts on this subject, but for now I present a maze that we collaborated on.  Nathaniel designed the maze, and I chose the graphical design to be based on the Sierpinski Triangle.  This one is a bit easier than the other one (which is a good thing).

Click to zoom in.

Rules:
1. Follow the colored paths from the empty light green circle to the filled dark green circle.
2. You may not travel along the black lines.  The black lines simply outline an infinite number of squares.  All squares are copies of each other, even when the lines are too small to see in the picture (except for the start and finish, which only occur in the largest square).
3. You may not jump from one color to another, except when passing through the boundary between squares.
4. The path you follow cannot go infinitely deep.  Finite solutions only!

If you'd like to check solutions, please e-mail me at skepticsplay at gmail dot com.  Describe the solution in any way you wish, or attach an image.

If any readers are having difficulties due to colorblindness, please e-mail me to suggest better colors to accommodate you.

miller said...

I don't follow instruction #2. Do you mean you can only change colors when two colors and a black line all intersect in the same point? As far as I can tell that doesn't happen anywhere.

miller said...

Now that I look closer, I see there are a few points where a line is one color on one side of a black line and a different color on the other side. Is that what instruction 2 is referring to?

miller said...

Yes it is.

The visual language used in the maze is an imitation of the original fractal maze designed by Mark Wolf. The difference is that I explicitly show the smaller copies of the maze.