Möbius Mazes

Comprehending Mobius mazes

A Möbius strip (sometimes spelled Moebius, or Möbius) is a novel surface with only a single side. You can make one easily by taking a strip of paper, giving one end a 180° twist, and then taping the two ends together. The result (assuming we used checkered paper) would look something like this:

An ant crawling along the surface of this strip of paper would find that it had traversed both sides before returning to its starting point. Like magic!

This appears to be a very suitable surface for a maze design, and it turns out that we can do so with very little effort. It’s actually very much like a cylinder maze, but with a twist—literally! We need to take that cylinder maze and give it a 180° twist. That's where we face a challenge. A cylinder maze only needs to exist on a single side of the paper since it ...