4D mazes

For today’s second post, I would like to talk about four-dimensional mazes. In a six-part series I wrote in January, I explained a few aspects of the fourth spatial dimension. This post is not a continuation of this series—it is more like a supplement to it.

Before I begin, though, I would like to clarify some points about mazes in general. When we see a maze drawn on paper, it is a two-dimensional maze. It utilizes the available 4 perpendicular directions that the second dimension possesses. When we see a physical maze, like those “corn mazes” out in the Midwest, this is also a 2D maze because it does not utilize all 6 directions of the third dimension. Thus, a true 3D maze would be a building where each floor contains a 2D maze, meaning that it is several 2D mazes stacked on top of each other. Likewise, a four-dimensional maze would consist of several three dimensional mazes stacked on top of each other. Surprisingly, such a maze can be drawn and solved. The maze below is one I created as an example.

This is how the maze works: Each 3x3 box is a two-dimensional slice of this maze. Each column is a three-dimensional maze, since all 3 of the boxes in each column are stacked on top of each other. Thus, the whole picture is really all three columns stacked on top of each other. But this is impossible to visualize, so it is better to explain it this way: the three boxes in each column are stacked, and all 3 boxes in each row are stacked in the same way. This means that it is possible to move from one box to the one above it, below it, or next to it.

The maze is played like this: begin at the yellow square and try to reach the green square. You can move into any adjacent square above, below, or next to you (no diagonals) that is not a wall (black square). You can also “jump” to the corresponding square in the box above you, below you, or next to you because they are on top/below the box you are in (again, no diagonals). You cannot do so if a wall is in the square you are trying to jump to. For example: on your first move you can either move to the square to the right or below or jump to the upper left corner in the box to the right or below. 

Of course, much harder mazes, such as 4 by 4 by 4 or larger ones, can be created as well. Perhaps in the future I will make a few more and put them up on this site. If you are still unclear as to how the maze works there are some articles on the internet that may be able to explain them—this idea was based off of similar puzzles I found on the internet.