Mazes for Programmers

Representing Four Dimensions

You’ve now seen how the pattern comes together. Zero-dimensional cells make one-dimensional rows (or columns), which come together to make two-dimensional levels, which stack to make three-dimensional worlds.

So what happens when you take those three-dimensional worlds and stack them along another axis, perpendicular to the three we already have? (Ignore for the moment that it’s rather difficult to imagine a direction that is simultaneously perpendicular to the three axes we’ve already got.) You can probably guess that we’re going to wind up with a four-dimensional grid, and you’ll be exactly right.

To illustrate stacking in the fourth dimension, we can take those three-dimensional grids and line them up vertically ...