Representing Four Dimensions

Mazes in a 4D grid

We’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 we 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.) We’re going to wind up with a four-dimensional grid. To illustrate stacking in the fourth dimension, we can take those three-dimensional grids and line them up vertically on the page, as shown below.