Quote from previous link, in answer to a similar question comparing CAs (1d) to Conway's Life (2d):

"The pictures you're looking at, one of the axes is time. One row "becomes" the row below it. Each time-step iteration adds a row to the bottom, while the rows above it are immutable (because they are in the past)."

It's fundamentally 1D, with the vertical dimension used to illustrate how it evolves over time.

The universe is 1D. When you plot the universe over time you get a 2D image.