There's been quite a lot of experimentation with 3D versions of Conway's Life -- including rules where you can easily emulate Life on a 2D slice of the 3D plane

There's been quite a lot of experimentation with 3D versions of Conway's Life -- including rules where you can easily emulate Life on a 2D slice of the 3D plane. Carter Bays did some investigations and published papers back in the 1980's: https://conwaylife.com/wiki/Three-dimensional_cellular_automaton There's been a little bit of revived interest lately, when newer versions of Golly ( https://golly.sourceforge.io/ https://golly.sourceforge.io/ ) started to include at least some support for 3D rules. Other programs have been showing up recently, though some of them are more ways of visualizing the history of a 2-dimensional rule in three dimensions. There are a couple of big difficulties that seem to prevent 3D rules from getting a lot of attention. It's just plain a lot more computationally intensive to emulate 3D rules. Also it's a lot harder to see what's going on in the middle of an active 3D pattern -- a lot of the detail tends to get hidden.