To understand what is Cellular Automata, I strongly recommend you to read wiki and the chapter of CA in Nature of Code.
Given that you've already know what CA is, there is a lot of variation possibilities from several aspects:
1. Grid
Usually the grid of 2D CA is square, but as long as the grid can be regular, they all apply to CA algorithm, such as Triangular, Hexagonal.
2. State
In classic CA there are two states of Alive or Dead. But it is also possible to have multi-state where more complicated rules can apply, resulting more complex and unpredictable outcome.
3. Neighborhood
In classic 2D square grid, one cell can have 4 neighbors using von Neumann Neighborhood Thoery, or 8 neighbors using Moore Neighborhood Theory. When this comes to 3D, the neighbors are 8 or 26 respectively. Based on different neighborhood counts, different rules can apply to it.
4.Rule
Rules can increase exponentially from 1D CA to 3D CA. So usually 2D and 3D CA adopt numbers of neighbors instead of exact state rule(for 3D CA one-to-one rule can reach 2^26 rules).
Demo
This is a research showing 3D CA application. Basically I adopted cubic grid, 2 states and Moore Neighborhood(26 neighbors).
The rule is : Survive : 13,14,16 to 26 | Birth: 17,18,19
Here’s another video showing the generation process.