Comment by wbolt

Actually most of CA simulations are done on torus which is referred to as periodic boundary conditions in the literature. Alternatively you can also have null (or fixed) boundaries or reflective ones. If the initial configuration has compact support (finite number of non-null states) and the CA keeps null-neighborhoods as null in the next step, you can simulate infinite grids… but not many people bother to do it. Many many papers use finite grids on torus.