Von Neumann’s results
A Turing machine can be embedded in the space
It is possible to embed an automaton A in the space. which can then build any other properly specified independent automaton B
A can equal B (self reproduction)
Further Results (Codd and others):
What other n-state, m-neighbor spaces are computation-universal in the above sense?
Minimum was found to be 8-state, 5-neighbor space.
Related to more general Holland iterative circuit computers where cell neighborhoods vary over space and time. (Explaining some quantum interactions “at a distance” might require this or a model with multiple CA spaces in coexistence etc.)
Turing Machines can simulate CA