Correspondence of Turing Machines (TM) and CA
Consider TM that can handle 2-D tapes (or a long 1-D tape with infinite segments)
The blank symbol is the quiescent state
The FDA is the state machine of the head
TM is more general than CA
CA can be expressed as a shape grammar (just draw the neighborhood as a shape)
What about reverse? Apply correspondence of TM and Shape Grammars (Stiny) for the rest