Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A grouped instance of a cellular automaton (CA) is another one obtained by grouping several states into blocks and by letting interact neighbor blocks. Based on this operation a preorder < on the set of one dimensional CA is introduced. It is shown that (CA,<) admits a global minimum and that on the bottom of (CA,<) very natural equivalence classes are located. These classes remind us the first two ll-known Wolfram ones because they capture global (or dynamical) properties as nilpotency or periodicity. Non trivial properties as the undecidability of ≤ and the existence of bounded infinite chains are also proved. Finally, it is shown that (CA,<) admits no maximum. This result allows us to conclude that, in a grouping sense, there is no universal CA.
['Jacques Mazoyer', 'Ivan Rapaport']
I am writing a research paper on a idea Inducing an order on cellular automata by a grouping operation
[{"from": "human", "value": "I am writing a research paper on a idea Inducing an order on cellular automata by a grouping operation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A grouped instance of a cellular automaton (CA) is another one obtained by grouping several states into blocks and by letting interact neighbor blocks. Based on this operation a preorder < on the set of one dimensional CA is introduced. It is shown that (CA,<) admits a global minimum and that on the bottom of (CA,<) very natural equivalence classes are located. These classes remind us the first two ll-known Wolfram ones because they capture global (or dynamical) properties as nilpotency or periodicity. Non trivial properties as the undecidability of \u2264 and the existence of bounded infinite chains are also proved. Finally, it is shown that (CA,<) admits no maximum. This result allows us to conclude that, in a grouping sense, there is no universal CA."}]