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Is there a 'simple' 2 dimensional cellular automaton to generate all prime twins ?

With 'simple' I mean not too many states per cell and not so many rules. Thus a universal turing machine equivalent cellular automaton is not 'simple'.

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    Is there one that generates all primes? That would seem to be a less specialized place to start.2012-10-02
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    @mjqxxxx : Well there are such because of the universality of cell auto. But if there exist such simple ones is another matter. I believe the answer to that is also yes. I believe I have seen such but Im not sure. Was there an example of that in NKS ? Maybe I saw it there.2012-10-02
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    Right, I meant a simple, potentially non-universal one, like you're asking about here.2012-10-02

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Sure, there is one for prime numbers in wolfram's site: http://demonstrations.wolfram.com/PrimeGeneratingCellularAutomaton/

Source Code is also available on the right side of the page.

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    Thanks , but I have no permission to the source code. Could you give it here ? Also Im not so good with code, maybe you can explain the rule ? Like in rule 30 or such.2012-10-03
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    @mick You can go [here](http://demonstrations.wolfram.com/sourcecode.html?demoname=PrimeGeneratingCellularAutomaton&demodisplayname=Prime-Generating%20Cellular%20Automaton) for the sourcecode.2012-10-10
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    Thanks Mahmud +1 But I do not understand the math behind it. ( Im not so good with code either )2012-10-11
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    I think that this is the author: https://www.facebook.com/joebolte you might want to contact him, perhaps he could father explain the logic.2012-10-14
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    It seems this is the classical construction by [P. C. Fischer](http://en.wikipedia.org/wiki/Patrick_C._Fischer) : P.C. Fisher "Generation on primes by one dimentional real time iterative array" J. ACM, 12 (1965), pp. 388–3942014-05-08
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You will need to pay Wolfram if you want to study and understand his code, he is not an 'open source' sort of guy! I have questions about the rules he supplies in his book 'A New Kind of Science': I am developing a browser based automaton and his prime automaton rules do not produce the same result for me. Very probably my understanding of how to interpret his given rules is incorrect but I have emailed him about this but he has not replied yet!