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This is more of a help call to find a specific rule set for the game of life. I'm currently reading the "Entanglement in the Quantum Game of Life", however they refere to the classical F12 rule. I'm familiar with the "conventional" rule naming, however they only name rules for the nearest neighbor of a site and not the next nearest neighbor as done here in the paper. I cannot find the F12 rule anywhere and ChatGPT also fails to find it.

I would greatly appreciate if someone knows something about it.

Here is the Literature: Entanglement in the Quantum Game of Life: https://arxiv.org/pdf/2104.14924 This points to: https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.55.601 There I cannot find it.

Here the original quantum game of life paper: https://arxiv.org/pdf/1010.4666 This points to: http://www.esalq.usp.br/lepse/imgs/conteudo/Quantum-Aspects-Of-Life.pdf There I cannot find it too.

I know this platform is not really here for this kind of tasks but I don't know where else I can ask for expertise. Thank you!

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Okay I figured it out!

For 1D Quantum Cellular Automata there are two typical rule sets. One rule set is T_R and the other is F_R, where T stands for Three and F stands for five. That is the size of the neighborhood we are looking at. (For T, the site itself + one neighbor left and one neighbor right.)

R is the ruling number. For the rule set T we can calculate R with R = c_00 * 2^0 + c_01 * 2^1 + c_10 * 2^2 + c_11 * 2^3. Where c_mn is 1 if we want to apply rule c_mn. m is the left neighbor and n is the right neighbor. So for example when we use rule T_6, what we mean by that is we update our site if it has exactly one active neighbor.

For the rule set F we describe R as: R = sum_{q=0}^4 c_q * 2^q. Note that don't care about the specific neighbors anymore but rather we count the numbers of active neighbors. Rule F12 can be described as c_2 * 2^2 + c_3 * 2^3 = 12. What this means is that we update the site if we have two or three neighbors. I hope this answers my question :D

I found the ruling in https://arxiv.org/pdf/2005.01763

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