A cellular automaton is a state machine which is controlled by external input. The input is given by geometrical space around a cell. In a square matrix, each automaton gets input from 4 surrounding cells, while a hexagon grid has 6 neighbor cells which can be used as automaton input. For example, a 4-cells input may be the string “1011”. This string specify a state of the cellular automaton. The automaton will switch to a different state according to the lookup table. I want to know if increasing the number of input cells in a hexagon automaton will make the resulting computer more powerful.

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I'd like to learn more about the differences between related automata which can be based on hexagonal cells instead of squares (rule 34/2), like in CoDi model which uses spiking neural network (SNN).

Is using a plane tiled with regular hexagons more efficient and reliable than using square cells? What is the difference and how do I know which one to use in which scenario?

In other words, the more efficiently flexible that it grows, the more difficult scenarios it can be used for (for me, hexagonal implicates more possibilities, because it can send/share the signal with/to more tiles). Or maybe one is more modern than the other, or they're both on the same level? In general, I'd like to learn the differences between them to know when I should use one over the other.

  • $\begingroup$ This seems more suited to Data Science, though I could be convinced otherwise. It's being discussed on meta. $\endgroup$ – Ben N Aug 5 '16 at 23:11
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    $\begingroup$ No, I think this question would be closed on Data Science. It might be on topic in CSTheory, and I think it could be on topic here if we wanted it to be. I would be surprised if you could find anyone who could answer this question in more detail than "there are more sides". I think this is the kind of thing that has long since been abandoned in research. Cellular Automata are to the best of my knowledge not used anywhere for a practical application, so measuring their efficiency is not a well defined idea. $\endgroup$ – Harsh Aug 6 '16 at 1:30
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    $\begingroup$ Interesting question! One thing that is known is that for example for games programming for Ai versus humans, hexagonal is preferred, because the Ai performs in a more interesting way. Does that mean it performs more efficiently? Well, it's also more susceptible to noise, or human bluffing of it... $\endgroup$ – Guido Jorg Aug 7 '16 at 19:34
  • $\begingroup$ @GuidoJorg I believe that should be an answer. $\endgroup$ – FreezePhoenix Apr 16 '18 at 16:59
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    $\begingroup$ Clearly it raises complexity, but, from some conversations with some skilled Go-variant designers, hexagons bring their own set of design problems. (imo, this makes them especially worth pursuing.) $\endgroup$ – DukeZhou Aug 24 '18 at 18:52

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