Conway's Game of Life is a simple and important mathematical game with some rules of evolution in a two dimensional space. It appears in many subjects in mathematics, artificial intelligence and theoretical computer science.

Question: Are there simulations of this game with similar rules in spaces of higher dimensions ($n\geq 3$)? Does this game have an interesting theory in spaces of infinite dimension? Does it relates to hypercomputation in such a way? Please provide links to animations if there is any.

  • $\begingroup$ For more on hypercomputation see this article. $\endgroup$
    – user180918
    Nov 16 '14 at 6:15

Yes, for example Carter Bays' 3D Life which conveniently comes with an online simulator.

You may also be interested in SmoothLife, a continuous (though still 2D) generalization of the Life rules (video here).

  • $\begingroup$ (+1) Really interesting! The last link to the video seems to be corrupted. $\endgroup$
    – user180918
    Nov 16 '14 at 6:18
  • 1
    $\begingroup$ I love SmoothLife especially. Its output resembles "real" cellular life even more closely than the original game. $\endgroup$
    – user139000
    Nov 16 '14 at 6:22
  • $\begingroup$ @AliSadeghDaghighi: I just clicked on the link and it opened without problems. $\endgroup$
    – user139000
    Nov 16 '14 at 6:23
  • $\begingroup$ Maybe I have some problem with my browser! $\endgroup$
    – user180918
    Nov 16 '14 at 6:24

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