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.
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).