TITLE: Undecidability in Conway's Game of Life
QUESTION [12 upvotes]: I strongly believe that - given the rules of Conway's Game of Life and an initial configuration - it is not decidable by a Turing Machine whether a given pattern will emerge, let alone as a stable pattern, be it static, moving, and/or rotating.

How can this be proven?

I guess, this kind of uncomputability would go far beyond the "simple" unpredictability of non-linear systems.

REPLY [5 votes]: This is proved (or, really, a sketch of the proof is given) in the second volume of the extraordinary [Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy, Winning Ways for your Mathematical Plays. Academic Press, 1982]