I strongly believe that - given the rules of Conway's [Game of Life][1] 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.


  [1]: http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life