Editing Conway's Game of Life (section)

==Undecidability==
Many patterns in the Game of Life eventually become a combination of still lifes, oscillators, and spaceships; other patterns may be called chaotic. A pattern may stay chaotic for a very long time until it eventually settles to such a combination.

The Game of Life is [[undecidable problem|undecidable]], which means that given an initial pattern and a later pattern, no algorithm exists that can tell whether the later pattern is ever going to appear. Given that the Game of Life is Turing-complete, this is a corollary of the [[halting problem]]: the problem of determining whether a given program will finish running or continue to run forever from an initial input.<ref name="bcg"/>