There should be no initial pattern for which there is a simple proof that the population can grow without limit.
There should be initial patterns that apparently do grow without limit.
There should be simple initial patterns that grow and change for a considerable period of time before coming to end in three possible ways: fading away completely (from overcrowding or becoming too sparse), settling into a stable configuration that remains unchanged thereafter, or entering an oscillating phase in which they repeat an endless cycle of two or more periods.
Martin Gardner, Scientific American 223 (October 1970): 120-123.
WAV available upon request, < info [at] stewartengart [dot] com >.
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