User blog comment:Wythagoras/Conway's game of life/@comment-1605058-20141127201841/@comment-1605058-20141130074648

I believe this could be comparable to BB_2(n), but you have to clarify the definitions of these two functions. Copy from my other comment:

"What do you mean by "stop growing in number of cells"? You mean that population will stay bounded? If so, at what point are we counting the number of cells/steps?"

I'm not going to talk about its growth rate because it's undefined concept.

And yes, I believe it could work with TMs.