Dear fellows,
If we call “Equilibration time” the number of steps that are needed to reach equilibrium in Game of Life, then it seems that this Eq. time grows with N, (being N the size of the system (NxN)) in open boundary conditions. However I didn't find a detailed study about this.
Are you aware of some results regarding this question? Can be proved that it has to be that way, linear with N?
Thank you
Alberto
I would try to build an argument along the following lines:
1. One can implement a universal Turing machine in GoL
2. A Turing machine with a tape of length N can have up to 2^N possible states...
So, potentially, the length of the longest possible cycle may well grow exponentially with N.
If one wanted an empirical estimate of the current game board, perhaps looking at things like the Langton parameter or the entropy variance (Kaz. & Sweet 2004) may prove useful - but hardly enough to produce a firm upper bound.
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