Dear colleagues,
What is special in 1109?
We can use straight lines as starting configurations in Game of Life. Then, if we check the equilibration time vs length, we will see that many lines with different lengths reach equilibrium exactly after 1109 steps. Why?
*More details in our project Mysteries of Game of Life
Dear Remi,
Thanks for your answer.
But, that is not the problem. What I call "equilibration time" is the number of steps untill the system is not changing anymore. So it is a clear, integer number, there is no truncation/ loss of precision isue.
If this is not the case, then your problem has some kind of attractor to the equations. You might then want to look at the problem analytically.
Yes, that is the point.
Some numbers seem to be "special" and different configurations reach equilibrium in that number of steps (1109 and others, as can be seen in the graph).
So that was the question: How to look at this problem analytically? Are these special numbers predictable? etc
Right, the question was cryptic...
Is just Conway's Came of Life, with the classic rules.
https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life
I use lines as starting configurations and I check the equilibration time seeing when the system stops evolving. Like in this video.
Here Initial L = 138, and equilibration time is 1109 steps
Hi Andrew,
Enclosed are two figures where can be seen that 1109 is a frequent equilibration time for starting lengths in the range 150-250. (First time for L=138).
(A table will be uploaded soon)
A
I would suggest perhaps that the number 1109 isn't special but rather a straight line of arbitrary length as a Game of Life starting configuration is special. I wasn't aware that the Game of Life ever reached equilibrium, by the way.
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