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[FearfulJesuit]

This isn't really creative...it's me trying to prove a math question. But in any case.

See, one of the things that I've noticed about Conway's Game of Life is that it's fun to play with straight, one-cell-thick lines of cells.

Now, just out of experimentation, some straight lines of cells collapse into nothingness, and others don't, leaving behind a stable pattern of live cells. At first, I tested 1-6: 1, 2 and 6 collapsed; 3, 4, and 5 left behind stable live cells. I tried 24, to check whether it might have something to do with factorials, which also collapsed, but 14 and 15 collapse too, and 120 doesn't.

Is there some sort of rhyme or reason to the sequence of collapsing lines here? It starts (I checked through 30) {1, 2, 6, 14, 15, 18, 19, 23, 24...}

Firstly, is it infinite? Is there a point after which all strings leave something behind?

And regardless of whether or not it is, can we predict which lines will collapse? There are pairs of numbers in that sequence, which look rather intriguing, but nothing definite.

And how would I go about trying to find the answer?

[theTrueMikeBrown]

An interesting problem.

If I were you, I would code it up and let it run - see what numbers stabilize and what ones do not. Obviously you would have to have a good algorithm to determine if it had stabilized or if it had not, but it might not be too hard to come up with one.

Unfortunately I already have a Mandelbrot set atlas running on my dedicated computing platform, or I might offer you some cycles.

There is also one other possible solution to the final state of a line that you did not consider (though it is rare, I would say that it should still be possible): a ever expanding but not stable end state. Something like a bunch of oscillators and a glider gun. I doubt that it would happen in reality, but I suppose that with a long enough line it might.

[darkflagrance]

If I had to make an abstract guess, the end results of single-cell lines are determined by several factors, which are likely periods of some deterministic pattern along which cells in a line decay. The aperiodicity of your results is likely due to the interaction of several such patterns. Therefore, there may not be a simple/elegant mathematical way of representing this/predicting it based only on the variables you have enumerated.