Conway's Game of Life: Collapsing Lines

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dhokarena56
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Conway's Game of Life: Collapsing Lines

Postby dhokarena56 » Thu Aug 23, 2012 7:57 pm UTC

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.

Where would I start to answer these questions?
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nadando
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Re: Conway's Game of Life: Collapsing Lines

Postby nadando » Thu Aug 23, 2012 9:46 pm UTC

Well you could start by writing a program to determine whether a line collapses or oscillates indefinitely.
Here's a (slow) python script I wrote (http://pastebin.com/mXTYUXbB). I don't know whether it's possible for a line to produce a glider, which I haven't checked for and would result in an infinite set of states without repetition.
I don't see any lines that collapse from 24-55. 56 doesn't collapse after > 1000 iterations.

Given the degree to which the game of life has been studied on the internet someone has probably investigated this question, but I wouldn't know what search terms to use to find it.

Harutsedo
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Re: Conway's Game of Life: Collapsing Lines

Postby Harutsedo » Fri Aug 24, 2012 1:02 am UTC

nadando wrote:Well you could start by writing a program to determine whether a line collapses or oscillates indefinitely.
Here's a (slow) python script I wrote (http://pastebin.com/mXTYUXbB). I don't know whether it's possible for a line to produce a glider, which I haven't checked for and would result in an infinite set of states without repetition.
I don't see any lines that collapse from 24-55. 56 doesn't collapse after > 1000 iterations.

Given the degree to which the game of life has been studied on the internet someone has probably investigated this question, but I wouldn't know what search terms to use to find it.


From what I can tell 56 actually produces 4 gliders as does 71, 75, 78, and 80. But 80's gliders hit each other, so they don't count. And none from 56 up to and including 80 collapse to nothing.

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NathanielJ
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Re: Conway's Game of Life: Collapsing Lines

Postby NathanielJ » Fri Aug 24, 2012 2:14 am UTC

All lines after some (reasonably small, less than 1000 for sure, and probably about 50 or so) length spit out a glider and thus don't collapse to nothing.

Also, many questions like this are discussed and answered on the (shameless plug) ConwayLife.com forums.
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tomtom2357
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Re: Conway's Game of Life: Collapsing Lines

Postby tomtom2357 » Fri Aug 24, 2012 6:05 am UTC

I wonder what would happen with an infinite length 1-cell thick start.
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Re: Conway's Game of Life: Collapsing Lines

Postby Giallo » Fri Aug 24, 2012 9:11 am UTC

tomtom2357 wrote:I wonder what would happen with an infinite length 1-cell thick start.

I think it would generate infinite parallel lines "moving away" from the original one.
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cyanyoshi
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Re: Conway's Game of Life: Collapsing Lines

Postby cyanyoshi » Fri Aug 24, 2012 2:31 pm UTC

tomtom2357 wrote:I wonder what would happen with an infinite length 1-cell thick start.

Unless I'm mistaken, that just reduces to the one-less-dimensional Wolfram's Rule 22. Just treat the vertical axis as time.

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Actaeus
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Re: Conway's Game of Life: Collapsing Lines

Postby Actaeus » Sat Aug 25, 2012 12:02 am UTC

More interesting question: infinite line of cells in one direction from the origin (I guess it's a ray, then).

This would also give us some results for sufficiently-large lines.

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Re: Conway's Game of Life: Collapsing Lines

Postby SetOfAllSubsets » Sat Nov 30, 2013 4:53 am UTC

I've found that with very long lines like 4096 live cells and above, it creates a Sierpinski Triangle made up of stable patterns as well as sending gliders out in all directions.


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