Timeline for Vanishing line on Conway's game of life
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2017 at 6:52 | answer | added | მამუკა ჯიბლაძე | timeline score: 6 | |
| Dec 15, 2017 at 6:39 | comment | added | მამუკა ჯიბლაძე | Btw the growth speed in the perpendicular direction is initially c, so there is indeed plenty of time to generate c/2 spaceships to destroy all gliders in sight... | |
| Dec 15, 2017 at 6:34 | comment | added | მამუკა ჯიბლაძე | Thanks for the information. I deleted my comment as too careless. So maybe then it is a sensible conjecture that the "pseudolimit" only can contain gliders, constant configurations and periodic areas of period 2 and 15? | |
| Dec 14, 2017 at 12:28 | comment | added | Sebastien Palcoux | @მამუკაჯიბლაძე: $n=41, 96, 102$ creates a perpetual pulsar, toad, spark coil (respectively). For $n \in [1,100]$, a perpetual glider appears iff $n \in \{ 56, 71, 75,78, 82, 85, 91, 92, 93, 94, 96, 98\}$. I know that there are always four "escaping" gliders created at generation $435$ for $n \ge 500$ (and this bound can certainly be improved to $n \ge 145$), but I don't know if there are perpetual, in particular I cannot rule out that for some $n$ they can be destroy by something quicker. This is relevant for the question but not for the improved question. | |
| Dec 14, 2017 at 0:17 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
for clarification, we introduce the notion of weak period and weakly-vanishing.
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| Dec 13, 2017 at 21:23 | comment | added | Sebastien Palcoux | @Wojowu: the LWSS can be created higher than the glider. | |
| Dec 13, 2017 at 21:17 | comment | added | Wojowu | @SebastienPalcoux In order to destroy a diagonal spaceship using c/2 horizontal/vertical movement, we would have to first move a certain distance vertically, and then a similar distance horizontally. Working this out shows that we have moved diagonally at, effectively, c/4 speed. Unless you have a more specific idea of how a glider could be destroyed like that, I don't see how it's possible. | |
| Dec 13, 2017 at 21:13 | comment | added | Sebastien Palcoux | @Wojowu: A horizontal line can cross a diagonal line. Perhaps the word "catch up" is not suitable, "destroy" could be better. | |
| Dec 13, 2017 at 21:01 | comment | added | Wojowu | @SebastienPalcoux LWSS cannot catch up to a glider, since a glider goes diagonally, whereas LWSS goes horizontally. | |
| Dec 13, 2017 at 20:00 | comment | added | Sebastien Palcoux | @WillSawin: you are right, this glider (of speed $c/4$) could be catch up for example by a Lightweight spaceship (of speed $c/2$). Off the top of my head, I cannot rule that out, but Nathaniel Johnston should be able to. It is a nice problem! Anyway, the new notion of "weakly-vanishing" (I will improve the post with) allows to avoid this problem. | |
| Dec 13, 2017 at 19:08 | comment | added | Will Sawin | How do you know the gliders are perpetual? Couldn't something else catch up and stop them? Or can you rule that out? | |
| Dec 13, 2017 at 18:59 | comment | added | Tobias Fritz | @SebastienPalcoux: Aha, nice! | |
| Dec 13, 2017 at 18:53 | comment | added | Sebastien Palcoux | @TobiasFritz: your comments are helpful, thanks! One can certainly define the stationary component in terms of periodicity, but I have better with the following: a pattern is called weakly-vanishing if any cell becomes perpetually dead after some generations (depending on the cell). I will improve the post with this new notion. | |
| Dec 13, 2017 at 18:26 | comment | added | Tobias Fritz | @SebastienPalcoux: so whether infinite growth is impossible in your case is part of the question? Assuming that it is indeed impossible, how is the stationary component defined? In terms of periodicity? | |
| Dec 13, 2017 at 18:19 | comment | added | Sebastien Palcoux | @TobiasFritz: according to this page, infinite growth has been discovered for a one-cell thick pattern which is disconnected. I don't know if it is possible in the connected case (i.e. "with all cells alive", which is implicitly the case for this question), but it is an interesting problem. | |
| Dec 13, 2017 at 18:05 | comment | added | Tobias Fritz | What do you mean by stationary component? Do you know that the pattern can be decomposed for long times into gliders/spaceships plus something that happens in a bounded region? This is not always the case, e.g. there even are patterns that grow quadratically (pentadecathlon.com/lifeNews/2011/05/…). | |
| Dec 13, 2017 at 18:01 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
"perpetual" gliders
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| Dec 13, 2017 at 17:48 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
An oeis sequence gives a checking up to n=1000 + improved question
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| Dec 13, 2017 at 15:14 | comment | added | Sebastien Palcoux | @JoelDavidHamkins: $n=10$ produces a pattern of period $15$, but that's not the point of this question. | |
| Dec 13, 2017 at 14:45 | comment | added | Sebastien Palcoux | @JoelDavidHamkins: for $n \in [0,100]$ I have checked that the vanishing happens iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. The question is about $n>24$ (and so $n>100$ after my checking). | |
| Dec 13, 2017 at 14:28 | comment | added | Joel David Hamkins | Is your question about all $n>24$ or just $n\in[25,100]$? Also, you state "iff", but are the non-vanishing instances actually known? (e.g. eventually periodic) | |
| Dec 13, 2017 at 12:21 | history | asked | Sebastien Palcoux | CC BY-SA 3.0 |