One cell thick patterns.
One cell thick patterns.
If you had to guess, what would you say the shortest horizontal line of on-cells was that produced a glider? Somewhere in the range 5-9 perhaps? Bigger? As big as 30? No, it's 56!
I became interested in patterns one cell thick when I read this page. It sounds like people had constructed large patterns one cell thick that lead to infinite growth, before someone brute-forced it down to:
Which is awesome.
Does anyone have any links showing the original patterns, or how they were constructed? What's the smallest one cell high pattern to emit a glider?
I became interested in patterns one cell thick when I read this page. It sounds like people had constructed large patterns one cell thick that lead to infinite growth, before someone brute-forced it down to:
Which is awesome.
Does anyone have any links showing the original patterns, or how they were constructed? What's the smallest one cell high pattern to emit a glider?
- Nathaniel
- Site Admin
- Posts: 861
- Joined: December 10th, 2008, 3:48 pm
- Location: New Brunswick, Canada
- Contact:
Re: One cell thick patterns.
This blog post contains a pretty in-depth analysis of the smallest patterns that are one cell thick. He provides an 18-cell wide pattern that produces 6 gliders, though he doesn't explicitly say whether or not smaller such patterns exist. He also doesn't mention the larger infinite growth patterns, so I'm not sure where to find those.
His results are based on a Golly script he wrote. Perhaps if we asked him nicely, he'd be willing to share?
His results are based on a Golly script he wrote. Perhaps if we asked him nicely, he'd be willing to share?
- DivusIulius
- Posts: 89
- Joined: April 1st, 2009, 11:23 am
- Contact:
Re: One cell thick patterns.
Infinite Growth's blog administrator here.
I am going to modify my script in order to provide a specific answer to your question.
Stay tuned.
I am going to modify my script in order to provide a specific answer to your question.
Stay tuned.
- DivusIulius
- Posts: 89
- Joined: April 1st, 2009, 11:23 am
- Contact:
Re: One cell thick patterns.
I modified the script to detect escaping gliders (this is a preliminary approach).
The shortest patterns that produce escaping gliders are the following two 15-bit patterns:
OOO·OOOOO·OOOOO (and its mirror image)
13 cells. It runs for 522 generations. Final population: 150 cells. (4 gliders).
OOOO··OOO·OOOOO (and its mirror image)
(this pattern was found previously during my one-cell pattern exploration)
12 cells. It runs for 3183 generations. Final population: 1059 cells. (6 gliders).
I hope that helps.
The shortest patterns that produce escaping gliders are the following two 15-bit patterns:
OOO·OOOOO·OOOOO (and its mirror image)
13 cells. It runs for 522 generations. Final population: 150 cells. (4 gliders).
OOOO··OOO·OOOOO (and its mirror image)
(this pattern was found previously during my one-cell pattern exploration)
12 cells. It runs for 3183 generations. Final population: 1059 cells. (6 gliders).
I hope that helps.
- Nathaniel
- Site Admin
- Posts: 861
- Joined: December 10th, 2008, 3:48 pm
- Location: New Brunswick, Canada
- Contact:
Re: One cell thick patterns.
ThanksDivusIulius wrote:I modified the script to detect escaping gliders (this is a preliminary approach).
The shortest patterns that produce escaping gliders are the following two 15-bit patterns:
OOO·OOOOO·OOOOO (and its mirror image)
13 cells. It runs for 522 generations. Final population: 150 cells. (4 gliders).
OOOO··OOO·OOOOO (and its mirror image)
(this pattern was found previously during my one-cell pattern exploration)
12 cells. It runs for 3183 generations. Final population: 1059 cells. (6 gliders).
I hope that helps.
I'll make a page on the wiki for uni-dimensional patterns at some point (or someone else can), and add those results.
- DivusIulius
- Posts: 89
- Joined: April 1st, 2009, 11:23 am
- Contact:
Re: One cell thick patterns.
A Life wiki has been created? 463 patterns as of April 2009? It sounds very interesting. I will take a look.
- Nathaniel
- Site Admin
- Posts: 861
- Joined: December 10th, 2008, 3:48 pm
- Location: New Brunswick, Canada
- Contact:
Re: One cell thick patterns.
Well, I finally got this page created: http://www.conwaylife.com/wiki/index.ph ... al_pattern Feel free to expand etc.
Re: One cell thick patterns.
What is the smallest uni-dimensional pattern to produce a spaceship other than the glider?
-
- Posts: 566
- Joined: May 31st, 2009, 12:08 am
Re: One cell thick patterns.
The following pattern generates two LWSS spaceships and two gliders and nothing else: (oooo-oooo-ooooo-ooooooo-ooo-oooo-oooooo). There are 33 cells in a 39x1 bounding box, This was found by Paul Callahan, it is simply 1/2 of the symmetrical pattern Paul created that completely dies out (see newly created wiki page for unidimensional life). This may not be the smallest, but Paul must have executed the smallest in his search. It seems likely this is the smallest given how infrequently spaceships other that gliders occur randomly.
- DivusIulius
- Posts: 89
- Joined: April 1st, 2009, 11:23 am
- Contact:
Re: One cell thick patterns.
I find the page on the wiki for uni-dimensional patterns very informative.
Congratulations!
Congratulations!
- ColorfulGalaxy
- Posts: 407
- Joined: July 16th, 2020, 3:37 am
- Location: Hacked by Trump {Bot}
Re: One thick cell patterns.
The 41x1 solid rectangle turns into 4 pulsars and other things.
The 67x1 solid rectangle produces 4 beacons and 4 integral signs.
The 67x1 solid rectangle produces 4 beacons and 4 integral signs.
- ColorfulGalaxy
- Posts: 407
- Joined: July 16th, 2020, 3:37 am
- Location: Hacked by Trump {Bot}
Re: One cell thick patterns.
Code: Select all
x = 103, y = 1, rule = B3/S23
103o!
EDIT: Then soon I found that this one produces sixteen escaping gliders.
Code: Select all
x = 105, y = 1, rule = B3/S23
105o!
Code: Select all
x = 106, y = 1, rule = B3/S23
106o!
Code: Select all
x = 115, y = 1, rule = B3/S23
115o! ------ Even if you extend this one cell longer, it will still give an eater.