One cell thick patterns.

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
Macbi
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Joined: March 29th, 2009, 4:58 am

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?

Nathaniel
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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?

DivusIulius
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Re: One cell thick patterns.

I am going to modify my script in order to provide a specific answer to your question.
Stay tuned.

DivusIulius
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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.

Nathaniel
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Joined: December 10th, 2008, 3:48 pm
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Re: One cell thick patterns.

DivusIulius 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.
Thanks

I'll make a page on the wiki for uni-dimensional patterns at some point (or someone else can), and add those results.

DivusIulius
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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
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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.

Lewis
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Re: One cell thick patterns.

What is the smallest uni-dimensional pattern to produce a spaceship other than the glider?

knightlife
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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
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Re: One cell thick patterns.

I find the page on the wiki for uni-dimensional patterns very informative.
Congratulations!

ColorfulGalaxy
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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.
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ColorfulGalaxy
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Re: One cell thick patterns.

Code: Select all

``````x = 103, y = 1, rule = B3/S23
103o!``````
The 103 by 1 solid rectangle is the smallest one-cell-high rectangle that ends up with eight escaping gliders.

EDIT: Then soon I found that this one produces sixteen escaping gliders.

Code: Select all

``````x = 105, y = 1, rule = B3/S23
105o!``````
EDIT: And then this one evolves into twelve escaping gliders.

Code: Select all

``````x = 106, y = 1, rule = B3/S23
106o!``````
And, this one gives you an EATER (it should be called a "fishhook"):

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.``````
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