## Thread in a Different Geometry

For discussion of other cellular automata.
Extrementhusiast
Posts: 1852
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Thread in a Different Geometry

This thread is for patterns that are in toroidal, spherical, etc. universes. (This is actually for any rule.) Currently, I have been making a competition with myself to design the longest-lasting methuselah in a 20x20 torus in CGoL. Currently, this pattern holds the record, with 413 generations:

Code: Select all

``````..OO
.O.O
.O..
.O..
....
O.O.``````
EDIT: A simple century lasts for 432 generations.

On another note, I have found 6xn toroidal oscillators with traffic lights. Starting with a 3x3 (or 3x6) filled square, here are the periods of various sizes of tori (up to 6x50):

For 3x3:

18: 56
19: 42
20: 50
21: 84
32: 236
37: 119
39: 78
41: 175

For 3x6:

18: 22
19: 34
20: 44
21: 84
31: 81
32: 64
33: 83
34: 104
36: 83
37: 83
38: 141
39: 78
41: 175
42: 84
48: 550
50: 228

In the case of the 3x6, the rectangle is oriented lengthwise in the torus. And here's the Klein bottle results (with the 6 dimension twisted):

For 3x3 (a surprisingly low number of oscillators):

20: 48
28: 82

For 3x6 (that's more like it):

17: 22
18: 22
25: 62
30: 81
32: 142
33: 83
38: 83
39: 83
41: 80
42: 218
46: 80
47: 156
48: 220
49: 140

Again, for the 3x6, the rectangle is oriented lengthwise in the Klein bottle.

EDIT: This is an interesting oscillator in B278/S3456/C6:

Code: Select all

``````x = 16, y = 18, rule = 3456/278/6:T200,200
.5A\$7A\$.A3.A2\$14.A\$13.3A\$14.A\$4.A\$3.3A\$4.A6\$4.A\$3.3A\$4.A!
``````
I Like My Heisenburps! (and others)

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

### Re: Thread in a Different Geometry

Here is a spacefiller in B345/S4567 (assimilation), in a cylindrical universe:

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``````x = 64, y = 2, rule = B345/S4567:T64,0
33ob30o\$33ob30o!
``````
Filling in the two empty squares gives a sawtooth which emulates a 1D cellular automata:

Code: Select all

``````x = 64, y = 2, rule = B345/S4567:T64,0
64o\$64o!
``````
Here is a gosper glider gun firing at an area near the south pole of a sphere, to create a p210 oscillator:

Code: Select all

``````x = 100, y = 100, rule = B3/S23:S100
42\$59bo\$57bobo\$47b2o6b2o12b2o\$46bo3bo4b2o12b2o\$35b2o8bo5bo3b2o\$35b2o8b
o3bob2o4bobo\$45bo5bo7bo\$46bo3bo\$47b2o!
``````
NOTE: the placement of the gun is critical, and the auto-rule change that happens when you paste a pattern in doesn't always get it right. To get the same results as me, change the rule to B3/S23:S100 BEFORE you paste the pattern.

calcyman
Posts: 2320
Joined: June 1st, 2009, 4:32 pm

### Re: Different topologies

and the auto-rule change that happens when you paste a pattern in doesn't always get it right.

'File --> Open Clipboard' should have the desired effect.
What do you do with ill crystallographers? Take them to the mono-clinic!

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

### Re: Thread in a Different Geometry

A rake flys around a torus and places a row of gliders right in front of the previous row, until there is no more room.
EDIT: ack, somehow lost the pattern itself. Here it is:

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``````x = 175, y = 183, rule = B3/S23:T175,183
36\$47b2o8bo\$46b4o8bo\$46b2ob2o3bo3bo\$48b2o5b4o4\$54bo\$55b2o\$56bo\$56bo\$
55bo3\$57bo\$58bo\$54bo3bo\$38b4o13b4o\$37bo3bo\$41bo\$40bo!
``````
Here is a p8 oscillator in a 16 cell universe:

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``````x = 4, y = 4, rule = B3/S23:T4,4
2bo\$3o\$2bo!
``````
And here is a p28 gun in the circle of life rule, in a cylindrical universe:

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``````x = 8, y = 34, rule = circleoflife:T8,0
.B.B.B.B2\$5.B.B12\$.B.B.B.B2\$5.B.B12\$.B.BCB.B\$3.A.A\$4.CBCB\$5.A\$3.B.B!
``````

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: Thread in a Different Geometry

On a T3 universe, Langton's Ant LLRL has a spaceship (!) and a wickstretcher:

Code: Select all

``````x = 10, y = 3, rule = LangtonsAnt_LRLL:T0,3
B7.BA\$K7.BH\$C7.BA!``````

ssaamm
Posts: 125
Joined: June 4th, 2010, 9:43 pm

### Re: Thread in a Different Geometry

Well, most every pattern in any looping universe could be considered an agar or a wick when copied in a grid in a non-looping one, so make sure that you're not posting a known one of those, or if it isn't known, make clear what kind of pattern it is.

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

### Re: Thread in a Different Geometry

A rake flying on a cross-surface is not deterred by its glider trail, but the glider trail actually collides with itself and is obliterated, leaving no debris. Thus this is a very strange p3800 oscillator:

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``````x = 1000, y = 1000, rule = B3/S23:C1000,1000
506\$535b2o5b4o\$533b2ob2o3bo3bo\$533b4o8bo\$534b2o8bo3\$541b2o\$541bobo\$
543bo\$541b3o5\$542b4o\$541bo3bo\$524b4o17bo\$523bo3bo16bo\$527bo\$526bo!
``````

knightlife
Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Thread in a Different Geometry

7-cell pattern in a CGOL 20x20 torus lasts 644 generations:

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``````x = 5, y = 2, rule = B3/S23:T20,20
3obo\$o2b2o!
``````
Adding a pre-block extends it to 748 generations:

Code: Select all

``````x = 8, y = 9, rule = B3/S23:T20,20
2o\$o6\$3bo2b2o\$3b3obo!
``````

Extrementhusiast
Posts: 1852
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Thread in a Different Geometry

ebcube wrote:On a T3 universe, Langton's Ant LLRL has a spaceship (!) and a wickstretcher:

Code: Select all

``````x = 10, y = 3, rule = LangtonsAnt_LRLL:T0,3
B7.BA\$K7.BH\$C7.BA!``````
I don't know of any other Langton's Ant variants besides the original, LLRR (in which the patterns do not work), and the various Turmites (which I have not tried). Also, there are three spaceships in T3 for the regular Langton's Ant:

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``````x = 27, y = 3, rule = Langtons-Ant:T0,3
A12.DA10.A\$F12.A12.E\$A13.A10.A!``````
They can be packed very tightly, as only the "ant" matters in the nearby region. A single ant, oriented widthwise in a T4 universe, creates a pattern that possibly grows forever, and if it does, it would probably grow logarithmically. Here it is at one million generations:

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``````x = 22, y = 4, rule = Langtons-Ant:T0,4
A.2A.2A2.5A2.A.A\$A.2A5.A.3A2.4A.A\$2A.A6.AFA2.A.A.A.A\$2A.A.2A2.A2.A2.A
!
``````
The appearance at generations circa 960 000 to circa 980 000 looks a bit like a puffer, but then the ant swallows its own debris.

Three spaceship speeds are shown here in a T5 Langton's Ant:

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``````x = 8, y = 5, rule = Langtons-Ant:T0,5
4.A2.A\$.A3.A.H\$AB3.A.A\$A4.A.A\$4.AB.A!
``````
There are presumably many spaceships with the speed of the rightmost spaceship.

EDIT: Okay, I just HAVE to post this oscillator:

Code: Select all

``````x = 18, y = 2, rule = Langtons-Ant:T0,5
B\$17.B!
``````
I Like My Heisenburps! (and others)

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: Thread in a Different Geometry

Extrementhusiast wrote: EDIT: Okay, I just HAVE to post this oscillator:

Code: Select all

``````x = 18, y = 2, rule = Langtons-Ant:T0,5
B\$17.B!
``````
Wow. Just... wow. Epic.

Also, Langton's Ant is RL, not RRLL.

I'm going to look for more spaceships... that's an interesting behavior for ants.

EDIT: For width 7, three spaceship speeds and many possible spaceships with the fastest speed, just like width 5 (but not the same speeds: c/14, 3c/70 and 2c/84). And two oscillators, not as cool as yours.

EDIT: Speeds for the width 5 spaceships you posted are c/10, 3c/50 and 2c/60. There is obviously a pattern, at least for the first two: c/2*width and 3c/10*width.

Code: Select all

``````x = 79, y = 7, rule = Langtons-Ant:T0,7
3.A16.A12.A.A14.G\$4.A14.A15.D40.B\$4.A13.A16.A\$3.A13.3A14.A36.B\$2.A14.
A.2A12.A\$2.A15.EA.A11.A20.G\$3.F17.A11.3A!
``````

Extrementhusiast
Posts: 1852
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Thread in a Different Geometry

Three million generations for the sideways ant in a T4 universe:

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``````x = 22, y = 4, rule = Langtons-Ant:T0,4
.2A3.2A.D2A.3A.5A\$4.A.2A.3A.3A3.3A\$A2.2A.2A.4A6.3A\$4A2.2A2.3A4.5A!
``````
Still quite small.

EDIT: Five million:

Code: Select all

``````x = 25, y = 4, rule = Langtons-Ant:T0,4
A3.A.2A.A3.A!
``````
Last edited by Extrementhusiast on December 5th, 2010, 2:39 pm, edited 1 time in total.
I Like My Heisenburps! (and others)

ebcube
Posts: 124
Joined: February 27th, 2010, 2:11 pm

### Re: Thread in a Different Geometry

A two-ant puffer:

Code: Select all

``````x = 3, y = 4, rule = Langtons-Ant:T0,4
GA\$.A\$A.A\$.EA!
``````
I'm not sure if using more than one ant is allowed, but the oscillators seen before look great, so I'm not complaining.

EDIT: Two spaceships with width 4, at 4c/40 and 2c/8. Each of them use two ants:

Code: Select all

``````x = 8, y = 4, rule = Langtons-Ant:T0,4
7.C\$BA5.C\$CA5.A\$A6.A!
``````

Extrementhusiast
Posts: 1852
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Thread in a Different Geometry

Width-6 torus spaceship in B3/S236:

Code: Select all

``````x = 9, y = 6, rule = B3/S236:T0,6
4bo3bo\$3b2o3bo\$4bo3bo\$bo4bobo\$o4b2obo\$bo4bobo!
``````
Long width-7 torus spaceship:

Code: Select all

``````x = 79, y = 7, rule = B3/S236:T0,7
2bobo3b2o17bo10bo11bo5b3o3bo5b2o4b2o2bo\$5b4obo17bo3b2o2b2o15bo5bob3o4b
o6bo2bo\$2b2obo2bobo16b2obob3ob2o10bob2obo5bo5b4o9bo\$3bobobobo15b3o3bo
4b3o11bo6bo4bo2b5ob2obo3bo\$bo7b2o14bo4bo2b3o2b2o7bo3bo6bo3b4obo3bo2bo
3bo\$bobo22bo2b3o5bo2bo6bo3bo2b3obobo3bo2b2o2b2o5bo\$2o7b2o15bobo2bo6b2o
9bo3bo2b2ob2o5bo4bo3bo2bo!
``````
Width-7 puffer:

Code: Select all

``````x = 13, y = 7, rule = B3/S236:T0,7
o2bo3bobo\$o6bo3bo\$o3bo6b2o\$o3bo6b2o\$o6bo3bo\$o2bo3bobo\$o2b3o2bob2o!
``````
Pattern that creates two more width-7 puffers:

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``````x = 20, y = 7, rule = B3/S236:T0,7
4bo4b2o2bo2b4o\$2o2bobo2bob6obo\$4obobo3b2o4bobo\$o4b2o2bob4o2bobo\$2bobo
2b7obo2bo\$2o2bobob2o4b2obo\$bob10ob6o!
``````

Code: Select all

``````x = 4, y = 9, rule = B3/S236:T0,9
2obo\$o\$o\$o\$o\$o\$o\$o\$2obo!
``````
See if you can find the hidden feature in this random soup. (Width-10 cylinder)

Code: Select all

``````x = 20, y = 10, rule = B3/S236:T0,10
o3bo2bo3bo\$o2bo5bo3bobo3bo\$2bobob2ob2o2b2o2b2o\$o8b3o2b2o2bo\$11b2o4b2o\$
b2obo2bo2b2obo4bo\$2bo2bo2bob3ob2obobo\$2b5o2bobob3obobo\$2o2bo4b2ob2ob3o
\$3o3b2o3bob2o!
``````
I Like My Heisenburps! (and others)

David
Posts: 212
Joined: November 3rd, 2009, 2:47 am
Location: Daejeon, South Korea

### Re: Thread in a Different Geometry

Extrementhusiast wrote: EDIT: This is an interesting oscillator in B278/S3456/C6:

Code: Select all

``````x = 16, y = 18, rule = 3456/278/6:T200,200
.5A\$7A\$.A3.A2\$14.A\$13.3A\$14.A\$4.A\$3.3A\$4.A6\$4.A\$3.3A\$4.A!
``````
Wow, It's kind of NOT gate.
Call me "Dannyu NDos" in Forum. Call me "Park Shinhwan"(박신환) in Wiki.

lifespeed
Posts: 11
Joined: December 7th, 2010, 10:56 pm

### Re: Thread in a Different Geometry

a p4 c space ship life

Code: Select all

``````x = 14, y = 21, rule = B3/S23:T0,21
13bo\$13bo\$10bo2bo\$12b2o\$12b2o\$10bo2bo\$13bo\$obob2o3bo3bo\$o4bo3bo3bo\$9bo
3bo\$bo3bo3bo3bo\$9bo3bo\$o4bo3bo3bo\$obob2o3bo3bo\$13bo\$10bo2bo\$12b2o\$12b
2o\$10bo2bo\$13bo\$13bo!
``````

Extrementhusiast
Posts: 1852
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Thread in a Different Geometry

lifespeed wrote:a p4 c space ship life

Code: Select all

``````x = 14, y = 21, rule = B3/S23:T0,21
13bo\$13bo\$10bo2bo\$12b2o\$12b2o\$10bo2bo\$13bo\$obob2o3bo3bo\$o4bo3bo3bo\$9bo
3bo\$bo3bo3bo3bo\$9bo3bo\$o4bo3bo3bo\$obob2o3bo3bo\$13bo\$10bo2bo\$12b2o\$12b
2o\$10bo2bo\$13bo\$13bo!
``````
Slight variant, still p4:

Code: Select all

``````x = 14, y = 21, rule = B3/S23:T0,21
7b3ob3o\$7b3ob3o\$o2b2o2b3ob3o\$o2b2o6b3o\$11b3o\$12b2o\$13bo\$13bo\$obob2o3bo
3bo\$o4bo3bo3bo\$9bo3bo\$o4bo3bo3bo\$obob2o3bo3bo\$13bo\$13bo\$12b2o\$11b3o\$o
2b2o6b3o\$o2b2o2b3ob3o\$7b3ob3o\$7b3ob3o!
``````
I Like My Heisenburps! (and others)

lifespeed
Posts: 11
Joined: December 7th, 2010, 10:56 pm

### Re: Thread in a Different Geometry

here's a p2 c ship

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``````x = 4, y = 10, rule = B3/S23:T0,10
3bo\$o2bo\$2b2o\$b3o\$b3o\$b3o\$b3o\$2b2o\$o2bo\$3bo!
``````

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

### Re: Thread in a Different Geometry

That spaceship can pull a block one cell:

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``````x = 36, y = 10, rule = B3/S23:T0,10
10bo\$7bo2bo\$9b2o\$8b3o\$8b3o14b2o\$8b3o14b2o\$8b3o\$9b2o\$7bo2bo\$10bo!
``````

ssaamm
Posts: 125
Joined: June 4th, 2010, 9:43 pm

### Re: Thread in a Different Geometry

For some strange reason, tubes seem to clog up for me.

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``````x = 3, y = 3, rule = B3/S23:T0,21
b2o\$2o\$bo!
``````
Look at this at 4x or higher speed and it really slows down towards the end.

Also, regarding the first post, top this:

Code: Select all

``````x = 10, y = 5, rule = B3/S23:T20,20
9bo\$9bo\$9bo\$b3o\$o2bo!
``````
668, I think

Extrementhusiast
Posts: 1852
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Thread in a Different Geometry

This soup lasts a while:

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``````x = 20, y = 20, rule = B3/S23:P20,20
bo2b3ob2ob3ob4o\$2ob4o2b5obob3o\$b2o2b5o2b2o3b2o\$4ob2ob3ob5ob2o\$2bob8ob
2ob3o\$3ob4obob2o5bo\$obobob3obo2b2o2bobo\$3bo3b2obobobo2b3o\$o4b3obo2b2ob
o2b2o\$bobo2b2obob8o\$8obo2bobo2bobo\$3b2ob3o4b5obo\$2bobo2b2o2b3ob2ob2o\$b
ob3obo3bobo3bobo\$2o2b2obob8ob2o\$2o5b3obob2o2b3o\$2b2obob3o2bob6o\$2o2b2o
bo2b2o2bo2b2o\$2obobo5b3ob4o\$o2b4obo3bob4o!
``````
---

Recently, I've been doing some hand censusing for B3/S236 in a 20x20 bounded plane. Out of 50 soups, here are the results:
• 29 blinkers, relative freq. 0.191, avg. # per soup 0.580
• 55 blocks, relative freq. 0.362, avg. # per soup 1.100
• 7 tubs, relative freq. 0.0461, avg. # per soup 0.140
• 11 boats, relative freq. 0.0724, avg. # per soup 0.220
• 28 beehives, relative freq. 0.184, avg. # per soup 0.560
• 5 barges, relative freq. 0.0329, avg. # per soup 0.100
• 15 loaves, relative freq. 0.0987, avg. # per soup 0.300
• 1 pond, relative freq. 0.00658, avg. # per soup 0.0200
• 1 house (side), relative freq. 0.00658, avg. # per soup 0.0200
There were a lot of temporary objects, including a table (on an edge), a bookend (also on an edge), a bookend with boat (yet again, on an edge), and an aircraft carrier (which also happened to lie on an edge); I am not including these temporary objects in my census. Interestingly enough, some of the soups did not leave any debris.

I will be continuously updating these findings at 50, 100, 250, 500, 750, and 1000 soups, until I'm not interested in it anymore.
I Like My Heisenburps! (and others)

137ben
Posts: 343
Joined: June 18th, 2010, 8:18 pm

### Re: Thread in a Different Geometry

Here is a single gosper glider gun in a sphere--it takes 10,242 generations to stabilize (much longer than most other placements of a single gun in a 100 by 100 sphere):

Code: Select all

``````x = 100, y = 100, rule = B3/S23:S100
13\$56bo\$54bobo\$44b2o6b2o12b2o\$43bo3bo4b2o12b2o\$32b2o8bo5bo3b2o\$32b2o8b
o3bob2o4bobo\$42bo5bo7bo\$43bo3bo\$44b2o!
``````

ColorfulGalaxy
Posts: 195
Joined: July 16th, 2020, 3:37 am
Location: China
Contact:

### Re: Thread in a Different Geometry

137ben wrote:
January 23rd, 2011, 5:45 pm
Here is a single gosper glider gun in a sphere--it takes 10,242 generations to stabilize (much longer than most other placements of a single gun in a 100 by 100 sphere):

Code: Select all

``````x = 100, y = 100, rule = B3/S23:S100
13\$56bo\$54bobo\$44b2o6b2o12b2o\$43bo3bo4b2o12b2o\$32b2o8bo5bo3b2o\$32b2o8b
o3bob2o4bobo\$42bo5bo7bo\$43bo3bo\$44b2o!
``````
Looks like you misplaced it...
Nothing special happened.

Code: Select all

``````x = 9, y = 9, rule = LifeColorful
6E.2B\$6E.2B\$7.2B\$2D5.2B\$2D5.2B\$2D5.2B\$2D\$2D.6C\$2D.6C!``````

dvgrn
Moderator
Posts: 7291
Joined: May 17th, 2009, 11:00 pm
Contact:

### Re: Thread in a Different Geometry

ColorfulGalaxy wrote:
July 19th, 2020, 12:06 am
Looks like you misplaced it...
Nothing special happened.
In this post you're talking to someone who hasn't visited the forums in more than three years, about a minor post that's almost a decade old. You've done a lot of necroposting in a very short time. Could you please cut down the rate of these necroposts to something more reasonable like, say, one per month?

If you copy the pattern in question into Golly you'll find that the pattern actually does last exactly 10,242 generations before stabilizing -- though the gun gets destroyed quite a bit before that. I'll post a link to this as a LifeViewer bug report.

bubblegum
Posts: 389
Joined: August 25th, 2019, 11:59 pm

### Re: Thread in a Different Geometry

dvrgn wrote:
July 19th, 2020, 6:38 pm
If you copy the pattern in question into Golly you'll find that the pattern actually does last exactly 10,242 generations before stabilizing -- though the gun gets destroyed quite a bit before that. I'll post a link to this as a LifeViewer bug report.
This is standard LifeViewer behaviour. LifeViewer automatically centres the pattern while Golly places it at the top-left. The standard solution is to include a #CXRLE tag at the top, like so:

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``````#CXRLE Pos=0,0 Gen=0
x = 100, y = 100, rule = B3/S23:S100
13\$56bo\$54bobo\$44b2o6b2o12b2o\$43bo3bo4b2o12b2o\$32b2o8bo5bo3b2o\$32b2o8b
o3bob2o4bobo\$42bo5bo7bo\$43bo3bo\$44b2o!``````
(Wait, am I teaching dvgrn something? Since when was I qualified to do that?)
Each day is a hidden opportunity, a frozen waterfall that's waiting to be realised, and one that I'll probably be ignoring
bubblegum wrote:
July 2nd, 2020, 8:33 pm
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FWKnightship
Posts: 677
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### Re: Thread in a Different Geometry

Code: Select all

``````x = 2, y = 5, rule = 1c23-y5e6c/34e6i/10:T0,5
\$.A\$2A\$.A!``````
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