## Thread in a Different Geometry

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
Extrementhusiast
Posts: 1828
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:

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``````..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:

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``````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:

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``````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: 2144
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:

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``````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:

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

Extrementhusiast
Posts: 1828
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:

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``````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:

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``````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:

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``````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: 1828
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:

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``````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:

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``````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:

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

Extrementhusiast
Posts: 1828
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Thread in a Different Geometry

Width-6 torus spaceship in B3/S236:

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

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

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``````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!
``````

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``````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)

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``````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:

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``````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

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``````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: 1828
Joined: June 16th, 2009, 11:24 pm
Location: USA

### Re: Thread in a Different Geometry

lifespeed wrote:a p4 c space ship life

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``````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:

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``````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:

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

Extrementhusiast
Posts: 1828
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):

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