Thread in a Different Geometry

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Extrementhusiast
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Thread in a Different Geometry

Post by Extrementhusiast » November 23rd, 2010, 1:36 pm

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!
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137ben
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Re: Thread in a Different Geometry

Post by 137ben » November 24th, 2010, 9:38 pm

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

Code: Select all

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.

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calcyman
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Re: Different topologies

Post by calcyman » November 25th, 2010, 3:22 am

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.
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137ben
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Re: Thread in a Different Geometry

Post by 137ben » November 25th, 2010, 9:51 am

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:

Code: Select all

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:

Code: Select all

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:

Code: Select all

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
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Re: Thread in a Different Geometry

Post by ebcube » November 25th, 2010, 1:28 pm

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!

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ssaamm
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Re: Thread in a Different Geometry

Post by ssaamm » November 25th, 2010, 3:31 pm

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
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Re: Thread in a Different Geometry

Post by 137ben » November 25th, 2010, 10:23 pm

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:

Code: Select all

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
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Re: Thread in a Different Geometry

Post by knightlife » November 26th, 2010, 3:07 pm

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

Code: Select all

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!

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Extrementhusiast
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Re: Thread in a Different Geometry

Post by Extrementhusiast » November 29th, 2010, 8:35 pm

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:

Code: Select all

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:

Code: Select all

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:

Code: Select all

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!
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ebcube
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Re: Thread in a Different Geometry

Post by ebcube » November 30th, 2010, 11:03 am

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!

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Extrementhusiast
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Re: Thread in a Different Geometry

Post by Extrementhusiast » November 30th, 2010, 8:21 pm

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

Code: Select all

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
2A2.A3.4AD2.A2.A.A$A3.A.A.A.3A.A.A4.3A$3.A.2A4.2A.A.2A3.4A$.A.A.A3.A.
A3.A.2A.A3.A!
Last edited by Extrementhusiast on December 5th, 2010, 2:39 pm, edited 1 time in total.
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ebcube
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Re: Thread in a Different Geometry

Post by ebcube » December 2nd, 2010, 10:14 am

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. :D

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!

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Extrementhusiast
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Re: Thread in a Different Geometry

Post by Extrementhusiast » December 2nd, 2010, 10:53 pm

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:

Code: Select all

x = 20, y = 7, rule = B3/S236:T0,7
4bo4b2o2bo2b4o$2o2bobo2bob6obo$4obobo3b2o4bobo$o4b2o2bob4o2bobo$2bobo
2b7obo2bo$2o2bobob2o4b2obo$bob10ob6o!
Width-9 blinker puffer:

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!
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David
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Re: Thread in a Different Geometry

Post by David » December 12th, 2010, 2:55 am

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.
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lifespeed
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Re: Thread in a Different Geometry

Post by lifespeed » December 19th, 2010, 3:51 pm

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!

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Extrementhusiast
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Re: Thread in a Different Geometry

Post by Extrementhusiast » December 20th, 2010, 1:16 am

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!
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lifespeed
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Re: Thread in a Different Geometry

Post by lifespeed » December 23rd, 2010, 6:28 pm

here's a p2 c ship

Code: Select all

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

137ben
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Re: Thread in a Different Geometry

Post by 137ben » December 23rd, 2010, 9:56 pm

That spaceship can pull a block one cell:

Code: Select all

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

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ssaamm
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Re: Thread in a Different Geometry

Post by ssaamm » December 23rd, 2010, 10:40 pm

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

Code: Select all

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

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Extrementhusiast
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Re: Thread in a Different Geometry

Post by Extrementhusiast » December 27th, 2010, 12:34 am

This soup lasts a while:

Code: Select all

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.
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137ben
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Re: Thread in a Different Geometry

Post by 137ben » 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!

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