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Smallest Glider-gun. Sayab-Rule

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Smallest Glider-gun. Sayab-Rule

Postby jmgomez » September 13th, 2017, 6:39 am

We presented here a new Cellular Automata capable of logic
Universality: Sayab-rule.

The Sayab-rule has the smallest glider-gun reported to date,
consisting of just four live cells at its minimal phases.


Sayab-rule is a binary 2D cellular automaton with a Moore neighborhood
and isotropic dynamics.

Sayab-rule, named after the Mayan-Yucatec word for a natural spring (of
running water).

for more details see: https://arxiv.org/pdf/1709.02655.pdf

Sayab-Rule in Alan Hensel's 'neighbors2' rule notation,

rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8


Smallest Glider-gun:
#C Smallest Glider-gun.
x = 92, y = 47, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
2o$2o2$90b2o$90b2o40$46b2o2$46bobo!


Slower Composed Glider-gun:
#C Slower Composed Glider-gun.
x = 378, y = 434, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
376bo$377bo$377bo13$361bo$362bo$362bo13$346bo$347bo$347bo13$331bo$332b
o$332bo13$316bo$317bo$317bo13$301bo$302bo$302bo13$286bo$287bo$287bo13$
271bo$272bo$272bo13$256bo$257bo$257bo13$241bo$242bo$242bo13$226bo$227b
o$227bo13$211bo$212bo$212bo13$196bo$197bo$197bo13$181bo7b2o$182bo10b2o
$182bo9bo3$176bo$177bo20b2o$177bo19bo2$169bobo$171bo$169bo5bo27b2o$
173b2o27bo4$180bo27b2o$178b2o27bo4$185bo27b2o$183b2o27bo5bo$216bo$216b
obo2$190bo19bo$188b2o20bo$211bo3$195bo9bo$193b2o10bo$200b2o4bo$199bo$
198b2obo2$198b2ob2o$200bo3$195bo$195bo$196bo13$180bo$180bo$181bo13$
165bo$165bo$166bo13$150bo$150bo$151bo13$135bo$135bo$136bo13$120bo$120b
o$121bo13$105bo$105bo$106bo13$90bo$90bo$91bo13$75bo$75bo$76bo13$60bo$
60bo$61bo13$45bo$45bo$46bo13$30bo$30bo$31bo13$15bo$15bo$16bo13$o$o$bo!


Glider-gun from collision of gliders:
#C Glider-gun from collision of gliders.
x = 85, y = 5, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
2bo$obo2$82bo$82bobo!


Glider-gun from collision Glider vs oscillator:
#C Glider-gun from collision Glider vs oscillator
x = 6, y = 5, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
3bo2$3bobo$2o$2bo!


Composed Glider-gun:
#C Composed Glider-gun.
x = 82, y = 86, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
74b2o$74b2o65$o$obo66b2o$bo16bo49bo$16bobo50bo$17bo7$80b2o$9b2o69b2o$
9b2o4$67bo$66bo$67b2o!


Gate AND:
#C Gate AND
x = 135, y = 126, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
22bo$20bobo4$27bo$25bobo4$32bo$30bobo40$80b2o$80b2o7$17bo$15bobo9$27bo
$25bobo4$32bo$30bobo21$30bobo$32bo4$25bobo$27bo4$20bobo$22bo4$15bobo$
17bo4$10bobo$12bo120b2o$2o3b2o126b2o$2o$5bo2$7b2o$9bo$7bo$7bo!


Gate OR:
#C Gate OR
x = 148, y = 198, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
7bo$7bo$9bo$7b2o2$5bo$2o$2o3b2o$12bo$10bobo4$17bo$15bobo4$22bo$20bobo
4$27bo$25bobo4$32bo$30bobo43$22bo$20bobo4$27bo$25bobo4$32bo$30bobo48$
17bo$15bobo58b2o$76b2o8$27bo$25bobo4$32bo$30bobo$146b2o$146b2o19$30bob
o$32bo4$25bobo$27bo4$20bobo$22bo4$15bobo$17bo4$10bobo$12bo$2o3b2o$2o$
5bo2$7b2o$9bo$7bo$7bo!



Gate NOT:
#C Gate NOT
x = 82, y = 75, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
80b2o$80b2o7$17bo$15bobo9$27bo$25bobo4$32bo$30bobo21$30bobo$32bo4$25bo
bo$27bo4$20bobo$22bo4$15bobo$17bo4$10bobo$12bo$2o3b2o$2o$5bo2$7b2o$9bo
$7bo$7bo!


Some Oscillators:
#C Some Oscillators
x = 55, y = 7, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
40bo11bo$48bo3bo$2b2o6b2o10b2o16bo7bo2bob2o$10b3o8bo8b3o6b3o4b2obo2bo$
2o9b3o7bo18bo7bo3bo$12b2o34bo$40bo!


Some Spaceships:
#C Some Spaceships
x = 155, y = 38, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
153bo$153bo2$153bo$6b3o3b3o19bo10bo20bo9bo14b3o2bo2b3o13b3o16bo2bo2bo
12bo$5bo4bo4bo19bo8bo20bo11bo17b3o17bobo35bo$5bo2bobobo2bo18bobo6bobo
18bobo4bo4bobo13bo3bo3bo11bo3bo3bo13b3ob3o11bobo$2b2o4bobobo4b2o50bobo
bo17b2o7b2o9b3o5b3o12bo2bo2bo11bobo$b2o2bo2b2ob2o2bo2b2o13b2obo6bob2o
17bo2bobobobobo2bo13bo3bo3bo11bo3bo3bo11b5ob5o$2bobo4bobo4bobo12bo2bob
2o4b2obo2bo15bo2bob2ob2obo2bo13bobobobobo14b3o$4o13b4o10b2o3bo6bo3b2o
17b2o2bobo2b2o18bobo14bo3bo3bo12bo2b3o2bo$o4b2o7b2o4bo10bo2bobo6bobo2b
o15bo2bo7bo2bo17bo14b2o7b2o10b2o7b2o$4bob2o5b2obo16bobobo4bobobo15bo2b
o2bo5bo2bo2bo31bo3bo3bo12bo3bo3bo$obobobo7bobobobo10bo16bo12b2o5bo5bo
5b2o30bobobobobo12bobobobobo$b3ob2o7b2ob3o12bobo2bo4bo2bobo14bo3bo9bo
3bo34bobo18bobo$3bobo9bobo15b3obo4bob3o15bobobobo5bobobobo35bo20bo$30b
2o4bobo2bobo4b2o15bobo7bobo$29b2obo4bob2obo4bob2o15bo9bo$30bobo14bobo$
30bo8b2o8bo$32bo6b2o6bo$30bobo4bo4bo4bobo$31bob4obo2bob4obo$32bo14bo$
33bobo2bo2bo2bobo$33bobo8bobo$38bo2bo$36b2o4b2o$36bo6bo$33b2o10b2o$32b
2o2bo6bo2b2o$33bobo8bobo$31b4o10b4o$31bo4b2o4b2o4bo$35bob2o2b2obo$31bo
bobobo4bobobobo$32b3ob2o4b2ob3o$34bobo6bobo!

Last edited by jmgomez on September 13th, 2017, 8:59 am, edited 3 times in total.
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Re: Smallest Glider-gun. Sayab-Rule

Postby Saka » September 13th, 2017, 7:37 am

Please edit your post instead of making new posts. That was a 11-post

Also, this seems like a non-totalistic rule, so you dont need to make a rule table.
Everyone, please stop posting B/S about CA
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)
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Re: Smallest Glider-gun. Sayab-Rule

Postby dvgrn » September 13th, 2017, 8:05 am

jmgomez wrote:Sayab-rule is a binary 2D cellular automaton with a Moore neighborhood
and isotropic dynamics.

It looks like "welcome to the forums" isn't quite right, since you've been posting for a while. Welcome back!

Saka wrote:Please edit your post instead of making new posts. That was a 11-post.

Here's a link to the forum rules -- Saka is referring to the request in there about avoiding unnecessary duplicate posts. (EDIT: All cleaned up now. @jmgomez, thanks for the quick work there!)

Saka wrote:Also, this seems like a non-totalistic rule, so you dont need to make a rule table.

That's correct -- and if you use Alan Hensel's 'neighbors2' rule notation, then LifeViewer can display your patterns in a forum post. You can also use the "viewer" tag, but it's probably better not to overuse that:

Code: Select all
#C some oscillators
x = 55, y = 7, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
40bo11bo$48bo3bo$2b2o6b2o10b2o16bo7bo2bob2o$10b3o8bo8b3o6b3o4b2obo2bo$
2o9b3o7bo18bo7bo3bo$12b2o34bo$40bo!
#C [[ THEME 4 GPS 5 AUTOSTART THUMBNAIL THUMBSIZE 2 HEIGHT 240 ]]

Here's the work I did to translate the neighborhood table in the linked paper into Hensel format:

  5: B2c
 10: B2e
 17: S1c
 18: S1e
 19: S2a
 27: S3a
 30: S3j
 40: B2i
 42: B3e
 58: S3e
 61: S4i
 70: B3q
 84: S2n
 85: S3c
 87: S4n
102: B4q
105: B4t
113: S3y
119: S5j
122: S4j
127: S6a
171: B5c
173: B5y
189: S5y
191: S6c
238: B6n
254: S6n
381: S6i
511: S8

When these are combined, you get the rule string "B2cei3eq4qt5cy6n/S1ce2an3acejy4ijn5jy6acin8" -- but the canonical form is a little shorter, using "6-ek" instead of "6acin". (That just means "all 6-neighbor neighborhoods besides e and k".)

The syntax takes a while to get used to, but it's definitely simpler than copying whole rule tables around.
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Re: Smallest Glider-gun. Sayab-Rule

Postby blah » September 13th, 2017, 9:27 am

I haven't read the entire paper, but I'm presuming that when it says "the smallest known gun to date" it means the smallest gun in an isotropic 2-state CA on a moore neighbourhood, because otherwise small guns become trivial:
@RULE BLAHTWOCELLGUN
@TABLE
n_states:2
neighborhood:Moore
symmetries:none
0,0,0,1,1,0,0,0,0,1
1,0,0,1,1,0,0,0,0,0
0,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,0,0,0

x = 1, y = 2, rule = BLAHTWOCELLGUN
o$o!

Though I'm not sure, since it says "The Sayab-rule’s glider-gun is the smallest reported to date in 2D CA, consisting of just four live cells at its minimal phases"
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Re: Smallest Glider-gun. Sayab-Rule

Postby Saka » September 13th, 2017, 9:30 am

wildmyron posted this gun in a non-totalistic CA also containing only 2 cells
x = 1, y = 2, rule = B01c/S26
o$o!


So no, Sayab is not the "smallest glider gun" rule.
Everyone, please stop posting B/S about CA
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)
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Re: Smallest Glider-gun. Sayab-Rule

Postby BlinkerSpawn » September 13th, 2017, 9:54 am

Saka wrote:wildmyron posted this gun in a non-totalistic CA also containing only 2 cells
x = 1, y = 2, rule = B01c/S26
o$o!


So no, Sayab is not the "smallest glider gun" rule.

I distinctly remember two one-cell guns being posted somewhere but I have no idea where to find the post.
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Re: Smallest Glider-gun. Sayab-Rule

Postby A for awesome » September 13th, 2017, 10:02 am

Saka wrote:wildmyron posted this gun in a non-totalistic CA also containing only 2 cells
x = 1, y = 2, rule = B01c/S26
o$o!

That's still not the smallest.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Smallest Glider-gun. Sayab-Rule

Postby jmgomez » September 13th, 2017, 10:09 am

Very Interesting. According to our research in papers we don't find another smaller. So is amazing that exist smaller glider-gun. The forum seems to be the best place to know about it.

Thanks for you feedback
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Re: Smallest Glider-gun. Sayab-Rule

Postby dvgrn » September 13th, 2017, 12:10 pm

jmgomez wrote:Very Interesting. According to our research in papers we don't find another smaller. So is amazing that exist smaller glider-gun. The forum seems to be the best place to know about it.

Yes, there's a certain amount of overlap between current cellular-automata investigations and the academic world, but published results often lag a few years (or more) behind the actual discoveries. For many of us on the conwaylife.com forums, solving CA problems is something like an alternative to Sudoku or crossword puzzles -- which means that once a puzzle has been solved, it doesn't necessarily seem like an interesting use of time to write a paper about it.

It turns out that there is some published prior art for a gun with fewer than four ON cells, though. Sort of. It's buried pretty deeply in the associated data for Emmanuel Sapin's 2008 paper, but it's out there.

The paper doesn't actually focus on record-setting small sizes, but probably there are quite a few more tiny alien guns in the collection, maybe even with a one- or two-cell minimum. Certainly there are a lot of four-cell guns, since a couple of them show up just in the samples I posted last year:

#C p16 2-barrel alternate east&west shotgun (mod = 8)
#C outputs two gliders per cycle in each direction, at times T and T+9 (mod 16)
#C From Emmanuel Sapin's large automated rule survey from 2008 --
#C   http://www.complex-systems.com/pdf/17-4-1
#C
#C All guns from survey in Golly-compatible format
#C   http://conwaylife.com/forums/viewtopic.php?f=&p=33876#p33876
#C
#C Original (WARNING: non-Golly-compatible) source of collection:
#C   http://uncomp.uwe.ac.uk/sapin/
#C
x = 2, y = 3, rule = B2cei3aekry4ciyz5ijkry6-cn/S1c2a3-air4akwyz5-cjr6ckn
bo$o$bo!

EDIT:The BLAHTWOCELLGUN rule is actually also natively supported by LifeViewer, and by Golly 3.0+. (I used the MAPper script to make this -- thanks, Rhombic!)

x = 1, y = 2, rule = MAPAMAgAAAAIAAAAAAAAAAAAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAAAAAAAAAAAAAAAAAAA
o$o!

Allowing anisotropic rules definitely does seem like cheating, though.
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Re: Smallest Glider-gun. Sayab-Rule

Postby A for awesome » September 13th, 2017, 6:31 pm

Two oscillators and a spaceship:
x = 20, y = 18, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
bo$bo$obo$bo$obo$bo$bo7bo$8bo2$7bobo2bo$11bo$9bo2$14b2o2$15bo$17bobo$
16bo2bo!

EDIT: Tagalong to the c/12:
x = 5, y = 16, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
2bo$2bo$2ob2o8$b3o2$2bo2$2bo$2bo!

Some c/3 and c/4 ships:
x = 112, y = 58, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8
2b3o7b3o11bo3bo3bo19bo19bo9bo13bo9bo$2bobo7bobo13bobobo21bo19bo9bo11bo
2bo7bo2bo$3bo9bo14bo3bo62b2o2bo7bo2b2o$2bobo7bobo12b3ob3o17bo2bo2bo16b
o9bo11bobo9bobo$3bo9bo14bo3bo16bo9bo12b2ob2o5b2ob2o10bo11bo$3bo9bo13bo
5bo15b3o5b3o11b2obob2o3b2obob2o14bobo$2bobo7bobo57bobobo5bobobo12bobo
3bobo$obo11bobo10bo5bo13b2obo7bob2o10bobobo5bobobo13bo2bo2bo$2bobob5ob
obo10bo4bo4bo11bo13bo11bobo7bobo16bobo$b2o11b2o10bo3bo3bo16bo5bo43bo3b
o$3bobo5bobo13b2obob2o18bo3bo44b5o$3bo9bo14bo3bo16b2o3bo3b2o13b2o9b2o
15b2ob2o$5bo2bo2bo16b5o16bo4bo4bo11b2o3bo5bo3b2o15bo$3b2o3bo3b2o14bo3b
o16bo3b3o3bo11bo3bobo3bobo3bo13bobobo$3b3o5b3o13bob3obo14b2obo5bob2o
11b2ob3obob3ob2o14bo3bo$5b2obob2o14bo3bo3bo14b2o7b2o19bo23bo$2b2o2bobo
bo2b2o10bo3b3o3bo36bobo3b3o3bobo15b3o$26b2o5b2o14bo9bo13bo11bo17bo$2b
2o2b2ob2o2b2o10bo3b3o3bo11b3o9b3o15bo3bo$5bo5bo14b2obobob2o11b2o2bo7bo
2b2o11bob2o3b2obo17b3o$6bo3bo16bobobobo15bo9bo14bobo5bobo17bobo$6bo3bo
15bo3bo3bo13bo11bo12bo11bo14b2o3b2o$5bo2bo2bo17bobo42bo9bo15b2o3b2o$6b
o3bo16bo5bo38bo13bo10bob2o5b2obo$8bo16b2o2bobo2b2o35b2o13b2o$8bo16bo2b
o3bo2bo36bob2o7b2obo9bob2o7b2obo$6bo3bo15bo7bo38b2o9b2o11bo11bo$7b3o$
6bobobo14b3o5b3o63bobo3bobo$8bo15bob2o5b2obo64bo3bo$22bobob2o5b2obobo
60bo2bobo2bo$24bobo7bobo61bob2o3b2obo$23bo2bo7bo2bo62bo5bo$22bo15bo59b
o9bo$26bo7bo63bo9bo$24bo11bo59b2o11b2o$23b2o11b2o58bo13bo$24bobo7bobo
61b2o7b2o$25bo9bo60bobo9bobo$23b2ob2o5b2ob2o$23b5o5b5o$24bobo7bobo$22b
7o3b7o$24b3o7b3o$23bobobo5bobobo$24bobo7bobo3$27bo5bo$26bo3bo3bo$27bo
5bo$30bo$28bobobo$27bo5bo$29b3o$30bo$26bobobobobo$29bobo!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

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Re: Smallest Glider-gun. Sayab-Rule

Postby jmgomez » September 17th, 2017, 10:22 am

Thanks awesome!
Nices oscillators, tagalong and spaceships.

-jm
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