## Smallest Glider-gun. Sayab-Rule

For discussion of other cellular automata.

### Smallest Glider-gun. Sayab-Rule

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-ek82o$2o2$90b2o$90b2o40$46b2o2$46bobo! Slower Composed Glider-gun: #C Slower Composed Glider-gun.x = 378, y = 434, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8376bo$377bo$377bo13$361bo$362bo$362bo13$346bo$347bo$347bo13$331bo$332bo$332bo13$316bo$317bo$317bo13$301bo$302bo$302bo13$286bo$287bo$287bo13$271bo$272bo$272bo13$256bo$257bo$257bo13$241bo$242bo$242bo13$226bo$227bo$227bo13$211bo$212bo$212bo13$196bo$197bo$197bo13$181bo7b2o$182bo10b2o$182bo9bo3$176bo$177bo20b2o$177bo19bo2$169bobo$171bo$169bo5bo27b2o$173b2o27bo4$180bo27b2o$178b2o27bo4$185bo27b2o$183b2o27bo5bo$216bo$216bobo2$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$120bo$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-ek82bo$obo2$82bo$82bobo!

Glider-gun from collision Glider vs oscillator:
#C Glider-gun from collision Glider vs oscillatorx = 6, y = 5, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek83bo2$3bobo$2o$2bo! Composed Glider-gun: #C Composed Glider-gun.x = 82, y = 86, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek874b2o$74b2o65$o$obo66b2o$bo16bo49bo$16bobo50bo$17bo7$80b2o$9b2o69b2o$9b2o4$67bo$66bo$67b2o! Gate AND: #C Gate ANDx = 135, y = 126, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek822bo$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 ORx = 148, y = 198, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek87bo$7bo$9bo$7b2o2$5bo$2o$2o3b2o$12bo$10bobo4$17bo$15bobo4$22bo$20bobo4$27bo$25bobo4$32bo$30bobo43$22bo$20bobo4$27bo$25bobo4$32bo$30bobo48$17bo$15bobo58b2o$76b2o8$27bo$25bobo4$32bo$30bobo$146b2o$146b2o19$30bobo$32bo4$25bobo$27bo4$20bobo$22bo4$15bobo$17bo4$10bobo$12bo$2o3b2o$2o$5bo2$7b2o$9bo$7bo$7bo! Gate NOT: #C Gate NOTx = 82, y = 75, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek880b2o$80b2o7$17bo$15bobo9$27bo$25bobo4$32bo$30bobo21$30bobo$32bo4$25bobo$27bo4$20bobo$22bo4$15bobo$17bo4$10bobo$12bo$2o3b2o$2o$5bo2$7b2o$9bo$7bo$7bo! Some Oscillators: #C Some Oscillatorsx = 55, y = 7, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek840bo11bo$48bo3bo$2b2o6b2o10b2o16bo7bo2bob2o$10b3o8bo8b3o6b3o4b2obo2bo$2o9b3o7bo18bo7bo3bo$12b2o34bo$40bo! Some Spaceships: #C Some Spaceshipsx = 155, y = 38, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8153bo$153bo2$153bo$6b3o3b3o19bo10bo20bo9bo14b3o2bo2b3o13b3o16bo2bo2bo12bo$5bo4bo4bo19bo8bo20bo11bo17b3o17bobo35bo$5bo2bobobo2bo18bobo6bobo18bobo4bo4bobo13bo3bo3bo11bo3bo3bo13b3ob3o11bobo$2b2o4bobobo4b2o50bobobo17b2o7b2o9b3o5b3o12bo2bo2bo11bobo$b2o2bo2b2ob2o2bo2b2o13b2obo6bob2o17bo2bobobobobo2bo13bo3bo3bo11bo3bo3bo11b5ob5o$2bobo4bobo4bobo12bo2bob2o4b2obo2bo15bo2bob2ob2obo2bo13bobobobobo14b3o$4o13b4o10b2o3bo6bo3b2o17b2o2bobo2b2o18bobo14bo3bo3bo12bo2b3o2bo$o4b2o7b2o4bo10bo2bobo6bobo2bo15bo2bo7bo2bo17bo14b2o7b2o10b2o7b2o$4bob2o5b2obo16bobobo4bobobo15bo2bo2bo5bo2bo2bo31bo3bo3bo12bo3bo3bo$obobobo7bobobobo10bo16bo12b2o5bo5bo5b2o30bobobobobo12bobobobobo$b3ob2o7b2ob3o12bobo2bo4bo2bobo14bo3bo9bo3bo34bobo18bobo$3bobo9bobo15b3obo4bob3o15bobobobo5bobobobo35bo20bo$30b2o4bobo2bobo4b2o15bobo7bobo$29b2obo4bob2obo4bob2o15bo9bo$30bobo14bobo$30bo8b2o8bo$32bo6b2o6bo$30bobo4bo4bo4bobo$31bob4obo2bob4obo$32bo14bo$33bobo2bo2bo2bobo$33bobo8bobo$38bo2bo$36b2o4b2o$36bo6bo$33b2o10b2o$32b2o2bo6bo2b2o$33bobo8bobo$31b4o10b4o$31bo4b2o4b2o4bo$35bob2o2b2obo$31bobobobo4bobobobo$32b3ob2o4b2ob3o$34bobo6bobo! Last edited by jmgomez on September 13th, 2017, 8:59 am, edited 3 times in total. jmgomez Posts: 43 Joined: October 6th, 2015, 1:42 am ### Re: Smallest Glider-gun. Sayab-Rule 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/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

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### Re: Smallest Glider-gun. Sayab-Rule

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!

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 oscillatorsx = 55, y = 7, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek840bo11bo$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: S4n102: B4q105: B4t113: S3y119: S5j122: S4j127: S6a171: B5c173: B5y189: S5y191: S6c238: B6n254: S6n381: S6i511: 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.
dvgrn
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### Re: Smallest Glider-gun. Sayab-Rule

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@TABLEn_states:2neighborhood:Mooresymmetries:none0,0,0,1,1,0,0,0,0,11,0,0,1,1,0,0,0,0,00,0,0,1,0,0,0,0,0,11,0,0,0,0,0,0,0,0,0

x = 1, y = 2, rule = BLAHTWOCELLGUNo$o! Though I'm not sure, since it says "The Sayab-rule’s glider-gun is the smallest reported to date in 2D CA, consisting of just four live cells at its minimal phases" succ blah Posts: 174 Joined: April 9th, 2016, 7:22 pm ### Re: Smallest Glider-gun. Sayab-Rule wildmyron posted this gun in a non-totalistic CA also containing only 2 cells x = 1, y = 2, rule = B01c/S26o$o!

So no, Sayab is not the "smallest glider gun" rule.
x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo! (Check gen 2) Saka Posts: 2182 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: Smallest Glider-gun. Sayab-Rule Saka wrote:wildmyron posted this gun in a non-totalistic CA also containing only 2 cells x = 1, y = 2, rule = B01c/S26o$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.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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### Re: Smallest Glider-gun. Sayab-Rule

Saka wrote:wildmyron posted this gun in a non-totalistic CA also containing only 2 cells
x = 1, y = 2, rule = B01c/S26o$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) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1409 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Smallest Glider-gun. Sayab-Rule 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 -jm jmgomez Posts: 43 Joined: October 6th, 2015, 1:42 am ### Re: Smallest Glider-gun. Sayab-Rule 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/#Cx = 2, y = 3, rule = B2cei3aekry4ciyz5ijkry6-cn/S1c2a3-air4akwyz5-cjr6cknbo$o$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 = MAPAMAgAAAAIAAAAAAAAAAAAAAAgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAAAAAAAAAAAAAAAAAAAo$o!

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

Two oscillators and a spaceship:
x = 20, y = 18, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek8bo$bo$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-ek82bo$2bo$2ob2o8$b3o2$2bo2$2bo$2bo!

Some c/3 and c/4 ships:
x = 112, y = 58, rule = B2cei3eq4qt5cy6n/S12an3acejy4ijn5jy6-ek82b3o7b3o11bo3bo3bo19bo19bo9bo13bo9bo$2bobo7bobo13bobobo21bo19bo9bo11bo2bo7bo2bo$3bo9bo14bo3bo62b2o2bo7bo2b2o$2bobo7bobo12b3ob3o17bo2bo2bo16bo9bo11bobo9bobo$3bo9bo14bo3bo16bo9bo12b2ob2o5b2ob2o10bo11bo$3bo9bo13bo5bo15b3o5b3o11b2obob2o3b2obob2o14bobo$2bobo7bobo57bobobo5bobobo12bobo3bobo$obo11bobo10bo5bo13b2obo7bob2o10bobobo5bobobo13bo2bo2bo$2bobob5obobo10bo4bo4bo11bo13bo11bobo7bobo16bobo$b2o11b2o10bo3bo3bo16bo5bo43bo3bo$3bobo5bobo13b2obob2o18bo3bo44b5o$3bo9bo14bo3bo16b2o3bo3b2o13b2o9b2o15b2ob2o$5bo2bo2bo16b5o16bo4bo4bo11b2o3bo5bo3b2o15bo$3b2o3bo3b2o14bo3bo16bo3b3o3bo11bo3bobo3bobo3bo13bobobo$3b3o5b3o13bob3obo14b2obo5bob2o11b2ob3obob3ob2o14bo3bo$5b2obob2o14bo3bo3bo14b2o7b2o19bo23bo$2b2o2bobobo2b2o10bo3b3o3bo36bobo3b3o3bobo15b3o$26b2o5b2o14bo9bo13bo11bo17bo$2b2o2b2ob2o2b2o10bo3b3o3bo11b3o9b3o15bo3bo$5bo5bo14b2obobob2o11b2o2bo7bo2b2o11bob2o3b2obo17b3o$6bo3bo16bobobobo15bo9bo14bobo5bobo17bobo$6bo3bo15bo3bo3bo13bo11bo12bo11bo14b2o3b2o$5bo2bo2bo17bobo42bo9bo15b2o3b2o$6bo3bo16bo5bo38bo13bo10bob2o5b2obo$8bo16b2o2bobo2b2o35b2o13b2o$8bo16bo2bo3bo2bo36bob2o7b2obo9bob2o7b2obo$6bo3bo15bo7bo38b2o9b2o11bo11bo$7b3o$6bobobo14b3o5b3o63bobo3bobo$8bo15bob2o5b2obo64bo3bo$22bobob2o5b2obobo60bo2bobo2bo$24bobo7bobo61bob2o3b2obo$23bo2bo7bo2bo62bo5bo$22bo15bo59bo9bo$26bo7bo63bo9bo$24bo11bo59b2o11b2o$23b2o11b2o58bo13bo$24bobo7bobo61b2o7b2o$25bo9bo60bobo9bobo$23b2ob2o5b2ob2o$23b5o5b5o$24bobo7bobo$22b7o3b7o$24b3o7b3o$23bobobo5bobobo$24bobo7bobo3$27bo5bo$26bo3bo3bo$27bo5bo$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)

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

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

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### Re: Smallest Glider-gun. Sayab-Rule

Thanks awesome!
Nices oscillators, tagalong and spaceships.

-jm
jmgomez

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