B2-m3-o/S2m3-p4-m5H

[Pavgran]

I decided to explore hexagonal neighborhood a bit because it is more symmetrical than Moore neighborhood (which has differently-behaved sides and corners), and more visually pleasing (for me) than von Neumann neighborhood. I soon discovered that totalistic rulespace is too small (7 raw bits for birth and survival), so I decided to look for isotropic non-totalistic, which has 13 raw bits for birth and survival. I've searched for somewhat life-like behavior: non-explosive, with spaceships from ash, with moving chaotic objects, with stable ash.

After a bit of transition-tailoring, I've found this rule: B2-m3-o/S2m3-p4-m5H
It doesn't have stable ash, but it does have p2 ash, so this is fine.
It has a lot less activity than CGoL, but it does contain some chaotic patterns that can persist for quite a long time (compared to everything else).
Examples:

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x = 32, y = 32, rule = B2-m3-o/S2m3-p4-m5H
2obo2b4o3bo3bo3b8ob2o$2bob3o3b10obobo5bo$4b2o2b3o4b3o4bo3b3o2bo$2bob2o
bo2bobob2obo2b7obobo$2o2bob3obobo3b2o3b2o2bobo$bob3ob3o3bo2b2o3bo3b3o
2b2o$3obo2b4ob3o2bo2b2ob3ob5o$b2obo2b6o2b3o2bo3b3obo2bo$bobob10obobo7b
3o$2ob2o2b3o2bo3b2obob5ob3o$3ob2o2bo2bo2bob3obo4bob4o$bob2ob5o2b2obob
2o5b2ob2o$o10bobob4obo2bo4bo$4b2ob2o2b3o5b3o2bo2b2o2bo$3o2b5o3b2obo2b
2ob2obobo$ob2o2bobob2obo6b2obobo2bob2o$2bo4bobo2bo5bo2bo5bobobo$b2o2bo
bo3b2obo7b2o3bob3o$bo2bo2b2o2bo2bobob2o7bobo$bobo3b2o2b2obobob2o2bob4o
bo$obobo2bobo3bo3bobo2b2obo3bo$b2obobob3obobo3bobobobo2bo2bo$5b2o2b2o
2b2ob2o5b2o6bo$4bo2bo4bobo4bo8bo2bo$2ob3o2bobob2o5bo4b2obo$obo2bob3obo
b2o6b9o$bobo2b3o2bobo3b4o3bo2bob3o$3bo2b2obob6o2bo4b2o2bobo$2o2bo2bobo
b3obob3ob2o3bob4o$b2o4bob5o3b3o3bo4b4o$o3bob3o4b2o2b2ob3o2b4ob2o$2o2bo
b7obob2o2bo2bobo3bobo!

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x = 32, y = 32, rule = B2-m3-o/S2m3-p4-m5H
b2obobo5b3o2b2o5bobo3b2o$bo2b5o2bobo2b3obob2obob2obo$ob3o3b3o2b2o3b2ob
o2b2o2bobo$b3o5bobobob3o3b2obobo2bo$bo2bo2b2obobob4o2bob3ob3ob2o$b2obo
4bob3obobo2b2ob3o3bo$3bo5bob2obob2o4bob2o3bo$2b2ob3ob3o4bo2b3o4bo2b2o$
ob4o2bo4bo3bo5b4o4bo$2bo5bobob2obob3o2b2ob4o2bo$3obo3bo4b2ob3o3bob5o2b
o$bo2b2o3bobo3bobobo2bobo2b2obo$obo3b2ob3ob2o3bobo2bo2bo2b2o$2obo2b2o
8b2obo2bo2b2o2b3o$obobob2ob4o2b2ob8ob2obo$4b2o3bo2bo2bo3b2o2b2ob2ob3o$
bo2bo3bob2o2b2o2bobo2bob4o$2bo4bo3b3o2b4o2b2o3bo2b2o$o2bo5b3ob2obo3bo
5bo4bo$2ob2ob2o6bob3obobo3bo3b2o$3obob2ob3o2b2o2b2o3bo5bobo$2ob2o2b2o
4b2o2b2obo4bo2bob2o$2o4bo2b7o3b3o2b4o$5b2o2b2o6bo2bob2ob7o$o2b2obobob
2obobob3o2bo2b5obo$b2obo2bobob4o2b2ob2o2b4obobo$4bo3b6obo3b3o4bobo2bo$
o2b2o6b4ob2o2b2obo2b4obo$o2b3o3bo4b5ob3ob2obobobo$3bobob2obob2obob2o2b
2obo5bo$3bobob2o2b2o2b2o2bo2bobobob2obo$bo2b2o3bo2bob5o2bo5bobo!

There are also a few interesting glider interactions.
Glider reflections:

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x = 598, y = 34, rule = B2-m3-o/S2m3-p4-m5H
302bo89bo$303bo89bo$202bo100bo89bo$94bo108bo99bo89bo$o94bo107bo99bo89b
o$bo93bo107bo277bo91bo$bo93bo107bo278bo91bo$bo93bo386bo91bo$bo480bo91b
o$482bo91bo15$356b3o82b3o$355b2o83b2o151b3o$358b2o83b2o151b2o$258b3o
333b2o$257b2o$152b3o105b2o265b3o$55b2o94b2o373b2o$55bo98b2o373b2o$55bo
$55bo!

Explosions:

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x = 508, y = 32, rule = B2-m3-o/S2m3-p4-m5H
o$bo$bo134bo$bo135bo$bo135bo179bo$137bo180bo$137bo180bo149bo$318bo150b
o$318bo150bo$469bo$469bo10$12b4o$16bo2$14bo3$190b4o$190bo161b3o$351b2o
$354b2o148b3o$503b2o$506b2o!

Most of the 2-glider collisions just vanish or create a small p2. A few happen to destroy one of the gliders.
I've not tried to search sparky oscillators or other things. I feel like if these things are found, the rule will be turing-complete.

Is anyone interested in exploring that rule or close relatives? Looks like B2o3-o/S2m part is responsible for a glider, and S3m4p5 part is responsible for keeping structures active for a longer time.

[dani]

Cool rule. I will search overnight. Here's a table I hacked together:

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@RULE B2-m3-o_S2m3-p4-m5H
@TABLE
n_states:2
neighborhood:hexagonal
symmetries:rotate6reflect
var a = {0, 1}
var b = a
var c = a
var d = a
var e = a
var f = a
0,1,1,0,0,0,0,1
0,1,0,0,1,0,0,1
0,1,0,1,1,0,0,1
0,1,0,1,0,1,0,1
1,1,0,1,0,0,0,1
1,1,1,1,0,0,0,1
1,1,0,1,1,0,0,1
1,1,1,1,1,0,0,1
1,1,1,0,1,1,0,1
1,1,1,1,1,1,0,1
1,a,b,c,d,e,f,0

p5 oscillator:

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x = 5, y = 5, rule = B2-m3-o_S2m3-p4-m5H
3o$3o2$4bo$3bo!

p20 sparky spaceship:

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x = 21, y = 8, rule = B2-m3-o_S2m3-p4-m5H
17bo$17bo$16b2o$o5b4o6b3o$obo2bobo2bo8bo$o2b3obobo8b3o$o18b2o$bo17bo!

Wickstrecher:

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x = 7, y = 9, rule = B2-m3-o_S2m3-p4-m5H
2o$o$o$o$3b2o$4bobo$5b2o$6bo$6bo!

Will post soup results later.

EDIT: 18c/64 engine:

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x = 14, y = 43, rule = B2-m3-o_S2m3-p4-m5H
4b2o$4bobo$10o$3obo3bobo$b2ob8o$2bobobobob3o$3b10o$4bobobobo$3b10o$4bo
bobobo$4b6o$4bobobo$2b10o$2bobo3bobobo$3b11o$4bobobobobo$3b11o$4bobo3b
obo$4b10o$4bobobobobo$3b4ob6o$4bobobobobo$2b12o$2bobobobobobo$3b11o$4b
obobobobo$4b2ob7o$4bobobobobo$3b11o$4bobobo3bo$2b12o$2bobobobobobo$2b
12o$2b3obobobobo$3b11o$6bobobobo$4b4ob5o$4b3obobo$5b9o$6bobo$7b3o3bo$
8b3o$9bo!

[dani]

105285M:

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x = 16, y = 16, rule = B2-m3-o/S2m3-p4-m5H
boboobooobobbooo$
booobbbbbobobooo$
booooboobooobboo$
boboobboooobobbb$
obboobbobbbobbbb$
oooobbbobbboobbb$
bbbboboobooobbbb$
boboobbobobbboob$
bboooobbobbobooo$
bobboboobobobobb$
bbobbbbboooobooo$
ooooooboobbbobbo$
oboobobbbbbobbbb$
bboobobobooooobb$
oobooobobbobbooo$
oooboboobboobooo!

I've also found a few ways to eat gliders:

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x = 73, y = 7, rule = B2-m3-o_S2m3-p4-m5H
2bo19bo27bo11bo$3bo19bo18bo20bo$o2bo7bo8bo2bo19bo6bobo7bo2bo$3bo6b2o
11bo16bo2bo19bo6bobo$3bo19bo19bo19bo$32bo10bo28bo$31b2o!

One time reflector:

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x = 12, y = 5, rule = B2-m3-o_S2m3-p4-m5H
2bo$3bo$o2bo$3bo7bo$3bo6b2o!

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x = 13, y = 8, rule = B2-m3-o_S2m3-p4-m5H
2bo$3bo$o2bo$3bo$3bo$10bo2$10bobo!

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x = 13, y = 8, rule = B2-m3-o_S2m3-p4-m5H
10bobo2$12bo$2bo$3bo$o2bo$3bo$3bo!

One time duplicator:

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x = 12, y = 5, rule = B2-m3-o_S2m3-p4-m5H
2bo$3bo6bo$o2bo7bo$3bo7bo$3bo!

There's a bunch of stuff on catagolue like a p9 and p21, but I haven't found a way to do anything with it.

[Pavgran]

Thank you for searching!
I've tried to launch a search myself, but it didn't work. After seeing that you successfully searched with the same versions of apgmera and lifelib as mine, I tried to compile and search again, and it worked. I don't know what that was. Anyway, I'm going to search something as well.

There are quite a few soups which have this unstable 18c/64 chaotically walking around and spawning it's copies which sometimes die and sometimes continue exploring. One notable example is:

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x = 16, y = 16, rule = B2-m3-o/S2m3-p4-m5H
oobooobobboboooo$
bbboboobbooobobo$
bobobboooooboooo$
obbobbbboobbobob$
bbbobbboobbbobbb$
obbbbbbooobboobo$
boboboobooooobob$
bobbobobboooobbb$
oobobbbobobbbbob$
booboboooooobbbb$
obobobbobobbbboo$
oobboobbbbbbboob$
booobboobbbboobo$
oobbooobbbbobobb$
bbbboooobooboooo$
bbbbboobbbobbboo!

I find that behavior amusing and I'm hoping there is a way to control it in some way, somewhat like herschel circuitry. Unfortunately, it leaves a lot of ash and it's not clear how one would clear it. Maybe there is a related rule with another transitions that allows for the same behavior but in more controlled way. I'll try to explore it a bit.

There's a bunch of stuff on catagolue like a p9 and p21, but I haven't found a way to do anything with it.

I also tried to make p21's interact, but also couldn't find anything useful. A glider gun would be a gem.

[Pavgran]

Stable c/2 puffer (period 272):

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x = 34, y = 28, rule = B2-m3-o/S2m3-p4-m5H
3$19bo$18b2obo$12bo4b7o$12b2o3bobobobo$6bo6b2ob9o$7b7o3bobobob2o$7b7ob
ob8o2$8b7obob8o$9b7o3bobobob2o$9bo6b2ob9o$16b2o3bobobobo$17bo4b7o$24b
2obo$26bo!

Edit:
Smaller unstable c/2 puffer:

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x = 13, y = 11, rule = B2-m3-o/S2m3-p4-m5H
2o$2bo$2bo$3b2o2bo$3b2ob3o$7b5o$4bobobob3o$4b9o$5bo2bobobo$5bobob4o$9b
o!

[Naszvadi]

Is there an official golly version that supports isotropic non-totalistic hexagonal rules? If not, would someone provide a correspoding MAP or ruletable - preferably for all such hexagonal 2-state isotropic rules? Thanks in advance!

[APPEND #1]
Widely known, but still worth mentioning one pioneer among the hexagonal rule investigators (pcallahan ../forums/memberlist.php?mode=viewprofile&u=1099 ):
http://www.mirekw.com/ca/files/hexrule.txt

[Naszvadi]

Push and delay collision:

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x = 41, y = 18, rule = B2-m3-o_S2m3-p4-m5H
6$34bo$32bob2o$35b2o$33bo2bo$4bo$5bo$2bo2bo$5bo$5bo!

[APPEND#1]
Push and delay + shift path collision:

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x = 37, y = 10, rule = B2-m3-o_S2m3-p4-m5H
34bo$32bob2o$35b2o$33bo2bo2$2bo$3bo$o2bo$3bo$3bo!

[wildmyron]

Very interesting hexagonal rule. I particularly like the honeycomb structures that exist without making the rule explosive.

Is there an official golly version that supports isotropic non-totalistic hexagonal rules?

Unfortunately not.

If not, would someone provide a correspoding MAP or ruletable - preferably for all such hexagonal 2-state isotropic rules? Thanks in advance!

Dani provided a rule table above.

Here's a script to calculate corresponding MAP rules:
https://conwaylife.com/forums/viewtopic ... 715#p55715

[Pavgran]

I've apgsearched this rule a lot. Looks like there are no useful natural oscillators. And linear growth is a little bit too common for my taste. But I think there's either this or no long-enough-lasting chaos at all for hexagonal rules.

Anyway, here's a small seed for a c/2 puffer with interesting interaction in the unstable ash and time to stabilization of about 60k.

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x = 13, y = 8, rule = B2-m3-o/S2m3-p4-m5H
4bo$4bo$4bo5bo$5bo4b2o$5b3o2b2o$obo3b3ob2o$6bob4o$2bo8b2o!

[Naszvadi]

Eater p2 oscillator on the left, the same p2's removal on the right:

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x = 79, y = 75, rule = B2-m3-o_S2m3-p4-m5H
14$7bo$7bo$6bobo$6bobo12bo49bo$8bo12b2o48b2o$58bo$58bo$57bobo$57bobo$
59bo$6bo$7bo$5bo2bo$9bo11bo49bo$9bo11b2o48b2o$57bo$58bo$56bo2bo$60bo$
60bo$7bo$6bobo$7bobo$9bo11bo49bo$10bo10b2o48b2o$58bo$57bobo$58bobo$60b
o$61bo$8bo$9bo$6bo2bo$9bo11bo49bo$9bo11b2o48b2o$59bo$60bo$57bo2bo$60bo
$60bo$9bo$9bo$8bobo$8bobo10bo49bo$10bo10b2o48b2o$60bo$60bo$59bobo$59bo
bo$61bo!

[confocaloid]

16 (pseudo-)symmetries are now apgsearched: census/b2-m3-os2m3-p4-m5h
In particular, searching in 1x256 yields branchy p2 phoenices like these:

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x = 46, y = 20, rule = B2-m3-o/S2m3-p4-m5H
28bobo2$3bo22bo3bo$3b2o$26bobobo$2o2bo$bobo28bo$5bo$7bobobobo20bo$6bo
6b2o20bo2$6bo30bobobobobo2$6bo30bo7bo2$6b2o29bo$7bo$37bo2$37bobo!