RFNERLGB2A (B2ac3q/S0[|1c|3ac])

[testitemqlstudop]

No the name is not "erlgebra." It stands for "replicator-free non-explosive rare linear-growth B2a."
This comes from a challenge from someone from the Discord server.

THIS RULE IS APGSEARCHABLE - http://gol.hatsya.co.uk/census/b2ac3qs0/C1
(Preferred haul size: around 500 soups)

THIS THREAD ALSO INCORPORATES DISCUSSION OF THE CLOSELY RELATED VARIANT B2ac3q/S01c AND B2ac3q/S03ac

The main spaceship is this 2c/2 (no speeds are known other than simplified c):

Code: Select all

x = 4, y = 4, rule = B2ac3q/S0
o$bobo$bobo$o!

There are a few intersesting reactions, primarily this: (gliders are transparent!)

Code: Select all

x = 37, y = 7, rule = B2ac3q/S0
$2bo15bo8bo$3bobo13bobo3bo$3bobo13bobo3bo$2bo15bo8bo!

A period doubler:

Code: Select all

x = 212, y = 14, rule = B2ac3q/S0
$198bo2$6bo15bo15bo15bo15bo15bo15bo15bo15bo15bo15bo15bo$7bobo13bobo13b
obo13bobo13bobo13bobo13bobo13bobo13bobo13bobo13bobo13bobo$7bobo13bobo
13bobo13bobo13bobo13bobo13bobo13bobo13bobo13bobo13bobo13bobo$6bo15bo
15bo15bo15bo15bo15bo15bo15bo15bo15bo15bo2$198bo!

What I believe to be the first natural ark in OCA (or isotropic CA, for the matter):

Code: Select all

x = 16, y = 16, rule = B2ac3q/S0
b2ob5o2b2obo$3o3b2ob2ob4o$b3obob3obob3o$o3b6ob2o$bo3bo2bo2bo2bo$ob2ob
7o3bo$bob6o3bo2bo$obo2b2o5bo$4o2bobo4b2o$bo4bob3o3bo$2b3o2bob3o2bo$ob
3o4b4o$4o2b5obo$5ob4o2b2o$b4o2bobo2bobo$7ob2o2bobo!

Most zz_linears on catagolue are also arks.

[Hunting]

You missed the Breps arks.

[testitemqlstudop]

*NATURAL arks.

[dani]

There have been many arks. E.g. the ones in 38life

Edit: they are natural. See the census.

[testitemqlstudop]

*NATURAL arks.

[Hunting]

*NATURAL arks.

B38/S23.

[testitemqlstudop]

Literally one that is powered by standard backward-shooting gliders, not 2G->2G transparency interactions.

Code: Select all

x = 16, y = 16, rule = B38/S23
2ob2o5b2obo$2bobo3b2o3bobo$6o4b5o$4bo2bo4b3o$2ob4o2bo3bo$ob2o2bo2bo$b
2obob3o2bob3o$obob2o3b3obo$3bob2obo3b2o$bobobobob3o2b2o$2bo3bo2b7o$3ob
ob2obobo2bo$2bobo2bob3o2b2o$2b2ob3obo3bo$3b3ob3o2b4o$6bo3b2o2b2o!

No one paying attention to the fact that this is a non-explosive apgsearchable B2a rule.

[Moosey]

I imagine there’s natural arks in that one other rule of mine.

Reflector:

Code: Select all

x = 11, y = 5, rule = B2ac3q/S0
bo$10bo$o7bo$8bo$10bo!

[Hunting]

No one paying attention to the fact that this is a non-explosive apgsearchable B2a rule.

That's not rare.

[Moosey]

Growing ship:

Code: Select all

x = 9, y = 12, rule = B2ac3q/S0
2bo$o$o2$8bo$o$o$8bo2$o$o$2bo!

Push:

Code: Select all

x = 35, y = 11, rule = B2ac3q/S0
34bo$32bo$o7bo23bo$26bo7bo$10bo13bo$8bo15bo$8bo17bo$10bo9bo$18bo$18bo$
20bo!

nobody is paying attention to the fact that this is an apgsearchable B2a rule.

that’s not rare

True.

Code: Select all

x = 109, y = 68, rule = B2ac3q/S01c
27b4obob3o5b2o4b2obob2o2b4o2bobob3o2bo3bo4b2o2b2ob5o6bo2bob3obo$28bob
3obo4bo2bob2obob5obobob4obob3o7b8ob3o2b2obo2b2o2bobo2bo2bo$28bo4bobobo
3b2ob2obobobobo8b3o2b2obob2o3b3o2b2o2bo3b6obob4obo2b2o$27bo4b4ob2o2bob
2o2b5ob3o5bobobobobo3b2o4bobob3o2bob4o8b6o$30b4obob4o2b5o2b3ob2obo6b2o
bo4bo2bobo3bo3bobob3o2b3o3b4obo2bo$27b5ob2ob5o2b3obobo2bo7bob2obo3b2o
5b4obob2o4bobobob3o3b3obob2o$27bo2bob3o2b2ob9o3b2o2bo2bo2bo3bo3b2o4b2o
2bo8bo7b2ob2o2bobobo$27bo3bob6o3b4o2b3ob2obo3bo4b3ob2ob3ob2ob2obob2obo
bo3b2ob2o2bobo2b5o$29bo4bo2bo3b2ob4o6b4o4bo4b3obobobo2b2o11bobobobo3bo
3b4o$27bobob3obobobo2bo2bob3obob3o2bo4b5o2bo8b4ob4o2b2o2bo4b2ob2o3b2o$
29bo4bo2b2o5bo2b3o2b2obo2b5ob6o6bobo3bob5o3bobobob2o2bobob3o$28bo2b7ob
2o3bob2ob4o2b2ob5obo4bobo3bo2b3o4b3o2b2o5bo2bo3bo3bo$28b2obobobob3ob2o
bobob6obobob5o3bo2bob2o2b2o4bo3bobobobobobo11bo$28bo2b2o2bob2obob2obob
3ob2o2bobob2ob4ob2obo5bo3b2o2bobob2ob3o6b2ob3o$28b3o2bobo2bo2b3ob2obob
5o2b2o2bo6b3o3b6o2bo3b2ob2o2b2ob2ob5ob2obo$27bob2o2b5o4b2ob3obob2obob
3o2bob3o3bob2o4bob5ob3obo3bob6obobo2bo$27b2obo2bob2obo2b2obobob2o2bobo
bo3b2o3bob4obo3bo3bob2ob2ob3o2bo2bo2b2obo3bo$27b5o2bobobo2b2o2b4obo3b
2o3bob2o3bo6bobob2ob2ob4o2bob2ob2obo5bobo$28b2obo2b6obobob4o4b3o2b2ob
2obo3bob2o5bobo6b2ob4ob3o7b2obo$30bobobo5bobob2obo6bo2bo4b4o3bo6b2o2bo
bobo4b4ob2ob4ob4o$27b3o3b7ob2o3b4obo3b3obob3o5b3obo2bo2bo3bo2bobo4b4ob
o2bo2bob2o$28bo2b2o2b3o5bobo9b2o3bob3o3b2obob2o5b2o3b2ob4o5bobob2obob
2o$27bo3bobo3b5obo2b5obo2b2obo2b2o3bo3bob4ob4obo2b3o2bobob2o3bo2b3obob
o$28b2obob3o5bo3bo2b2o3b2obo2bobo2b3obob3o2b2o4bo3bo2b2o3b3o2b4o3b2obo
$28bobob4o2b5obob3obob2ob2o4bo4bobob2ob2o3bobob4ob5ob5obobo2b3o$31b2ob
ob2o2bo2b2o3bo2b2o2b3o5b3o2b7o2b2obo2bob6o2b2obobob2o3b2obo$29bobo2b3o
2bo2bobobo4b3obob2o3b2o6b2o2bo4b3o2b2obo2bob4o3bob2ob4o$27bo2bob2obob
2o2b2o2bo2b2obo3bo3bo2b2obo2b2o3b2ob2o2b10o2bob3obob2o3b2o$27b2obo2bob
3ob3o5bo3bobobob2ob3o3bo2b7ob2o6b2o2bo3b4obo4b2ob2o$27b2obob6obo5b2ob
2obob3obobobo3b2ob3obo2b2o2b2o5bo2bob3ob5obo5bo$31b3obo2bo3bob4ob7o2bo
b2ob3ob4ob2o2bob4o3bobo4b6obobo4b2o$27bo3bob3o6b4o4b2o7bo4b2obo2bo2bo
2b2o2b2obob2o3b2obo2bobobo2bobo2bo$29b3ob2o3bob13o3bobo6bobo3b2o4bo8bo
bobob2ob2obob2ob3ob2o$27bob2o2b2obo2bob4ob2o2b3ob2obo3bob3obo5b5o2bo3b
4o4b4o4b3ob2obo$28b2o2bobob2o2b3obo2bo2b6ob5ob2obob3o3b3o5b3o2b4o2b2ob
6ob2o2bo$27b2o2bobo6b5o2bo2bo4bobobobo2bo2bo3b2o2bobob3obob5obo2bob2o
6bob2o$27b2o2bobob2o2b2o2bob2ob8ob2o2bob2ob4obo2bo2bob3o2b6obob2o2b2o
2b2obob3o$b2o24b6o2b2obob4obo6b2ob2ob3ob4ob3o2b7obob2o2bo3b5o2bo2bo3bo
b2o$29b2ob3o2b3o2bo2b4ob2o3bo6bobo2bo2b2ob2ob3obo3b2ob2o3bo2bo2b3o3b2o
2bo$o2bo23b2obobo2bobo2bo2bobob7ob3o4b2o8b6o3bob4o4b2o2bo2b2o3b3o$27b
5obob3ob7obo2bob2obobo2b3obobobobob4ob7o2b4o6bobobo4bobo$29bo2bob2o2bo
2bo2bo2bob2o2b3o2bo2bob4obobobobob4ob3obobo4bob4o2bo2bobob2o$29b5obo3b
ob2o2bobo2b3ob3ob2o2b2obob7o2bo4b2obob2ob5obo2bo4bo3b2o$27b2obo2b3obob
2obob3o2bobob2ob3o2bob2o3b3obobo2b2obob3o6b4o4bo3b2o$28b4o3b3obo4b2o2b
2obo2b2o5b3o10bo2b2obob2o3b2obobo2b2ob2o4bo$30b6o3b2ob2o3bobob2o5b3o6b
3ob2ob5ob3o2b2o3bo2bob4o2b3o2bo$33bob2ob3o3b3o2b2o2bob5o5bob6o3bobob2o
3b3o3bob4obobob2ob4o$27b2obo2b2o3bobo3bob3o2bob3o2b3o2b2o2bo2bo2b2o2bo
b2obobo2b2obo2b2ob3ob4o2bobo$29bo2b3ob2obo2bo2bob2ob2o6b2o6bob2obobobo
3b2o2b2o2bo3bo2bo3b3o3bo2b2o$27bo9b3obo2b3obob2o5b3ob5ob2o2b2obo2b3o2b
o4bo2bob6o2bo3b2o$27b4obo3bob2obobob2o2bo2b2o2b3o2bobobobob2obob2ob2ob
o2bo8b3ob2obobo2bob2o$27b7o2b2o2b3obob3obob2o3b2obobo5b6o2bo2bob2ob2o
4bo2bobob3o2b2obobo$27bo2bo3b3ob2o2bobob2obo2bob2o5b3o2b3o2bob6obo2b4o
bobobo6bobo2bo3bo$28bo2bo2bo5bobo3b3ob3ob2o3b3ob3ob2o4bob2ob2o5bobo2bo
3b2o3b2o3bo$29b3obobobob3o2b4ob2obobobo3bo4b3o2bobob2ob2o4b2o6bob3o2b
2o2b2o3b2o$30b2obobobo5bo2b2ob2obo3b4o2bob2o2bob2ob3ob2obobobo2b4obobo
2bobobobobo2bo$27bob2o5b5ob3o4bob2ob2ob3o4bo2bo2bobo2b2o2b2o4b2o3b2ob
3obo3b2ob5o$27bobobo3bo3bobobo2b3o6bo3bobobo3bo2b2o4b2o2bo3bobob6o3b2o
b5o3bo$27bobo4b3obob3ob4ob3obo2bo2b5ob2ob2ob3o2bo4b3obo3bo2b2o3bo4b5ob
o$31bob3ob3obobobob2o3bob2o4b3obo6b4o2b6o5b2o3b2o2b3o4bob2o$27bobo6bo
3b2ob3o3b3o2bobobob2obob2o2bob6o6bob2obo3b2ob7obo4bo$30b2o2bo3bobo3bo
3b3o2b2o4bo3b2o3bo3b4o2bo3bo3b4o2b2o2b2o5b2obo$27bob3o5b2ob2o2b2o3bo4b
2ob2ob3o4bo4b3obo2bob7o6bob2obobo2b3obo$27bob6o2b3ob2obob2ob5obob4o2b
3o2bo3b2obo2bo4b2ob2obo2bo3b2o2b3o2bob2o$30b2o3b3ob2o3b4ob2ob3obobob4o
2bo2b5ob4o2b4o6b4o3bo2b3o4bo$27bo3b4o3b2o2bo3bo4b3o3bo6bob2o2bo6bobo3b
4o2bob2obob5obo2b2obo$27bob8obob2o2b4o2bo2bobo3b2o2bobo2bo5b2obo2b2ob
8ob3o3b2ob4o2b2o$27b2obob3o4b7ob4o2b2o2b2o4bo3b2o3bobob2obob7ob3o2bobo
5bo2bobo!

Should we discuss this relative as well? It seems to have more catalyst potential.

Code: Select all

x = 11, y = 17, rule = B2ac3q/S01c
4bo$6bo$o$2bo$2bo$o7$o$2bo$2bo7bo$o$9bo!

Switch

Code: Select all

x = 31, y = 8, rule = B2ac3q/S01c
3bo17bo$12bo7bo9bo$10bo17bo$bo8bo8bo8bo$o11bo5bo11bo2$5bo17bo$3bo17bo!

[dani]

Is this the first gun? p12 photon shooter in S1c

Code: Select all

x = 16, y = 10, rule = B2ac3q/S01c
15bo$14bo$2bo$o$12bo$12bo$o$2bo$14bo$15bo!

[Moosey]

Is this the first gun? p12 photon shooter in S1c

Code: Select all

x = 16, y = 10, rule = B2ac3q/S01c
15bo$14bo$2bo$o$12bo$12bo$o$2bo$14bo$15bo!

Yes

[testitemqlstudop]

The 180-degree reflector also works in the original rule:

Code: Select all

x = 7, y = 5, rule = B2ac3q/S0
o$2bo$2bo3bo$o$5bo!

Backrake in relative:

Code: Select all

x = 19, y = 10, rule = B2ac3q/S01c
2$3bo12bo$2bobo10bobo$3bo12bo$4b2o3b2o3b2o2$4b2o3b2o3b2o!

I, too, think the 1c relative is both more apgsearchable (less YL from what I've saw, manually experimenting) and more engineerable (there's only one still life in S0, but there's multiple in S01c.)

EDIT: Sadly the 1c relative doesn't have the same glider transparency.

[2718281828]

two ships, and two push reactions:

Code: Select all

x = 125, y = 124, rule = B2ac3q/S0
6$84bo4bo20bo4bo$109bobo2bobo3$81b2o8b2o$86b2o19b2o8b2o$80bo2bo6bo2bo$
85bo2bo17bo2bo6bo2bo2$81b2o8b2o$110b2o2b2o$80bo2bo6bo2bo$109bo6bo2$81b
2o8b2o$86b2o19b2o8b2o$81b2o8b2o$80bo2bo2b2o2bo2bo12bo2bo6bo2bo$85bo2bo
$81b2o8b2o$110b2o2b2o$81b2o8b2o$80bo2bo6bo2bo15bo6bo2$81b2o8b2o$86b2o
19b2o8b2o$80bo2bo6bo2bo$85bo2bo17bo2bo6bo2bo2$81b2o8b2o$110b2o2b2o$80b
o2bo6bo2bo$109bo6bo2$81b2o8b2o$86b2o19b2o8b2o$81b2o8b2o$80bo2bo2b2o2bo
2bo12bo2bo6bo2bo$85bo2bo$81b2o8b2o$110b2o2b2o$81b2o8b2o$80bo2bo6bo2bo
15bo6bo2$81b2o8b2o$86b2o19b2o8b2o$80bo2bo6bo2bo$85bo2bo17bo2bo6bo2bo2$
81b2o8b2o$110b2o2b2o$80bo2bo6bo2bo$109bo6bo2$22b2o13bo4bo13bo4bo19b2o
8b2o$5b2o2b2o7b2o66b2o19b2o8b2o$22b2o29b2o8b2o16b2o8b2o$4bo6bo6b2o4bo
9b2o8b2o34bo2bo2b2o2bo2bo12bo2bo6bo2bo$17bo4bo16b2o12b2o8b2o20bo2bo$
19bo14b2o8b2o6bo2bo6bo2bo15b2o8b2o$33bo2bo2b2o2bo2bo63b2o2b2o$21bo16bo
2bo14b2o2b2o19b2o8b2o$34b2o8b2o34bo2bo6bo2bo15bo6bo$56b2o2b2o$34b2o8b
2o9bo6bo18b2o8b2o$33bo2bo6bo2bo39b2o19b2o8b2o$80bo2bo6bo2bo$85bo2bo17b
o2bo6bo2bo2$81b2o8b2o$110b2o2b2o$80bo2bo6bo2bo$109bo6bo2$81b2o8b2o$86b
2o19b2o8b2o$81b2o8b2o$80bo2bo2b2o2bo2bo12bo2bo6bo2bo$85bo2bo$81b2o8b2o
$110b2o2b2o$81b2o8b2o$80bo2bo6bo2bo15bo6bo2$81b2o8b2o$86b2o19b2o8b2o$
80bo2bo6bo2bo$85bo2bo17bo2bo6bo2bo2$81b2o8b2o$110b2o2b2o$80bo2bo6bo2bo
$109bo6bo2$81b2o8b2o$86b2o19b2o8b2o$81b2o8b2o$80bo2bo2b2o2bo2bo12bo2bo
6bo2bo$85bo2bo$81b2o8b2o$110b2o2b2o$81b2o8b2o$80bo2bo6bo2bo15bo6bo2$
81b2o8b2o$86b2o$80bo2bo6bo2bo$85bo2bo2$81b2o8b2o2$80bo2bo6bo2bo!

[Moosey]

two ships, and two push reactions:

Code: Select all

snip

Enumerating ships might be a mistake.
There is certainly an infinite amount of ships.

Code: Select all

x = 12, y = 8, rule = B2ac3q/S01c
3bo$bo7bobo$bo4bo3bo$9bobo$2bo$o$o$2bo!

Code: Select all

x = 15, y = 15, rule = B2ac3q/S01c
12bobo$10bo$10bo$2bo9bobo$o$o4$o$o$2bo9bobo$10bo$10bo$12bobo!

There is also almost certainly an infinite amount of visibly distinct ships.
EDIT:

Code: Select all

x = 16, y = 4, rule = B2ac3q/S01c
o14bo$2bo10bo$2bo10bo$o14bo!

[testitemqlstudop]

Good point. I'm using ntgfind to search for c/3 ships because ntzfind is being absurd with 2a rules:

Code: Select all

$ ./ntzfind B2ac3q/S01c p3 k1 w9 v
ntzfind 3.0 by "zdr", Matthias Merzenich, Aidan Pierce, and Tomas Rokicki, 24 February 2018
- ./ntzfind B2ac3q/S01c p3 k1 w9 v
Rule: B2ac3q/S01c
Period: 3
Offset: 1
Width:  9
Symmetry: even
Depth limit: 2000
Stop search if a ship is found.
Starting search
Length: -6
Search complete: 0 spaceships found.
Calculations: 28
CPU time: 0.006035 seconds

Umm... Length -6?

[testitemqlstudop]

Four-barreled gun in explosive relative: (this is the reason it's explosive, actually)

Code: Select all

x = 4, y = 4, rule = B2ac3q/S045678
b2o$4o$4o$b2o!

[Hdjensofjfnen]

Holy heck, I've been waiting for a rule like this for ages! (EDIT: Not that rare, but it's only four transitions.)
EDIT: I suppose this dot tagalong on Catagolue deserves some recognition as the second-smallest orthogonal ship:

Code: Select all

x = 6, y = 4, rule = B2ac3q/S0
obo$3bobo$3bobo$2bo!

EDIT:

Four-barreled gun in explosive relative: (this is the reason it's explosive, actually)

Code: Select all

x = 4, y = 4, rule = B2ac3q/S045678
b2o$4o$4o$b2o!

+1 dot = absolute chaos. In LifeViewer, due to the bounds of the universe, it stabilizes after about 2^14 generations.

Code: Select all

x = 6, y = 4, rule = B2ac3q/S045678
b2o$4obo$4o$b2o!

[Hunting]

This rule is interesting, anyway!

Since nobody have made a G+dot tabulation, I'll make one:

Code: Select all

x = 25, y = 10, rule = B2ac3q/S0
bo2bo6bo2bo6bo2bo2$2b2o8b2o8b2o7$o10bo10bo!

Yeah, only three option. But those three reaction shows three different effect:
1. Move
2. Destruct
3. Duplicate

EDIT: And for S1c, too. Some are dirty.

Code: Select all

x = 118, y = 11, rule = B2ac3q/S01c
2bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo2bo6bo
2bo2$3b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o8b2o7$o10bo10bo10bo6b
o10bo10bo10bo10bo10bo10bo10bo$39bo10bo10bo10bo10bo10bo10bo10bo!

So we got a stable eater:

Code: Select all

x = 4, y = 11, rule = B2ac3q/S01c
o2bo2$b2o7$bo$o!

Along with a near-miss 180-degree stable reflector:

Code: Select all

x = 4, y = 11, rule = B2ac3q/S01c
o2bo2$b2o7$3bo$2bo!

I think this rule is as engineerable as Dominoplex.

[testitemqlstudop]

There's this (catagolue):

Code: Select all

x = 16, y = 4, rule = B2ac3q/S0
2bo$obo12bo2$bo12bo!

[Hunting]

Snowflakes has 2G transparent reaction...

[testitemqlstudop]

1) What is your point?
2) Cleanliness?
3) Ark formation?

Spaceship formed by puffer whose exhaust deletes its ash:

Code: Select all

x = 16, y = 16, rule = B2ac3q/S0
boobboobboobboob$
oboobbbbbbbboboo$
oobbbobbboobbbbo$
bobbbbooobbbbbob$
obbooobooooboobb$
ooobbobooboobobo$
obobbobboobbbobb$
bbbboobbbboooobo$
bboobbbobbbobbbo$
booobbobboobbbbo$
oooobobbbobooobo$
oobbbobbbboboboo$
bbbbbboobbobbobo$
obooboobbooobbbb$
obboobobobbbobbo$
bbbooboobbooboob!

[testitemqlstudop]

Another even more apgsearchable rule with less infinite growth, less rakes, and much less arks:

B2ac3q/S03ac

Discounting YL recognition, the speed is above 90 soups/second on a 4-core computer.

[LaundryPizza03]

No the name is not "erlgebra." It stands for "replicator-free non-explosive rare linear-growth B2a."
This comes from a challenge from someone from the Discord server.

THIS RULE IS APGSEARCHABLE - http://gol.hatsya.co.uk/census/b2ac3qs0/C1
(Preferred haul size: around 500 soups)

Thanks. I discovered the rule a while ago and tried to apgsearch it, but I guess I didn't wait long enough.