B2ein3aikq67e/S1c23-nqr4ci6ci

[googleplex]

This rule has a family of table-based c/2 ships with Tagalongs. It also has naturally-occurring oscillators up to p8, and a very sparky p28. also, it has 2 naturally occurring puffers.

[77topaz]

Small, natural p28 oscillator:

Code: Select all

x = 17, y = 6, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
$3b2o2bo$2b2o2bo2bo$3b2o2bo!

A few small, natural spaceships (c/3 diagonal, c/2 orthogonal (x2), c/13 diagonal):

Code: Select all

x = 27, y = 4, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
24bo$obo14bo5b2o$bo5bo2bo4bo2bo7bo$2bo4b4o4b4o6b2o!

[googleplex]

The table is a ship in this rule, and it has many tagalongs:

Code: Select all

x = 13, y = 6, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
5b2o$4bo2bobo$4bo5bo$7bo$3o8b2o$o9bobo!

[googleplex]

A very sparky p16:

Code: Select all

x = 7, y = 5, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2b3o$o5bo$bo3bo$o5bo$2b3o!

Reflector, anyone?

[77topaz]

A very sparky p16:

Code: Select all

x = 7, y = 5, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2b3o$o5bo$bo3bo$o5bo$2b3o!

Reflector, anyone?

p16 converts c/3 diagonal to a block that interacts with the p16 without destroying it:

Code: Select all

x = 19, y = 9, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
16bobo$17bo$18bo2$2b3o$o5bo$bo3bo$o5bo$2b3o!

p16 converts c/2 orthogonal to a block that interacts with the p16 without destroying it:

Code: Select all

x = 19, y = 5, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2b3o12b2o$o5bo10bo$bo3bo11bo$o5bo10b2o$2b3o!

Ibid:

Code: Select all

x = 19, y = 9, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
17b2o$17bo$17bo$17b2o$2b3o$o5bo$bo3bo$o5bo$2b3o!

p16 shifts c/3 diagonal by one half-diagonal:

Code: Select all

x = 19, y = 5, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2b3o$o5bo9bobo$bo3bo11bo$o5bo11bo$2b3o!

c/2 orthogonal converts p16 to p28:

Code: Select all

x = 21, y = 10, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
19b2o$19bo$19bo$19b2o2$2b3o$o5bo$bo3bo$o5bo$2b3o!

p16 + c/2 orthogonal -> block + c/3 diagonal:

Code: Select all

x = 15, y = 11, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
13b2o$13bo$13bo$13b2o3$2b3o$o5bo$bo3bo$o5bo$2b3o!

[googleplex]

A natural puffer!:

Code: Select all

x = 14, y = 3, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
5b3o$o2bobobobo2bo$4ob3ob4o!

[googleplex]

a 5 cell still life can eat a table:

Code: Select all

x = 6, y = 7, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
3bobo$4bo$3bobo3$4o$o2bo!

[77topaz]

A natural puffer!:

Code: Select all

x = 14, y = 3, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
5b3o$o2bobobobo2bo$4ob3ob4o!

Another puffer with a similar shape:

Code: Select all

x = 13, y = 3, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
6bo$o2bob3obo2bo$4o2bo2b4o!

This one is p26, while the other is p20.

EDIT: If you shift it slightly, it becomes a p12 ship:

Code: Select all

x = 13, y = 4, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
5b3o$5bobo$o2bob3obo2bo$4o5b4o!

And another variation becomes a p32 ship:

Code: Select all

x = 13, y = 3, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
bo4bo4bo$o2bob3obo2bo$4o2bo2b4o!

[googleplex]

A natural puffer!:

Code: Select all

x = 14, y = 3, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
5b3o$o2bobobobo2bo$4ob3ob4o!

Another puffer with a similar shape:

Code: Select all

x = 13, y = 3, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
6bo$o2bob3obo2bo$4o2bo2b4o!

Wow! That bumps up that still life to #7 on the D2_+1 census!

[googleplex]

Natural trivial p20 oscillator:

Code: Select all

x = 7, y = 11, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
obo$bo$obo$4bobo$4b3o2$4b2o$5bo2$bo$b2o!

Trivial p10 oscillator:

Code: Select all

x = 12, y = 8, rule =  B2ein3aikq67e/S1c23-nqr4ci6ci
obo5b2o$bo6b2o$obo$3b2o4b3o$3b2o4bobo$5bobo$6bo$5bobo!

And now, a trivial p28:

Code: Select all

x = 10, y = 8, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2bobob2o$2b3ob2o2$3b2obo$4bo2bo$8b2o$o7b2o$2o!

[googleplex]

Summing up the Catagolue census left running overnight on D2_+1 symmetry at http://catagolue.appspot.com/census/b2e ... i6ci/D2_+1, here are my discoveries:

There are now oscillators of all periods but 9 up to period 12,
still lives up to 41 bits,
lots of spaceships,
and 2 natural puffers.

[googleplex]

Here's a collection of all Spaceships known thus far:
P2/3:

Code: Select all

x = 35, y = 8, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
9bo$8b3o3b4o3b4o7b3o$4b4o3b4o2bo3bo2bo9bo$4bo2bo3bo2bo17bobo$18bobo$bo
bo$o$o!

P10:

Code: Select all

x = 4, y = 15, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2o$2bo$2bo$bo$o2$2b2o$3bo$2b2o2$o$bo$2bo$2bo$2o!

P12:

Code: Select all

x = 4, y = 13, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2o$o$o$2o2$b3o$bo$b3o2$2o$o$o$2o!

P13:

Code: Select all

x = 4, y = 4, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
bo$2o$3bo$2b2o!

P14:

Code: Select all

x = 10, y = 13, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2o$o$o$2o$4bo$b2o2bo$bob4o2bo$b2o2bo$4bo$2o$o$o$2o!

P18:

Code: Select all

x = 17, y = 5, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
4o9b4o$o2bo9bo2bo$4bo2b3o2bo$3bobobobobobo$3bo3bobo3bo!

P24:

Code: Select all

x = 3, y = 13, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
b2o$2bo$2bo$b2o2$2o$bo$2o2$2o$bo$bo$2o!

P32:

Code: Select all

x = 11, y = 13, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
b2o$o$o2bo$bobo2$b2o2b2o2b2o$bo2bo2bob2o$b2o2b2o2b2o2$bobo$o2bo$o$b2o!

[googleplex]

Now there's a natural p70 that is made out of still lives in 6 of its phases.
Once we get all the c/3 ship collisions it should be pretty easy to synthesize:

Code: Select all

x = 8, y = 19, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
3b2o$2o2bob2o$bob2obo$2o4b2o2$2o$o$2o4$2o$o$2o2$2o4b2o$bob2obo$2o2bob2o$3b2o!

and the soup it was found in:

Code: Select all

x = 16, y = 31, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
bbboboobooboboob$
bbobboobobbobbbb$
obbooobooobbboob$
obooobbobooobbob$
booobobobobbboob$
bbbobobobbboooob$
oboobobbboobobbb$
oboobbbobbbboboo$
obobobbobobobboo$
bboboobbobooobbo$
ooboobbooboooobb$
oobobbbobbobboob$
bbboboobbbbbbbbo$
bboobbbbbobbobob$
bbbobobbbboobbob$
oooboobobooboobo$
bbbobobbbboobbob$
bboobbbbbobbobob$
bbboboobbbbbbbbo$
oobobbbobbobboob$
ooboobbooboooobb$
bboboobbobooobbo$
obobobbobobobboo$
oboobbbobbbboboo$
oboobobbboobobbb$
bbbobobobbboooob$
booobobobobbboob$
obooobbobooobbob$
obbooobooobbboob$
bbobboobobbobbbb$
bbboboobooboboob!

[77topaz]

A p8 ship:

Code: Select all

x = 11, y = 13, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
b2o$bo$bo$b2o$2bobo$bo3b2o2b2o$2o4bo3bo$bo3b2o2b2o$2bobo$b2o$bo$bo$b2o!

A p30 oscillator:

Code: Select all

x = 15, y = 5, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
obo9bobo$bo11bo$obo2bo6bobo$4b2o3bo$5bo!

[googleplex]

P10 spaceship:

Code: Select all

x = 12, y = 3, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
3o6b3o$bo2bo2bo2bo$b4o2b4o!

P10 spaceship interacting non-trivially with another ship:

Code: Select all

x = 11, y = 12, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2bo$3o$obo$o$2o8bo$9bo$9bo$2o8bo$o$obo$3o$2bo!

P12 spaceship:

Code: Select all

x = 8, y = 6, rule = B2ein3aikq67e/S1c23-nqr4ci6ci
2b4o$obo2bobo$2o4b2o2$2bo2bo$3b2o!