2D Replicator Classes

[drc]

That's actually a spacefiller.

It's also a (failed) replicator. If you look closely you can see the puffer being generated again, and even again before crashing into the oscillators.

[GUYTU6J]

Code: Select all

x = 4, y = 4, rule = B2i34ceiknry8/S23-a4city
3o$o2bo$o2bo$b3o!

Notice that the engine goes at (14,1)c/36

Code: Select all

x = 4, y = 4, rule = B2i34ceiknry8/S23-a4city
b3o$o2bo$o2bo$3o!
#C [[ TRACKBOX 14/36 1/36 0 0 ]]

EDIT:Similarly,

Code: Select all

x = 3, y = 3, rule = B2n34eiqrtz5eijnr8/S23-a4city
2o$b2o$bo!

EDIT2:How about this?

Code: Select all

x = 4, y = 3, rule = B2in3aeikn4city8/S23-a4city
2bo$b3o$o2bo!

And this one?

Code: Select all

x = 4, y = 4, rule = B2in3aceir4city8/S23-a4city
b2o$2o$b3o$2bo!

[AbhpzTa]

EDIT2:How about this?

Code: Select all

x = 4, y = 3, rule = B2in3aeikn4city8/S23-a4city
2bo$b3o$o2bo!

It's class F. I've edited the OP.

[GUYTU6J]

Code: Select all

x = 5, y = 4, rule = B2k3aeiqy4city8/S23-a4city
b3o$bo2bo$bob2o$o!

EDIT:

Code: Select all

x = 3, y = 3, rule = B2k3aeinr4city7c/S23-a4city
bo$3o$2bo!

Code: Select all

x = 4, y = 4, rule = B2k3aeinr4city7e/S23-a4city
3o$o2bo$o2bo$b3o!

[GUYTU6J]

Code: Select all

x = 4, y = 4, rule = B2ik3aeikr4ceijqry78/S23-a4city78
b3o$o2bo$o$2o!

[toroidalet]

Class-S:

Code: Select all

x = 7, y = 2, rule = B3-y5a/S234c5ek
3ob3o$bo3bo!

Code: Select all

x = 31, y = 27, rule = B3-y5a/S234c5ek
bo3bo19bo3bo$3ob3o17b3ob3o24$3ob3o$bo3bo!

[muzik]

Possibly a class u:

Code: Select all

x = 1, y = 1, rule = B1e2e3e/S0
o!

[BlinkerSpawn]

Possibly a class r:

Code: Select all

x = 1, y = 1, rule = B1e2e3e/S0
o!

It's an XOR but with diamonds, if that makes any sense.
Not sure if that's a class; I haven't studied the OP in forever.

[praosylen]

Possibly a class r:

Code: Select all

x = 1, y = 1, rule = B1e2e3e/S0
o!

It seems to follow OEIS A189007 (1, 4, 8, 16, 16, 32, 32, 64, 32, ...), so it does not appear to be in any existing class.

[muzik]

And another (technically this is von Neumann Fredkin)

Code: Select all

x = 1, y = 1, rule = B1e/S04e
o!

Do these count as replicators, or spacefillers?

Code: Select all

x = 1, y = 1, rule = B12cn4c/S0
o!

Code: Select all

x = 1, y = 1, rule = B1c2c4c/S
o!

[muzik]

How about this one?

Code: Select all

x = 1, y = 1, rule = B12ci3ci4c6i8/S02i8
o!

[AbhpzTa]

Do these count as replicators, or spacefillers?

Code: Select all

x = 1, y = 1, rule = B12cn4c/S0
o!

Code: Select all

x = 1, y = 1, rule = B1c2c4c/S
o!

Spacefillers.

[Saka]

New class?

Code: Select all

x = 1, y = 1, rule = B1e2e/S2c
o!

More interesting example

Code: Select all

x = 1, y = 1, rule = B1e2e/S2c3i4w5y
o!

It's interesting, it replicates at 1,4,8,12,20,20,36,36,68,36,68,68,132,68,132,132,260,68...

These also don't have the "dying edge replicators" muzik talked about

[Saka]

Class Q?

Code: Select all

x = 3, y = 7, rule = B3-cny4cekryz5c6in7e8/S2-cn3-aeky4eit5ackn6ei7e8
3o$obo$obo2$obo$obo$3o!

Oblique?

Code: Select all

x = 4, y = 4, rule = B2kn3-ckny4irt5r8/S2aek3ijnqr4i
b3o$o2bo$o2bo$3o!

Aha! Another oblique!

Code: Select all

x = 7, y = 8, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i
2bo$b3o$2obo3$3bob2o$3b3o$4bo!

If the B's are separated, they will turn into 10c/208o ships
That rule has a second replicator!

Code: Select all

x = 5, y = 4, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i
2ob2o$o3bo$b3o$2bo!

[AforAmpere]

(7,4) oblique 2D replicator, class S, I think

Code: Select all

x = 4, y = 3, rule = B2in3aijr4eq5j6c/S2-in3ijnqr4i5cnr6k
b3o$bobo$2obo!

Code: Select all

x = 26, y = 17, rule = B2in3aijr4eq5j6c/S2-in3ijnqr4i5cnr6k
b3o$bobo$2obo4$23b3o$23bobo$22b2obo6$9b3o$9bobo$8b2obo!

[Saka]

Oblique?

Code: Select all

x = 4, y = 4, rule = B2kn3-ckny4irt5r8/S2aek3ijnqr4i
b3o$o2bo$o2bo$3o!

[muzik]

So it appears that 2D class S replicators can fill out areas that are either square, rectangular or rhombic.

Are there any other polygons it can trace out? I doubt so, but if so, those with 4n sides seem to be most likely.

[LaundryPizza03]

Okay, I found 3 of these back in November:

Code: Select all

x = 3, y = 3, rule = B34j5k6en/S235e6c
2o$b2o$2bo!

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!

Code: Select all

x = 4, y = 2, rule = B2n3aijnr4jrz5r6-e/S2-in3knr4aeijknq5-r8
b2o$4o!

The second one can be hassled by blocks:

Code: Select all

x = 19, y = 19, rule = B3-q4z5y/S234k5j
12b2o$12b2o3$b5o$o3bo3b2o$o$bobo4$9b2o$3b2o3b2o7b2o$7b2o8b2o4$5b2o$5b
2o!

The rule doesn't have the glider or the XWSS's, but does support the hat ship.

Could Class S replicator hasslers be used for signal circuitry?

[LaundryPizza03]

Purely by accident

Code: Select all

x = 3, y = 3, rule = B3aei/S12-a3i
o$o$3o!

[LaundryPizza03]

Code: Select all

x = 3, y = 3, rule = B2k3578/S3-e456k8
3o$3o$obo!

Code: Select all

x = 3, y = 3, rule = B2a/S3n4y
2o$obo$b2o!

3-way:

Code: Select all

x = 3, y = 2, rule = B2a3ir5aik7e/S2k4z
obo$3o!

Closely related to the third, a potentially new family:

Code: Select all

x = 3, y = 2, rule = B2a3ir4i5aik7e/S2k3y4z
obo$3o!

Code: Select all

x = 3, y = 2, rule = B2a3ir4ik5aik7e/S2k3y4z
obo$3o!

EDIT: Bingo! Another new family!

Code: Select all

x = 3, y = 2, rule = B1e2i3a4i5eiq6i/S2a3eiq4inr
bo$3o!

[muzik]

Haha that 3-way one is awesome.

Technically it would be a 1.5849D replicator though?

[KittyTac]

The 3-way one's trail looks like two Sierpinski Triangles with tilted triangles, if that makes any sense.

[gameoflifemaniac]

The 3-way one's trail looks like two Sierpinski Triangles with tilted triangles, if that makes any sense.

Rather squashed.

[muzik]

Hm.

Code: Select all

x = 11, y = 11, rule = B2ce3y4e5y6c/S1c2i3ciy4ct5ey6i7e8
5bo$4bobo$5bo$5bo$bo7bo$ob2o3b2obo$bo7bo$5bo$5bo$4bobo$5bo!

[praosylen]

Hm.

Code: Select all

x = 11, y = 11, rule = B2ce3y4e5y6c/S1c2i3ciy4ct5ey6i7e8
5bo$4bobo$5bo$5bo$bo7bo$ob2o3b2obo$bo7bo$5bo$5bo$4bobo$5bo!

That's interesting — it's a replicator with infinite growth and finite copies.