## 2D Replicator Classes

For discussion of other cellular automata.

### Re: 2D Replicator Classes

Gamedziner wrote: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.
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### Re: 2D Replicator Classes

x = 4, y = 4, rule = B2i34ceiknry8/S23-a4city
3o$o2bo$o2bo$b3o! Notice that the engine goes at (14,1)c/36 x = 4, y = 4, rule = B2i34ceiknry8/S23-a4city b3o$o2bo$o2bo$3o!
#C [[ TRACKBOX 14/36 1/36 0 0 ]]

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

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

And this one?
x = 4, y = 4, rule = B2in3aceir4city8/S23-a4city
b2o$2o$b3o$2bo! Welcome to share your ideas about etymology of names! GUYTU6J Posts: 347 Joined: August 5th, 2016, 10:27 am Location: outside Plain of Life ### Re: 2D Replicator Classes GUYTU6J wrote:EDIT2:How about this? x = 4, y = 3, rule = B2in3aeikn4city8/S23-a4city 2bo$b3o$o2bo! It's class F. I've edited the OP. Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) : 965808 is period 336 (max = 207085118608). AbhpzTa Posts: 429 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan ### Re: 2D Replicator Classes x = 5, y = 4, rule = B2k3aeiqy4city8/S23-a4city b3o$bo2bo$bob2o$o!

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

x = 4, y = 4, rule = B2k3aeinr4city7e/S23-a4city
3o$o2bo$o2bo$b3o! Welcome to share your ideas about etymology of names! GUYTU6J Posts: 347 Joined: August 5th, 2016, 10:27 am Location: outside Plain of Life ### Re: 2D Replicator Classes x = 4, y = 4, rule = B2ik3aeikr4ceijqry78/S23-a4city78 b3o$o2bo$o$2o!
etymology of names!

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### Re: 2D Replicator Classes

Class-S:
x = 7, y = 2, rule = B3-y5a/S234c5ek
3ob3o$bo3bo! x = 31, y = 27, rule = B3-y5a/S234c5ek bo3bo19bo3bo$3ob3o17b3ob3o24$3ob3o$bo3bo!
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toroidalet

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### Re: 2D Replicator Classes

Possibly a class u:
x = 1, y = 1, rule = B1e2e3e/S0
o!
Last edited by muzik on October 13th, 2017, 6:07 pm, edited 1 time in total.
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### Re: 2D Replicator Classes

muzik wrote:Possibly a class r:
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.
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### Re: 2D Replicator Classes

muzik wrote:Possibly a class r:
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.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

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### Re: 2D Replicator Classes

And another (technically this is von Neumann Fredkin)
x = 1, y = 1, rule = B1e/S04e
o!

Do these count as replicators, or spacefillers?
x = 1, y = 1, rule = B12cn4c/S0
o!

x = 1, y = 1, rule = B1c2c4c/S
o!
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### Re: 2D Replicator Classes

x = 1, y = 1, rule = B12ci3ci4c6i8/S02i8
o!
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### Re: 2D Replicator Classes

muzik wrote:Do these count as replicators, or spacefillers?
x = 1, y = 1, rule = B12cn4c/S0
o!

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

Spacefillers.
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

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### Re: 2D Replicator Classes

New class?
x = 1, y = 1, rule = B1e2e/S2c
o!

More interesting example
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
Proud owner and founder of Sakagolue
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo! (Check gen 2) Saka Posts: 2482 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: 2D Replicator Classes Class Q? x = 3, y = 7, rule = B3-cny4cekryz5c6in7e8/S2-cn3-aeky4eit5ackn6ei7e8 3o$obo$obo2$obo$obo$3o!

Oblique?
x = 4, y = 4, rule = B2kn3-ckny4irt5r8/S2aek3ijnqr4i
b3o$o2bo$o2bo$3o! Aha! Another oblique! x = 7, y = 8, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i 2bo$b3o$2obo3$3bob2o$3b3o$4bo!

If the B's are separated, they will turn into 10c/208o ships
That rule has a second replicator!
x = 5, y = 4, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i
2ob2o$o3bo$b3o$2bo! Proud owner and founder of Sakagolue x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

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### Re: 2D Replicator Classes

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

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

x = 26, y = 17, rule = B2in3aijr4eq5j6c/S2-in3ijnqr4i5cnr6k
b3o$bobo$2obo4$23b3o$23bobo$22b2obo6$9b3o$9bobo$8b2obo!
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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### Re: 2D Replicator Classes

Oblique?
x = 4, y = 4, rule = B2kn3-ckny4irt5r8/S2aek3ijnqr4i
b3o$o2bo$o2bo$3o! Proud owner and founder of Sakagolue x = 17, y = 10, rule = B3/S23 b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

Saka

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### Re: 2D Replicator Classes

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.
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### Re: 2D Replicator Classes

Okay, I found 3 of these back in November:
x = 3, y = 3, rule = B34j5k6en/S235e6c
2o$b2o$2bo!

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

x = 4, y = 2, rule = B2n3aijnr4jrz5r6-e/S2-in3knr4aeijknq5-r8
b2o$4o! The second one can be hassled by blocks: x = 19, y = 19, rule = B3-q4z5y/S234k5j 12b2o$12b2o3$b5o$o3bo3b2o$o$bobo4$9b2o$3b2o3b2o7b2o$7b2o8b2o4$5b2o$5b 2o! The rule doesn't have the glider or the XWSS's, but does support the hat ship. Could Class S replicator hasslers be used for signal circuitry? x = 4, y = 3, rule = B3-q4z5y/S234k5j 2b2o$b2o$2o! LaundryPizza03 at Wikipedia LaundryPizza03 Posts: 203 Joined: December 15th, 2017, 12:05 am Location: Unidentified location "https://en.wikipedia.org/wiki/Texas" ### Re: 2D Replicator Classes Purely by accident x = 3, y = 3, rule = B3aei/S12-a3i o$o$3o! x = 4, y = 3, rule = B3-q4z5y/S234k5j 2b2o$b2o$2o! LaundryPizza03 at Wikipedia LaundryPizza03 Posts: 203 Joined: December 15th, 2017, 12:05 am Location: Unidentified location "https://en.wikipedia.org/wiki/Texas" ### Re: 2D Replicator Classes x = 3, y = 3, rule = B2k3578/S3-e456k8 3o$3o$obo! x = 3, y = 3, rule = B2a/S3n4y 2o$obo$b2o! 3-way: x = 3, y = 2, rule = B2a3ir5aik7e/S2k4z obo$3o!

Closely related to the third, a potentially new family:
x = 3, y = 2, rule = B2a3ir4i5aik7e/S2k3y4z
obo$3o! x = 3, y = 2, rule = B2a3ir4ik5aik7e/S2k3y4z obo$3o!

EDIT: Bingo! Another new family!
x = 3, y = 2, rule = B1e2i3a4i5eiq6i/S2a3eiq4inr
bo$3o! x = 4, y = 3, rule = B3-q4z5y/S234k5j 2b2o$b2o$2o! LaundryPizza03 at Wikipedia LaundryPizza03 Posts: 203 Joined: December 15th, 2017, 12:05 am Location: Unidentified location "https://en.wikipedia.org/wiki/Texas" ### Re: 2D Replicator Classes Haha that 3-way one is awesome. Technically it would be a 1.5849D replicator though? 2c/n spaceships project Current priorities: see here muzik Posts: 2733 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: 2D Replicator Classes The 3-way one's trail looks like two Sierpinski Triangles with tilted triangles, if that makes any sense. KittyTac Posts: 265 Joined: December 21st, 2017, 9:58 am ### Re: 2D Replicator Classes KittyTac wrote:The 3-way one's trail looks like two Sierpinski Triangles with tilted triangles, if that makes any sense. Rather squashed. https://www.youtube.com/watch?v=q6EoRBvdVPQ One big dirty Oro. Yeeeeeeeeee... gameoflifemaniac Posts: 583 Joined: January 22nd, 2017, 11:17 am Location: Poland ### Re: 2D Replicator Classes Hm. x = 11, y = 11, rule = B2ce3y4e5y6c/S1c2i3ciy4ct5ey6i7e8 5bo$4bobo$5bo$5bo$bo7bo$ob2o3b2obo$bo7bo$5bo$5bo$4bobo$5bo! 2c/n spaceships project Current priorities: see here muzik Posts: 2733 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: 2D Replicator Classes muzik wrote:Hm. 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.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

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

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