2D Replicator Classes

For discussion of other cellular automata.
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drc
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Re: 2D Replicator Classes

Post by drc » August 25th, 2017, 12:23 pm

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

Post by GUYTU6J » September 1st, 2017, 8:55 am

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!
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An awesome gun firing cool spaceships:

Code: Select all

x = 3, y = 5, rule = B2kn3-ekq4i/S23ijkqr4eikry
2bo$2o$o$obo$b2o!

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Re: 2D Replicator Classes

Post by AbhpzTa » September 10th, 2017, 12:49 pm

GUYTU6J wrote: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.
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).

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Re: 2D Replicator Classes

Post by GUYTU6J » September 15th, 2017, 10:57 am

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!
Current status: outside the continent of cellular automata. Specifically, not on the plain of life.
An awesome gun firing cool spaceships:

Code: Select all

x = 3, y = 5, rule = B2kn3-ekq4i/S23ijkqr4eikry
2bo$2o$o$obo$b2o!

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GUYTU6J
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Re: 2D Replicator Classes

Post by GUYTU6J » September 23rd, 2017, 4:40 am

Code: Select all

x = 4, y = 4, rule = B2ik3aeikr4ceijqry78/S23-a4city78
b3o$o2bo$o$2o!
Current status: outside the continent of cellular automata. Specifically, not on the plain of life.
An awesome gun firing cool spaceships:

Code: Select all

x = 3, y = 5, rule = B2kn3-ekq4i/S23ijkqr4eikry
2bo$2o$o$obo$b2o!

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toroidalet
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Re: 2D Replicator Classes

Post by toroidalet » September 29th, 2017, 6:17 pm

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!
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Re: 2D Replicator Classes

Post by muzik » October 13th, 2017, 3:53 pm

Possibly a class u:

Code: Select all

x = 1, y = 1, rule = B1e2e3e/S0
o!
Last edited by muzik on October 13th, 2017, 6:07 pm, edited 1 time in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: 2D Replicator Classes

Post by BlinkerSpawn » October 13th, 2017, 5:21 pm

muzik wrote: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.
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Re: 2D Replicator Classes

Post by A for awesome » October 13th, 2017, 5:40 pm

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

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

http://conwaylife.com/wiki/A_for_all

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Re: 2D Replicator Classes

Post by muzik » October 13th, 2017, 5:51 pm

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!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

muzik
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Re: 2D Replicator Classes

Post by muzik » October 24th, 2017, 4:23 am

How about this one?

Code: Select all

x = 1, y = 1, rule = B12ci3ci4c6i8/S02i8
o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: 2D Replicator Classes

Post by AbhpzTa » October 25th, 2017, 3:57 pm

muzik wrote: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.
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).

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Re: 2D Replicator Classes

Post by Saka » November 29th, 2017, 3:32 am

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
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

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Re: 2D Replicator Classes

Post by Saka » December 6th, 2017, 3:10 am

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!
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

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Re: 2D Replicator Classes

Post by AforAmpere » December 8th, 2017, 7:18 pm

(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!
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

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Re: 2D Replicator Classes

Post by Saka » December 9th, 2017, 4:51 am

Oblique?

Code: Select all

x = 4, y = 4, rule = B2kn3-ckny4irt5r8/S2aek3ijnqr4i
b3o$o2bo$o2bo$3o!
Airy Clave White It Nay

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

muzik
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Re: 2D Replicator Classes

Post by muzik » December 12th, 2017, 4:45 am

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.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: 2D Replicator Classes

Post by LaundryPizza03 » December 15th, 2017, 12:22 am

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?

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
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Re: 2D Replicator Classes

Post by LaundryPizza03 » December 25th, 2017, 7:11 pm

Purely by accident

Code: Select all

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

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
LaundryPizza03 at Wikipedia

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Re: 2D Replicator Classes

Post by LaundryPizza03 » December 25th, 2017, 9:34 pm

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!

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
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muzik
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Re: 2D Replicator Classes

Post by muzik » January 5th, 2018, 8:40 am

Haha that 3-way one is awesome.

Technically it would be a 1.5849D replicator though?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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KittyTac
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Re: 2D Replicator Classes

Post by KittyTac » January 5th, 2018, 8:47 am

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

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Re: 2D Replicator Classes

Post by gameoflifemaniac » January 7th, 2018, 4:20 am

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
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Re: 2D Replicator Classes

Post by muzik » January 10th, 2018, 7:32 am

Hm.

Code: Select all

x = 11, y = 11, rule = B2ce3y4e5y6c/S1c2i3ciy4ct5ey6i7e8
5bo$4bobo$5bo$5bo$bo7bo$ob2o3b2obo$bo7bo$5bo$5bo$4bobo$5bo!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!

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Re: 2D Replicator Classes

Post by A for awesome » January 10th, 2018, 11:04 am

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

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

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce

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