## 2D Replicator Classes

For discussion of other cellular automata.
drc
Posts: 1664
Joined: December 3rd, 2015, 4:11 pm
Location: creating useless things in OCA

### 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.
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3-ir4a5y/S2-c3-y

GUYTU6J
Posts: 695
Joined: August 5th, 2016, 10:27 am
Location: My Glimmering Garden

### Re: 2D Replicator Classes

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!


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!  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! AbhpzTa Posts: 475 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan ### Re: 2D Replicator Classes 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). GUYTU6J Posts: 695 Joined: August 5th, 2016, 10:27 am Location: My Glimmering Garden ### Re: 2D Replicator Classes 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! GUYTU6J Posts: 695 Joined: August 5th, 2016, 10:27 am Location: My Glimmering Garden ### Re: 2D Replicator Classes 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!

toroidalet
Posts: 1019
Joined: August 7th, 2016, 1:48 pm
Location: my computer
Contact:

### Re: 2D Replicator Classes

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!

"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."

-Terry Pratchett

muzik
Posts: 3499
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 2D Replicator Classes

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!

Posts: 1906
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

### Re: 2D Replicator Classes

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.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

A for awesome
Posts: 1901
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1
Contact:

### Re: 2D Replicator Classes

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

Aidan F. Pierce

muzik
Posts: 3499
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 2D Replicator Classes

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
Posts: 3499
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: 2D Replicator Classes

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!

AbhpzTa
Posts: 475
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: 2D Replicator Classes

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).

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: 2D Replicator Classes

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$4bob2o2bobobo!  (Check gen 2) Saka Posts: 3138 Joined: June 19th, 2015, 8:50 pm Location: In the kingdom of Sultan Hamengkubuwono X ### Re: 2D Replicator Classes Class Q? Code: Select all x = 3, y = 7, rule = B3-cny4cekryz5c6in7e8/S2-cn3-aeky4eit5ackn6ei7e8 3o$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)

AforAmpere
Posts: 1049
Joined: July 1st, 2016, 3:58 pm

### Re: 2D Replicator Classes

(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)

Saka
Posts: 3138
Joined: June 19th, 2015, 8:50 pm
Location: In the kingdom of Sultan Hamengkubuwono X

### Re: 2D Replicator Classes

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
Posts: 3499
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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

LaundryPizza03
Posts: 457
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

### Re: 2D Replicator Classes

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$2o!  LaundryPizza03 at Wikipedia LaundryPizza03 Posts: 457 Joined: December 15th, 2017, 12:05 am Location: Unidentified location "https://en.wikipedia.org/wiki/Texas" ### Re: 2D Replicator Classes Purely by accident Code: Select all x = 3, y = 3, rule = B3aei/S12-a3i o$o$3o!  Code: Select all x = 4, y = 3, rule = B3-q4z5y/S234k5j 2b2o$b2o$2o!  LaundryPizza03 at Wikipedia LaundryPizza03 Posts: 457 Joined: December 15th, 2017, 12:05 am Location: Unidentified location "https://en.wikipedia.org/wiki/Texas" ### Re: 2D Replicator Classes 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!  LaundryPizza03 at Wikipedia muzik Posts: 3499 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: 2D Replicator Classes 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! KittyTac Posts: 533 Joined: December 21st, 2017, 9:58 am ### Re: 2D Replicator Classes The 3-way one's trail looks like two Sierpinski Triangles with tilted triangles, if that makes any sense. gameoflifemaniac Posts: 774 Joined: January 22nd, 2017, 11:17 am Location: There too ### 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... muzik Posts: 3499 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: 2D Replicator Classes 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! A for awesome Posts: 1901 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: ### Re: 2D Replicator Classes 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