## Replicators and other patterns that simulate even 1D rules

For discussion of other cellular automata.

### Replicators and other patterns that simulate even 1D rules

W0:
x = 1, y = 1, rule = B/S
o!

W2, W16:
x = 3, y = 2, rule = B2a3r/S
obo\$o!

W4:
x = 1, y = 1, rule = B/S0
o!

W22:
x = 1, y = 2, rule = B2a3j5y6i/S1e2i3a
o\$o!

W32:
x = 31, y = 2, rule = B4i/S
obobobobobobobobobobobobobobobo\$obobobobobobobobobobobobobobobo!

W50:
x = 1, y = 2, rule = B2a4i/S
o\$o!

W90:
x = 1, y = 2, rule = B2a/S
o\$o!

W108:
x = 25, y = 2, rule = B4i/S1e3a
obo6bob3o6bobobo\$obo6bob3o6bobobo!

W128:
x = 32, y = 1, rule = B/S2i
32o!

W150:
x = 1, y = 5, rule = B2a/S1e3eiy5i
o\$o2\$o\$o!

W254:
x = 2, y = 1, rule = B1e2i/S1e2i
2o!

W1208925819614629174771760:
x = 1, y = 5, rule = B2ei3aein4e5e/S1e2aek3-cein4ikz
o\$o\$o\$o\$o!

Undetermined 1:
x = 1, y = 5, rule = B2ae3n6i/S1e2n3r
o\$o2\$o\$o!

Undetermined:
x = 5, y = 4, rule = B3-e4ny56i7e/S2-ck3r4-nt5jq6
b3o\$2ob2o\$2ob2o\$b3o!

Undetermined:
x = 3, y = 2, rule = B2a3j4i/S1e2k
3o\$3o!
Last edited by muzik on June 29th, 2018, 7:38 pm, edited 3 times in total.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3310
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Replicators that simulate even 1D rules

muzik wrote:W1839132(?):
x = 1, y = 5, rule = B2ei3aein4e5e/S1e2aek3-cein4ikz
o\$o\$o\$o\$o!

This seems to be W1208925819614629174771760, range 3, link to Wolfram. I may be wrong, though.
muzik wrote:Undetermined:

Both of the ones in undetermined don't really align well with Wolfram rules, because of period differences when replicating. I'll try to see if multiple on states will work.
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
AforAmpere

Posts: 1019
Joined: July 1st, 2016, 3:58 pm

### Re: Replicators that simulate even 1D rules

Can anyone convert this rule table into a Wolfram rule? It is 7 states and emulates the first of the undetermined rules above:
@RULE Undetermined_1

@TABLE

n_states: 7
neighborhood:Moore
symmetries:none

0,6,0,0,0,0,0,0,0,6
0,0,6,0,0,0,0,0,0,6
0,0,0,0,0,0,0,0,6,6
0,6,6,0,0,0,0,0,0,5
0,6,6,0,0,0,0,0,6,1
0,6,0,0,0,0,0,0,6,5
0,6,5,0,0,0,0,0,0,4
0,6,0,0,0,0,0,0,5,4
0,6,4,0,0,0,0,0,0,5
0,6,0,0,0,0,0,0,4,5
0,5,0,0,0,0,0,0,6,2
0,5,6,0,0,0,0,0,0,2
0,2,0,0,0,0,0,0,4,6
0,2,4,0,0,0,0,0,0,6
0,4,2,0,0,0,0,0,6,3
0,4,6,0,0,0,0,0,2,3
0,5,0,0,0,0,0,0,3,2
0,5,3,0,0,0,0,0,0,2
0,6,4,0,0,0,0,0,6,1
0,6,6,0,0,0,0,0,4,1
0,4,2,0,0,0,0,0,0,1
0,4,0,0,0,0,0,0,2,1

@COLORS
1 255 0 0
2 170 85 0
3 127 127 0
4 0 170 85
5 85 0 170
6 170 0 85

The rulestring may end up extremely long, but there might be a lower state rule that emulates the replicating pattern somewhere.
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
AforAmpere

Posts: 1019
Joined: July 1st, 2016, 3:58 pm

### Re: Replicators and other patterns that simulate even 1D rules

As for symmetrical rules, here are the ones we're currently missing <128:

18
36
54
72
76
94
104
122
126
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3310
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Replicators and other patterns that simulate even 1D rules

I am not sure, but this seems to be a 1D replicator:
x = 4, y = 5, rule = B2kn3aijn4acik8/S2n3-cek4aint5-aky67c8
b2o\$3o\$4o\$3o\$b2o!

2718281828

Posts: 707
Joined: August 8th, 2017, 5:38 pm

### Re: Replicators and other patterns that simulate even 1D rules

As I understand the definition of a necropost, it's a post in a thread that hasn't had any posts in at least a year, or quotes a post from at least a year earlier. This thread has had activity in June.
The second unknown rule works via rule 8229, k=3.
http://www.wolframalpha.com/input/?i=rule+8229,+k%3D3
When two replicators in different states (off by 1 is the only one that ever occurs on its own), they annihilate. Otherwise, they leave a replicator in the middle, but one generation behind the replicators that created it. The result is almost the same as rule 8229, k=3. For 8229, k=3, just take the number of generations a replicator is lagging behind, modulo 2, and add 1. If there is no replicator present, then the value for that spot is 0.

wwei23

Posts: 935
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: Replicators and other patterns that simulate even 1D rules

wwei23 wrote:As I understand the definition of a necropost, it's a post in a thread that hasn't had any posts in at least a year, or quotes a post from at least a year earlier. This thread has had activity in June.

Actually, a necropost is a post in a thread that’s considered inactive or dead that doesn’t add anything useful to the topic, so it’s okay to post in a very old thread so long as the post is appropriate and useful.

2718281828 wrote:I am not sure, but this seems to be a 1D replicator:
x = 4, y = 5, rule = B2kn3aijn4acik8/S2n3-cek4aint5-aky67c8
b2o\$3o\$4o\$3o\$b2o!

seems to simulate a 3 state range 1 rule, i don’t know if it can be converted to range 2.
Here’s the rule with emulated history in Moore neighborhood
the history seems to be a slanted sierpinski triangle, hence the rule’s name.
@RULE SlantPinski
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
var a{0,1,2}
var b=a
var c=a
var d=a
var e=a
var f=a
var g=a
var h=a
0,a,b,c,d,1,f,g,h,1
#C    R       L   C'
0,a,b,c,d,e,f,1,h,1
1,a,b,c,d,e,f,1,h,2
2,a,b,c,d,e,f,g,h,0
Last edited by Redstoneboi on October 28th, 2018, 1:42 am, edited 1 time in total.
c(>^w^<c)~*
This is 「Fluffy」
「Fluffy」is my sutando.
「Fluffy」has the ability to engineer r e p l i c a t o r s.
「Fluffy」likes to watch spaceship guns in Golly.
「Fluffy」knows Natsuki best girl.

Redstoneboi

Posts: 339
Joined: May 14th, 2018, 3:57 am

### Re: Replicators and other patterns that simulate even 1D rules

Also undetermined:
x = 8, y = 4, rule = B2ek3aijkn4a5r/S1c2cei3ar4ar5i6ac
o\$2o4b2o\$2o4b2o\$o!

PHPBB12345

Posts: 514
Joined: August 5th, 2015, 11:55 pm

### Re: Replicators and other patterns that simulate even 1D rules

What about using MAP strings for asymmetrical rules?

KittyTac

Posts: 533
Joined: December 21st, 2017, 9:58 am

### Re: Replicators and other patterns that simulate even 1D rules

Close to Pascal modulo 4, but still unknown:

x = 4, y = 3, rule = B2ei3-akny4acnqrw5aqy6aen/S1c2-ik3ack4cjknrw5acjk6c7
b2o\$o2bo\$b2o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3310
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Replicators and other patterns that simulate even 1D rules

x = 1, y = 2, rule = B2a3j4i/S1e3a4ar
o\$o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3310
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Replicators and other patterns that simulate even 1D rules

x = 1, y = 2, rule = B2ac4i5y/S2i4t
o\$o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3310
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: Replicators and other patterns that simulate even 1D rules

What rule would stand for this:
x = 100, y = 1, rule = B1c/S:T100+1,1
48bo3bo!
x = 81, y = 96, rule = LifeHistory
58.2A\$58.2A3\$59.2A17.2A\$59.2A17.2A3\$79.2A\$79.2A2\$57.A\$56.A\$56.3A4\$27.
A\$27.A.A\$27.2A21\$3.2A\$3.2A2.2A\$7.2A18\$7.2A\$7.2A2.2A\$11.2A11\$2A\$2A2.2A
\$4.2A18\$4.2A\$4.2A2.2A\$8.2A!
Gamedziner

Posts: 743
Joined: May 30th, 2016, 8:47 pm
Location: Milky Way Galaxy: Planet Earth

### Re: Replicators and other patterns that simulate even 1D rules

Gamedziner wrote:What rule would stand for this:
x = 100, y = 1, rule = B1c/S:T100+1,1
48bo3bo!

Has a rule 90 replication habit.

wwei23

Posts: 935
Joined: May 22nd, 2017, 6:14 pm
Location: The (Life?) Universe

### Re: Replicators and other patterns that simulate even 1D rules

wwei23 wrote:
Gamedziner wrote:What rule would stand for this:
x = 100, y = 1, rule = B1c/S:T100+1,1
48bo3bo!

Has a rule 90 replication habit.

correction: rule 18 for range 1.
range 2 would be more accurate for this.
x = 5, y = 1, rule = W18
ob3o!
c(>^w^<c)~*
This is 「Fluffy」
「Fluffy」is my sutando.
「Fluffy」has the ability to engineer r e p l i c a t o r s.
「Fluffy」likes to watch spaceship guns in Golly.
「Fluffy」knows Natsuki best girl.

Redstoneboi

Posts: 339
Joined: May 14th, 2018, 3:57 am