Replicators and other patterns that simulate even 1D rules

[muzik]

W0:

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

W2, W16:

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x = 3, y = 2, rule = B2a3r/S
obo$o!

W4:

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

W22:

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

W32:

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

W50:

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

W90:

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

W108:

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

W128:

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

W150:

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

W254:

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

W1208925819614629174771760:

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

Undetermined 1:

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

Undetermined:

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

Undetermined:

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x = 3, y = 2, rule = B2a3j4i/S1e2k
3o$3o!

[AforAmpere]

W1839132(?):

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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.

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.

[AforAmpere]

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

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@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.

[muzik]

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

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18
36
54
72
76
94
104
122
126

[2718281828]

I am not sure, but this seems to be a 1D replicator:

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x = 4, y = 5, rule = B2kn3aijn4acik8/S2n3-cek4aint5-aky67c8
b2o$3o$4o$3o$b2o!

[wwei23]

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.

[Redstoneboi]

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.

I am not sure, but this seems to be a 1D replicator:

Code: Select all

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.

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@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

[PHPBB12345]

Also undetermined:

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x = 8, y = 4, rule = B2ek3aijkn4a5r/S1c2cei3ar4ar5i6ac
o$2o4b2o$2o4b2o$o!

[KittyTac]

What about using MAP strings for asymmetrical rules?

[muzik]

Close to Pascal modulo 4, but still unknown:

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x = 4, y = 3, rule = B2ei3-akny4acnqrw5aqy6aen/S1c2-ik3ack4cjknrw5acjk6c7
b2o$o2bo$b2o!

[muzik]

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x = 1, y = 2, rule = B2a3j4i/S1e3a4ar
o$o!

[muzik]

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x = 1, y = 2, rule = B2ac4i5y/S2i4t
o$o!

[Gamedziner]

What rule would stand for this:

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x = 100, y = 1, rule = B1c/S:T100+1,1
48bo3bo!

[wwei23]

What rule would stand for this:

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x = 100, y = 1, rule = B1c/S:T100+1,1
48bo3bo!

Has a rule 90 replication habit.

[Redstoneboi]

What rule would stand for this:

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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.

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x = 5, y = 1, rule = W18
ob3o!

[635318657]

What about this replicator?

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x = 19, y = 3, rule = B36/S245
6o7b6o$o4bo7bo4bo$b4o9b4o!

Also undetermined:

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x = 8, y = 4, rule = B2ek3aijkn4a5r/S1c2cei3ar4ar5i6ac
o$2o4b2o$2o4b2o$o!

This just evolves into blocks. Also, nice rule.

[muzik]

Also undetermined:

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x = 8, y = 4, rule = B2ek3aijkn4a5r/S1c2cei3ar4ar5i6ac
o$2o4b2o$2o4b2o$o!

This just evolves into blocks.

...and therefore it simulates a 1D rule in which such a configuration would evolve into the 1D equivalent of blocks.

[ihatecorderships]

W36 was easy to engineer:

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x = 8, y = 2, rule = B4i/S1e
obo4bo$obo4bo!

edit: W72

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x = 2, y = 2, rule = B/S3a
2o$2o!

edit 2: W76

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x = 6, y = 2, rule = B/S1e3a
o3b2o$o3b2o!