## New method of classifying two-dimensional replicators

For discussion of other cellular automata.

### New method of classifying two-dimensional replicators

We first set the requirements that the replicator be a sawtooth, hereby excluding U-class, X-class, and failed replicators, and that it must be a square, rectangle or rhombus.

These replicators can be classified using the notation (E,C), where:

E - Edge rule; the one-dimensional rule which is simulated by the edge of the replicator

C - Core rule; the one-dimensional rule found on the diagonal of the square.
x = 46, y = 17, rule = bs012345678History
24.A\$23.3A\$22.A3.A\$21.2A.A.2A\$20.A.A.A.A.A\$3C9.3C4.3A5.3A\$C11.C.C3.A
5.A5.A\$C3.3C.3C.3C2.2C.2C.3C.2C.CE\$C3.C.C.C3.C5.A5.A5.E\$3C.3C.C3.3C4.
3A5.2AE\$20.A.A.A.A.E\$21.2A.A.AE\$22.A3.E4.3E3.E5.3E\$23.2AE5.E5.E5.E.E\$
24.E6.3E.3E.3E.3E\$31.E3.E.E3.E.E\$31.3E.3E.3E.3E!

Through these, we can currently identify four classes of replicators:

90,90 (includes all S, R and Q-class replicators):
x = 1, y = 1, rule = B1e/S
o!

90,150
x = 1, y = 1, rule = B1e/S04e
o!

150,90
x = 1, y = 1, rule = B13ci/S
o!

150,150
x = 1, y = 1, rule = B13i/S08
o!

150,1721342310
x = 65, y = 55, rule = R2,C0,S1,3,5,7,9,11,B1,3,5,7,9,11,NN
o!

150,2523490710
x = 65, y = 55, rule = R2,C0,S0,2,4,6,8,10,12,B1,3,5,7,9,11,NN
o!

2523490710,1721342310
x = 1, y = 1, rule = r2b555555s555555
o!

2523490710,2523490710
x = 1, y = 1, rule = r2b555555saaaaaaz
o!

199931532107794273605284333428918544790,140117185019831836588493434554119984790
x = 1, y = 1, rule = r3b555555555555s555555555555
o!

199931532107794273605284333428918544790,199931532107794273605284333428918544790
x = 1, y = 1, rule = r3b555555555555saaaaaaaaaaaaz
o!

0-fold and 1-fold replication rules have been excluded.
Last edited by muzik on January 26th, 2019, 12:22 pm, edited 6 times in total.
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muzik

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### Re: New method of classifying two-dimensional replicators

Examples of replicators:

90,90:

step2
x = 2, y = 2, rule = B2a/S3a4a
2o\$2o!

step18
x = 3, y = 5, rule = B2e3aijkq4ac7c/S2-an3-a
bo\$obo\$3o\$obo\$bo!

step24
x = 7, y = 7, rule = B3578/S23
3o\$obo\$3o2\$4b3o\$bo2bobo\$4b3o!

90,150:

step2
x = 2, y = 2, rule = B2a3i4w/S3a4a7c
2o\$2o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Location: Scotland

### Re: New method of classifying two-dimensional replicators

Why exclude so many of them?

Here are some replicators that have an "Edge rule" and "Core rule." However, they are not saw-tooths:

x = 512, y = 512, rule = B12c4e/S1e2c4c
ooo\$obo\$ooo\$!

x = 512, y = 512, rule = B1e2i4te/S
bo\$obo\$bo\$!
Layz Boi

Posts: 24
Joined: October 25th, 2018, 3:57 pm

### Re: New method of classifying two-dimensional replicators

These classes also match up with "Replicator"-type rules:

x = 16, y = 16, rule = B1e2ak3einqy4jnry5einqy6ak7e/S1e2ak3einqy4jnry5einqy6ak7e
3b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$o
b2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2ob
obo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obo
bob3o\$8b4obobo!

x = 16, y = 16, rule = B1e2ak3einqy4jnry5einqy6ak7e/S01c2-ak3acjkr4-jnry5acjkr6-ak7c8
3b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$o
b2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2ob
obo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obo
bob3o\$8b4obobo!

x = 16, y = 16, rule = B1357/S1357
3b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$o
b2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2ob
obo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obo
bob3o\$8b4obobo!

x = 16, y = 16, rule = B1357/S02468
3b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$o
b2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2ob
obo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obo
bob3o\$8b4obobo!

It is possible to see such behaviour in some S-class replicators:
x = 5, y = 6, rule = B1e2ak3einqy4jnry5einqy6ak7e/S1e2ak3einqy4jnry5einqy6ak7e
2bo\$3bo\$obobo\$bo\$2bo\$3bo!

x = 47, y = 55, rule = B3578/S23
24b3o\$24bobo\$24b3o2\$28b3o\$25bo2bobo\$28b3o2\$32b3o\$32bobo\$32b3o2\$36b3o\$
33bo2bobo\$36b3o2\$24b3o13b3o\$24bobo2bo10bobo\$24b3o13b3o2\$28b3o13b3o\$28b
obo10bo2bobo\$28b3o13b3o2\$3o13b3o\$obo2bo10bobo\$3o13b3o2\$4b3o13b3o\$4bobo
10bo2bobo\$4b3o13b3o2\$8b3o\$8bobo2bo\$8b3o2\$12b3o\$12bobo\$12b3o2\$16b3o\$16b
obo2bo\$16b3o2\$20b3o\$20bobo\$20b3o2\$24b3o\$24bobo2bo\$24b3o2\$28b3o\$28bobo\$
28b3o!
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muzik

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Location: Scotland

### Re: New method of classifying two-dimensional replicators

What i believe to be the first five iterations of the 2523490710,1721342310 replication habit, as seen in R2B(1,3,5,7,9,11,13,15,17,19,21,23)/S(1,3,5,7,9,11,13,15,17,19,21,23):

x = 17, y = 129, rule = W0
8bo28\$6b5o\$6b5o\$6b2ob2o\$6b5o\$6b5o24\$4bobobobobo2\$4bobobobobo2\$4bobo3bo
bo2\$4bobobobobo2\$4bobobobobo20\$2b2o2bobobo2b2o\$2b2o2bobobo2b2o\$4bobobo
bobo2\$2b3ob5ob3o\$6b5o\$2b3ob2ob2ob3o\$6b5o\$2b3ob5ob3o2\$4bobobobobo\$2b2o
2bobobo2b2o\$2b2o2bobobo2b2o16\$o3bo3bo3bo3bo4\$o3bo3bo3bo3bo4\$o3bo7bo3bo
4\$o3bo3bo3bo3bo4\$o3bo3bo3bo3bo!

Is there anything that can simulate such rules?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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

### Re: New method of classifying two-dimensional replicators

From what I can tell:
E90 basically does this:
000
A00
0B0

Or this:
000
000
A0B

E150 does this:
000
000
ABC

C90 does this:
000
A0B
000

Or this:
A00
000
00B

C150 does this:
A00
0B0
00C

Or this:
000
ABC
000

So I think XOR 4 edge would do the following:
00000
00000
00000
00000
AB0CD

Center:
00000
00000
AB0CD
00000
00000

A0000
0B000
00000
000C0
0000D

I also think that the results of all the inputs are XORd.
And no, I am not going to go through all 2D range 2 neighborhoods.
UPDATE:
It's a bit more complicated, you OR the neighborhoods, then take the XOR of that.
x = 23, y = 10, rule = B1357S02468History

So...this is probably what muzik is looking for.
x = 39, y = 13, rule = BS012345678History
13B.7B\$B4.AB5.B.BA4.B\$B4.AB5.B.B.A3.B5.D\$B2.D.AB2.D2.B.B2.D2.B6.D4.7B
\$B4.AB5.B.B3.A.B7.D3.B5AB\$B4.AB5AB.B4.AB8.D2.B2A.2AB\$13B.7B.9D.BA.D.A
B\$B5ABA4.B.B4.AB8.D2.B2A.2AB\$B5.BA4.B.B3.A.B7.D3.B5AB\$B2.D2.BA.D2.B.B
2.D2.B6.D4.7B\$B5.BA4.B.B.A3.B5.D\$B5.BA4.B.BA4.B\$13B.7B!

wwei23

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

### Re: New method of classifying two-dimensional replicators

While I've yet to modify the classification system that integrates these, here are the rule tales for modulo-n replicators generated by FredkinModN-gen.py:

@RULE Fredkin_mod3_vonNeumann

@TREE

num_states=3
num_neighbors=4
num_nodes=13
1 0 0 0
1 1 1 1
1 2 2 2
2 0 1 2
2 1 2 0
2 2 0 1
3 3 4 5
3 4 5 3
3 5 3 4
4 6 7 8
4 7 8 6
4 8 6 7
5 9 10 11

@RULE Fredkin_mod4_vonNeumann

@TREE

num_states=4
num_neighbors=4
num_nodes=17
1 0 0 0 0
1 1 1 1 1
1 2 2 2 2
1 3 3 3 3
2 0 1 2 3
2 1 2 3 0
2 2 3 0 1
2 3 0 1 2
3 4 5 6 7
3 5 6 7 4
3 6 7 4 5
3 7 4 5 6
4 8 9 10 11
4 9 10 11 8
4 10 11 8 9
4 11 8 9 10
5 12 13 14 15

@RULE Fredkin_mod5_vonNeumann

@TREE

num_states=5
num_neighbors=4
num_nodes=21
1 0 0 0 0 0
1 1 1 1 1 1
1 2 2 2 2 2
1 3 3 3 3 3
1 4 4 4 4 4
2 0 1 2 3 4
2 1 2 3 4 0
2 2 3 4 0 1
2 3 4 0 1 2
2 4 0 1 2 3
3 5 6 7 8 9
3 6 7 8 9 5
3 7 8 9 5 6
3 8 9 5 6 7
3 9 5 6 7 8
4 10 11 12 13 14
4 11 12 13 14 10
4 12 13 14 10 11
4 13 14 10 11 12
4 14 10 11 12 13
5 15 16 17 18 19

@RULE Fredkin_mod6_vonNeumann

@TREE

num_states=6
num_neighbors=4
num_nodes=25
1 0 0 0 0 0 0
1 1 1 1 1 1 1
1 2 2 2 2 2 2
1 3 3 3 3 3 3
1 4 4 4 4 4 4
1 5 5 5 5 5 5
2 0 1 2 3 4 5
2 1 2 3 4 5 0
2 2 3 4 5 0 1
2 3 4 5 0 1 2
2 4 5 0 1 2 3
2 5 0 1 2 3 4
3 6 7 8 9 10 11
3 7 8 9 10 11 6
3 8 9 10 11 6 7
3 9 10 11 6 7 8
3 10 11 6 7 8 9
3 11 6 7 8 9 10
4 12 13 14 15 16 17
4 13 14 15 16 17 12
4 14 15 16 17 12 13
4 15 16 17 12 13 14
4 16 17 12 13 14 15
4 17 12 13 14 15 16
5 18 19 20 21 22 23

@RULE Fredkin_mod7_vonNeumann

@TREE

num_states=7
num_neighbors=4
num_nodes=29
1 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1
1 2 2 2 2 2 2 2
1 3 3 3 3 3 3 3
1 4 4 4 4 4 4 4
1 5 5 5 5 5 5 5
1 6 6 6 6 6 6 6
2 0 1 2 3 4 5 6
2 1 2 3 4 5 6 0
2 2 3 4 5 6 0 1
2 3 4 5 6 0 1 2
2 4 5 6 0 1 2 3
2 5 6 0 1 2 3 4
2 6 0 1 2 3 4 5
3 7 8 9 10 11 12 13
3 8 9 10 11 12 13 7
3 9 10 11 12 13 7 8
3 10 11 12 13 7 8 9
3 11 12 13 7 8 9 10
3 12 13 7 8 9 10 11
3 13 7 8 9 10 11 12
4 14 15 16 17 18 19 20
4 15 16 17 18 19 20 14
4 16 17 18 19 20 14 15
4 17 18 19 20 14 15 16
4 18 19 20 14 15 16 17
4 19 20 14 15 16 17 18
4 20 14 15 16 17 18 19
5 21 22 23 24 25 26 27

@RULE Fredkin_mod8_vonNeumann

@TREE

num_states=8
num_neighbors=4
num_nodes=33
1 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1
1 2 2 2 2 2 2 2 2
1 3 3 3 3 3 3 3 3
1 4 4 4 4 4 4 4 4
1 5 5 5 5 5 5 5 5
1 6 6 6 6 6 6 6 6
1 7 7 7 7 7 7 7 7
2 0 1 2 3 4 5 6 7
2 1 2 3 4 5 6 7 0
2 2 3 4 5 6 7 0 1
2 3 4 5 6 7 0 1 2
2 4 5 6 7 0 1 2 3
2 5 6 7 0 1 2 3 4
2 6 7 0 1 2 3 4 5
2 7 0 1 2 3 4 5 6
3 8 9 10 11 12 13 14 15
3 9 10 11 12 13 14 15 8
3 10 11 12 13 14 15 8 9
3 11 12 13 14 15 8 9 10
3 12 13 14 15 8 9 10 11
3 13 14 15 8 9 10 11 12
3 14 15 8 9 10 11 12 13
3 15 8 9 10 11 12 13 14
4 16 17 18 19 20 21 22 23
4 17 18 19 20 21 22 23 16
4 18 19 20 21 22 23 16 17
4 19 20 21 22 23 16 17 18
4 20 21 22 23 16 17 18 19
4 21 22 23 16 17 18 19 20
4 22 23 16 17 18 19 20 21
4 23 16 17 18 19 20 21 22
5 24 25 26 27 28 29 30 31

@RULE Fredkin_mod9_vonNeumann

@TREE

num_states=9
num_neighbors=4
num_nodes=37
1 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1
1 2 2 2 2 2 2 2 2 2
1 3 3 3 3 3 3 3 3 3
1 4 4 4 4 4 4 4 4 4
1 5 5 5 5 5 5 5 5 5
1 6 6 6 6 6 6 6 6 6
1 7 7 7 7 7 7 7 7 7
1 8 8 8 8 8 8 8 8 8
2 0 1 2 3 4 5 6 7 8
2 1 2 3 4 5 6 7 8 0
2 2 3 4 5 6 7 8 0 1
2 3 4 5 6 7 8 0 1 2
2 4 5 6 7 8 0 1 2 3
2 5 6 7 8 0 1 2 3 4
2 6 7 8 0 1 2 3 4 5
2 7 8 0 1 2 3 4 5 6
2 8 0 1 2 3 4 5 6 7
3 9 10 11 12 13 14 15 16 17
3 10 11 12 13 14 15 16 17 9
3 11 12 13 14 15 16 17 9 10
3 12 13 14 15 16 17 9 10 11
3 13 14 15 16 17 9 10 11 12
3 14 15 16 17 9 10 11 12 13
3 15 16 17 9 10 11 12 13 14
3 16 17 9 10 11 12 13 14 15
3 17 9 10 11 12 13 14 15 16
4 18 19 20 21 22 23 24 25 26
4 19 20 21 22 23 24 25 26 18
4 20 21 22 23 24 25 26 18 19
4 21 22 23 24 25 26 18 19 20
4 22 23 24 25 26 18 19 20 21
4 23 24 25 26 18 19 20 21 22
4 24 25 26 18 19 20 21 22 23
4 25 26 18 19 20 21 22 23 24
4 26 18 19 20 21 22 23 24 25
5 27 28 29 30 31 32 33 34 35

To my knowledge, no replicators have been found in any 2-state CA that are bound by these rules (indeed, no one-dimensional replicators that truly follow a composite Pascal triangle, either).
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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Location: Scotland

### Re: New method of classifying two-dimensional replicators

"Range-3 Moore" seems to be bound by the following edge rule:
x = 55, y = 28, rule = Fredkin_mod3_Moore
27.A\$26.3A\$25.AB.BA\$24.A2.A2.A\$23.9A\$22.AB7.BA\$21.A2.B5.B2.A\$20.3A3B
3.3B3A\$19.AB.AB.AB.BA.BA.BA\$18.A8.A8.A\$17.3A6.3A6.3A\$16.AB.BA4.AB.BA
4.AB.BA\$15.A2.A2.A2.A2.A2.A2.A2.A2.A\$14.27A\$13.AB25.BA\$12.A2.B23.B2.A
\$11.3A3B21.3B3A\$10.AB.AB.AB19.BA.BA.BA\$9.A8.B17.B8.A\$8.3A6.3B15.3B6.
3A\$7.AB.BA4.BA.AB13.BA.AB4.AB.BA\$6.A2.A2.A2.B2.B2.B11.B2.B2.B2.A2.A2.
A\$5.9A9B9.9B9A\$4.AB7.AB7.AB7.BA7.BA7.BA\$3.A2.B5.A2.B5.A2.B5.B2.A5.B2.
A5.B2.A\$2.3A3B3.3A3B3.3A3B3.3B3A3.3B3A3.3B3A\$.AB.AB.AB.AB.AB.AB.AB.AB
.AB.BA.BA.BA.BA.BA.BA.BA.BA.BA\$A26.A26.A!

and this core rule:
x = 55, y = 28, rule = Fredkin_mod3_Moore
27.A\$26.A.A\$25.A3BA\$24.A5.A\$23.A.A3.A.A\$22.A2B.B.B.2BA\$21.A2.B2.B2.B
2.A\$20.A.AB.2B.2B.BA.A\$19.A2B.9A.2BA\$18.A17.A\$17.A.A15.A.A\$16.A3BA13.
A3BA\$15.A5.A11.A5.A\$14.A.A3.A.A9.A.A3.A.A\$13.A2B.B.B.B.B7.B.B.B.B.2BA
\$12.A2.B2.B5.B5.B5.B2.B2.A\$11.A.AB.2B.B3.B.B3.B.B3.B.2B.BA.A\$10.A2B.
5AB2.A.2AB.B2A.A2.B5A.2BA\$9.A8.B8.B8.B8.A\$8.A.A6.B.B6.B.B6.B.B6.A.A\$
7.A3BA4.B3AB4.B3AB4.B3AB4.A3BA\$6.A5.A2.B5.B2.B5.B2.B5.B2.A5.A\$5.A.A3.
A.AB.B3.B.2B.B3.B.2B.B3.B.BA.A3.A.A\$4.A2B.B.B.B.2A.A.A.4A.A.A.4A.A.A.
2A.B.B.B.2BA\$3.A2.B2.B5.A2.A2.A2.A2.A2.A2.A2.A2.A5.B2.B2.A\$2.A.AB.2B.
B3.A.2A.2A.2A.2A.2A.2A.2A.2A.A3.B.2B.BA.A\$.A2B.5AB2.A27BA2.B5A.2BA\$A
53.A!

What Wolfram 3-state rule integers do these rules have?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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

### Re: New method of classifying two-dimensional replicators

A bunch of (90,90)s (which I'm considering changing to (2,2), since these rulestrings can get unwieldy)

x = 35, y = 19, rule = B2k3578/S3-e456k8
3o13b3o13b3o\$3o13b3o13b3o\$obo13bobo13bobo4\$obo5bobo5bobo13bobo\$3o5b3o
5b3o13b3o\$3o5b3o5b3o13b3o8\$3o13b3o13b3o\$3o13b3o13b3o\$obo13bobo13bobo!

x = 104, y = 104, rule = B34-ac/S23
33b3o\$32bo3bo\$32bo4bo\$33b3o2bo\$35b2o2bo\$36bo2bo\$36bo2bo\$37b2o3\$23b2o\$
22bo2bo\$22bo2bo\$22bo2b2o\$23bo2b3o\$24bo4bo\$25bo3bo\$26b3o9\$39b2o\$38bo2bo
\$38bo2bo\$38bo2b2o\$39bo2b3o\$40bo4bo\$b3o37bo3bo19b3o\$o3bo37b3o19bo3bo\$o
4bo58bo4bo\$b3o2bo58b3o2bo\$3b2o2bo59b2o2bo\$4bo2bo60bo2bo\$4bo2bo60bo2bo\$
5b2o62b2o3\$55b2o\$54bo2bo\$54bo2bo\$54bo2b2o\$55bo2b3o\$56bo4bo\$57bo3bo\$58b
3o15\$33b3o61b3o\$32bo3bo59bo3bo\$32bo4bo58bo4bo\$33b3o2bo58b3o2bo\$35b2o2b
o59b2o2bo\$36bo2bo60bo2bo\$36bo2bo60bo2bo\$37b2o62b2o3\$87b2o\$86bo2bo\$86bo
2bo\$86bo2b2o\$87bo2b3o\$88bo4bo\$89bo3bo\$90b3o15\$65b3o\$64bo3bo\$64bo4bo\$
65b3o2bo\$67b2o2bo\$68bo2bo\$68bo2bo\$69b2o!

x = 54, y = 37, rule = B2in3aijr4eq5j6c/S2-in3ijnqr4i5cnr6k
7b3o\$7bobo\$6b2obo4\$29b3o\$29bobo\$28b2obo\$5bob2o\$5bobo\$5b3o\$16bob2o31b3o
\$16bobo32bobo\$16b3o31b2obo\$27bob2o\$27bobo\$27b3o4\$49bob2o\$b3o45bobo\$bob
o45b3o\$2obo4\$23b3o\$23bobo\$22b2obo4\$45b3o\$45bobo\$44b2obo!

x = 73, y = 35, rule = B3578/S23-c
2o5b2o23b2o5b2o23b2o5b2o\$2o5b2o23b2o5b2o23b2o5b2o\$2o5b2o23b2o5b2o23b2o
5b2o14\$2o5b2o7b2o5b2o7b2o5b2o23b2o5b2o\$2o5b2o7b2o5b2o7b2o5b2o23b2o5b2o
\$2o5b2o7b2o5b2o7b2o5b2o23b2o5b2o14\$2o5b2o23b2o5b2o23b2o5b2o\$2o5b2o23b
2o5b2o23b2o5b2o\$2o5b2o23b2o5b2o23b2o5b2o!

x = 79, y = 40, rule = B34jy6n/S2-i3
2b3o33b3o33b3o\$bo3bo31bo3bo31bo3bo\$o5bo29bo5bo29bo5bo\$b2ob2o31b2ob2o
31b2ob2o18\$b2ob2o13b2ob2o13b2ob2o31b2ob2o\$o5bo11bo5bo11bo5bo29bo5bo\$bo
3bo13bo3bo13bo3bo31bo3bo\$2b3o15b3o15b3o33b3o12\$2b3o33b3o33b3o\$bo3bo31b
o3bo31bo3bo\$o5bo29bo5bo29bo5bo\$b2ob2o31b2ob2o31b2ob2o!

x = 55, y = 55, rule = B3578/S23
20b3o\$20bobo\$20b3o2\$16b3o\$16bobo2bo\$16b3o2\$12b3o\$12bobo\$12b3o2\$8b3o\$8b
obo2bo\$8b3o2\$4b3o13b3o13b3o\$4bobo10bo2bobo10bo2bobo\$4b3o13b3o13b3o2\$3o
13b3o13b3o\$obo2bo10bobo13bobo\$3o13b3o13b3o2\$28b3o\$28bobo\$28b3o2\$24b3o\$
24bobo2bo\$24b3o2\$20b3o29b3o\$17bo2bobo29bobo\$20b3o29b3o2\$16b3o29b3o\$16b
obo29bobo2bo\$16b3o29b3o2\$44b3o\$41bo2bobo\$44b3o2\$40b3o\$40bobo\$40b3o2\$
36b3o\$36bobo\$36b3o2\$32b3o\$32bobo2bo\$32b3o!

x = 103, y = 50, rule = B3-y5a/S234c5ek
bo3bo43bo3bo43bo3bo\$3ob3o41b3ob3o41b3ob3o24\$3ob3o17b3ob3o17b3ob3o41b3o
b3o\$bo3bo19bo3bo19bo3bo43bo3bo22\$bo3bo43bo3bo43bo3bo\$3ob3o41b3ob3o41b
3ob3o!

x = 31, y = 24, rule = B3-nq4nt5ar/S2-k34aiw
6bo\$5b2o\$4b2o\$5b2o\$18bo\$17b2o\$4bo11b2o\$3b2o12b2o\$2b2o3b2o21bo\$3b2o3b2o
19b2o\$7b2o7bo11b2o\$7bo7b2o12b2o\$2bo11b2o\$b2o12b2o\$2o26bo\$b2o24b2o\$14bo
11b2o\$13b2o12b2o\$12b2o\$13b2o\$26bo\$25b2o\$24b2o\$25b2o!

x = 51, y = 26, rule = B3-jny/S1c23
bo23bo23bo\$3o21b3o21b3o10\$3o9b3o9b3o21b3o\$bo11bo11bo23bo12\$bo23bo23bo\$
3o21b3o21b3o!

x = 81, y = 81, rule = B34e5-ey7e8/S23
30b3o\$30b3o\$30b3o4\$24b3o\$24b3o\$24b3o4\$18b3o\$18b3o\$18b3o4\$12b3o\$12b3o\$
12b3o4\$6b3o21b3o21b3o\$6b3o21b3o21b3o\$6b3o21b3o21b3o4\$3o21b3o21b3o\$3o
21b3o21b3o\$3o21b3o21b3o4\$42b3o\$42b3o\$42b3o4\$36b3o\$36b3o\$36b3o4\$30b3o
45b3o\$30b3o45b3o\$30b3o45b3o4\$24b3o45b3o\$24b3o45b3o\$24b3o45b3o4\$66b3o\$
66b3o\$66b3o4\$60b3o\$60b3o\$60b3o4\$54b3o\$54b3o\$54b3o4\$48b3o\$48b3o\$48b3o!

x = 173, y = 89, rule = B3/S23-ac4eiy6
2bo83bo83bo\$b3o81b3o81b3o\$2ob2o79b2ob2o79b2ob2o\$bobo81bobo81bobo\$2bo
83bo83bo38\$2bo41bo41bo83bo\$bobo39bobo39bobo81bobo\$2ob2o37b2ob2o37b2ob
2o79b2ob2o\$b3o39b3o39b3o81b3o\$2bo41bo41bo83bo38\$2bo83bo83bo\$b3o81b3o
81b3o\$2ob2o79b2ob2o79b2ob2o\$bobo81bobo81bobo\$2bo83bo83bo!

x = 117, y = 66, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i
2bo\$b3o\$2obo52bo\$55b3o\$54b2obo52bo\$3bob2o102b3o\$3b3o102b2obo\$4bo52bob
2o\$57b3o\$58bo52bob2o\$111b3o\$112bo16\$3bo\$2b3o25bo\$b2obo24b3o25bo\$28b2ob
o24b3o\$55b2obo52bo\$4bob2o102b3o\$4b3o24bob2o74b2obo\$5bo25b3o24bob2o\$32b
o25b3o\$59bo52bob2o\$112b3o\$113bo16\$4bo\$3b3o\$2b2obo52bo\$57b3o\$56b2obo52b
o\$5bob2o102b3o\$5b3o102b2obo\$6bo52bob2o\$59b3o\$60bo52bob2o\$113b3o\$114bo!

x = 43, y = 23, rule = B2ei3/S1e2
3o17b3o17b3o\$obo17bobo17bobo\$obo17bobo17bobo8\$obo7bobo7bobo17bobo\$obo
7bobo7bobo17bobo\$3o7b3o7b3o17b3o8\$3o17b3o17b3o\$obo17bobo17bobo\$obo17bo
bo17bobo!

x = 96, y = 96, rule = B3-ckq6/S2-c34ci6
29b3o\$28bo2bo\$28bo2bo\$28b3o5\$37b3o\$36bo2bo\$36bo2bo\$36b3o3\$15b3o\$14bo2b
o\$14bo2bo\$14b3o5\$23b3o\$22bo2bo\$22bo2bo\$22b3o3\$b3o25b3o25b3o\$o2bo24bo2b
o24bo2bo\$o2bo24bo2bo24bo2bo\$3o25b3o25b3o5\$9b3o25b3o25b3o\$8bo2bo24bo2bo
24bo2bo\$8bo2bo24bo2bo24bo2bo\$8b3o25b3o25b3o3\$43b3o\$42bo2bo\$42bo2bo\$42b
3o5\$51b3o\$50bo2bo\$50bo2bo\$50b3o3\$29b3o53b3o\$28bo2bo52bo2bo\$28bo2bo52bo
2bo\$28b3o53b3o5\$37b3o53b3o\$36bo2bo52bo2bo\$36bo2bo52bo2bo\$36b3o53b3o3\$
71b3o\$70bo2bo\$70bo2bo\$70b3o5\$79b3o\$78bo2bo\$78bo2bo\$78b3o3\$57b3o\$56bo2b
o\$56bo2bo\$56b3o5\$65b3o\$64bo2bo\$64bo2bo\$64b3o!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3236
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: New method of classifying two-dimensional replicators

Some more:

x = 61, y = 32, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i
2bo27bo27bo\$b3o25b3o25b3o\$o3bo23bo3bo23bo3bo\$2ob2o23b2ob2o23b2ob2o8\$2o
b2o9b2ob2o9b2ob2o23b2ob2o\$o3bo9bo3bo9bo3bo23bo3bo\$b3o11b3o11b3o25b3o\$
2bo13bo13bo27bo14\$2bo27bo27bo\$b3o25b3o25b3o\$o3bo23bo3bo23bo3bo\$2ob2o
23b2ob2o23b2ob2o!

x = 52, y = 52, rule = B3-n4a/S1e2-a3ijnr
33bo\$32b2o\$33b3o\$34bo5\$41bo\$40b2o\$41b3o\$42bo5\$17bo31bo\$16b2o30b2o\$17b
3o29b3o\$18bo31bo5\$25bo\$24b2o\$25b3o\$26bo5\$bo31bo\$2o14bo15b2o\$b3o11b3o
15b3o\$2bo14b2o15bo\$17bo4\$9bo\$8b2o\$9b3o\$10bo5\$17bo\$16b2o\$17b3o\$18bo!

x = 81, y = 81, rule = B34ew/S23
24b3o\$24b3o\$24b3o4\$30b3o\$30b3o\$30b3o4\$12b3o\$12b3o\$12b3o4\$18b3o\$18b3o\$
18b3o4\$3o21b3o21b3o\$3o21b3o21b3o\$3o21b3o21b3o4\$6b3o21b3o21b3o\$6b3o21b
3o21b3o\$6b3o21b3o21b3o4\$36b3o\$36b3o\$36b3o4\$42b3o\$42b3o\$42b3o4\$24b3o45b
3o\$24b3o45b3o\$24b3o45b3o4\$30b3o45b3o\$30b3o45b3o\$30b3o45b3o4\$60b3o\$60b
3o\$60b3o4\$66b3o\$66b3o\$66b3o4\$48b3o\$48b3o\$48b3o4\$54b3o\$54b3o\$54b3o!

x = 76, y = 52, rule = B2ac3e/S1e5i
27bo\$27bo\$24bo\$24bo5\$15bo\$15bo\$12bo\$12bo5\$3bo23bo23bo\$3bo23bo23bo\$o23b
o23bo\$o23bo23bo5\$39bo\$39bo\$36bo\$36bo5\$27bo47bo\$27bo47bo\$24bo47bo\$24bo
47bo5\$63bo\$63bo\$60bo\$60bo5\$51bo\$51bo\$48bo\$48bo!

x = 43, y = 25, rule = B2e3aijkq4ac7c/S2-an3-a
bo19bo19bo\$obo17bobo17bobo\$3o17b3o17b3o\$obo17bobo17bobo\$bo19bo19bo6\$bo
9bo9bo19bo\$obo7bobo7bobo17bobo\$3o7b3o7b3o17b3o\$obo7bobo7bobo17bobo\$bo
9bo9bo19bo6\$bo19bo19bo\$obo17bobo17bobo\$3o17b3o17b3o\$obo17bobo17bobo\$bo
19bo19bo!

x = 52, y = 29, rule = B34c/S2-i34wy5ay6i
b2o22b2o22b2o\$2obo20b2obo20b2obo\$o2bo20bo2bo20bo2bo\$2obo20b2obo20b2obo
\$b2o22b2o22b2o8\$b2o7b2o13b2o22b2o\$2obo5bob2o11b2obo20b2obo\$o2bo5bo2bo
11bo2bo20bo2bo\$2obo5bob2o11b2obo20b2obo\$b2o7b2o13b2o22b2o8\$b2o22b2o22b
2o\$2obo20b2obo20b2obo\$o2bo20bo2bo20bo2bo\$2obo20b2obo20b2obo\$b2o22b2o
22b2o!

x = 109, y = 79, rule = B34ej5y6n/S23
2bo\$b3o\$2o2bo3\$7bobo\$5b5o\$5b3o\$3b5o\$3bobo3\$8bo2b2o\$9b3o\$10bo2\$46bo\$45b
3o\$44b2o2bo2\$30bo2b2o\$31b3o17bobo\$32bo16b5o\$49b3o\$47b5o\$47bobo3\$52bo2b
2o\$53b3o\$54bo2\$90bo\$89b3o\$88b2o2bo3\$95bobo\$93b5o\$93b3o\$91b5o\$91bobo3\$
18bo77bo2b2o\$17b3o77b3o\$16b2o2bo77bo14\$62bo\$61b3o\$60b2o2bo14\$106bo\$
105b3o\$104b2o2bo!
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3236
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

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