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New method of classifying two-dimensional replicators

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New method of classifying two-dimensional replicators

Postby muzik » November 1st, 2018, 7:01 pm

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!


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 2nd, 2019, 3:39 pm, edited 5 times in total.
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Re: New method of classifying two-dimensional replicators

Postby muzik » November 1st, 2018, 7:15 pm

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!
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Re: New method of classifying two-dimensional replicators

Postby Layz Boi » November 1st, 2018, 11:14 pm

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$!
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Re: New method of classifying two-dimensional replicators

Postby muzik » November 2nd, 2018, 5:49 am

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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Re: New method of classifying two-dimensional replicators

Postby muzik » November 5th, 2018, 9:18 am

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?
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Re: New method of classifying two-dimensional replicators

Postby wwei23 » November 10th, 2018, 5:31 pm

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
4.A3.3A3.A5.3A$.D2.AD3.D3.DA5.ACA$3A.A9.A5.3A5$A5.A$.C3.C$2.A.A!

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!
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Re: New method of classifying two-dimensional replicators

Postby muzik » November 14th, 2018, 7:15 pm

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).
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Re: New method of classifying two-dimensional replicators

Postby muzik » November 15th, 2018, 7:23 am

"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?
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Re: New method of classifying two-dimensional replicators

Postby muzik » December 30th, 2018, 10:30 pm

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!
waiting for apgsearch to support one-dimensional rules
muzik
 
Posts: 2975
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

Re: New method of classifying two-dimensional replicators

Postby muzik » December 30th, 2018, 10:33 pm

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!
waiting for apgsearch to support one-dimensional rules
muzik
 
Posts: 2975
Joined: January 28th, 2016, 2:47 pm
Location: Scotland


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